Document Zbl 1357.81168

Miransky, Vladimir A.; Shovkovy, Igor A.

Quantum field theory in a magnetic field: from quantum chromodynamics to graphene and Dirac semimetals. (English) Zbl 1357.81168

Phys. Rep. 576, 1-209 (2015).

Summary: A range of quantum field theoretical phenomena driven by external magnetic fields and their applications in relativistic systems and quasirelativistic condensed matter ones, such as graphene and Dirac/Weyl semimetals, are reviewed. We start by introducing the underlying physics of the magnetic catalysis. The dimensional reduction of the low-energy dynamics of relativistic fermions in an external magnetic field is explained and its role in catalyzing spontaneous symmetry breaking is emphasized. The general theoretical consideration is supplemented by the analysis of the magnetic catalysis in quantum electrodynamics, chromodynamics and quasirelativistic models relevant for condensed matter physics. By generalizing the ideas of the magnetic catalysis to the case of nonzero density and temperature, we argue that other interesting phenomena take place. The chiral magnetic and chiral separation effects are perhaps the most interesting among them. In addition to the general discussion of the physics underlying chiral magnetic and separation effects, we also review their possible phenomenological implications in heavy-ion collisions and compact stars. We also discuss the application of the magnetic catalysis ideas for the description of the quantum Hall effect in monolayer and bilayer graphene, and conclude that the generalized magnetic catalysis, including both the magnetic catalysis condensates and the quantum Hall ferromagnetic ones, lies at the basis of this phenomenon. We also consider how an external magnetic field affects the underlying physics in a class of three-dimensional quasirelativistic condensed matter systems, Dirac semimetals. While at sufficiently low temperatures and zero density of charge carriers, such semimetals are expected to reveal the regime of the magnetic catalysis, the regime of Weyl semimetals with chiral asymmetry is realized at nonzero density. Finally, we discuss the interplay between relativistic quantum field theories (including quantum electrodynamics and quantum chromodynamics) in a magnetic field and noncommutative field theories, which leads to a new type of the latter, nonlocal noncommutative field theories.

Cited in 53 Documents

MSC:

81V70	Many-body theory; quantum Hall effect
81V05	Strong interaction, including quantum chromodynamics
81T10	Model quantum field theories
82D80	Statistical mechanics of nanostructures and nanoparticles

Keywords:

magnetic catalysis; spontaneous symmetry breaking; relativistic matter; chiral asymmetry; graphene; Dirac semimetals

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References:

[1]	Pauli, W., Über Gasentartung und paramagnetismus, Z. Phys., 41, 81-102 (1927) · JFM 53.0861.01
[2]	Pauli, W., Zur Quantenmechanik des magnetischen elektrons, Z. Phys., 43, 601-623 (1927) · JFM 53.0858.02
[3]	Landau, L., Diamagnetismus der metalle, Z. Phys., 64, 629-637 (1930) · JFM 56.1318.10
[4]	Heisenberg, W., Zur theorie des ferromagnetismus, Z. Phys., 49, 619-636 (1928) · JFM 54.0979.02
[5]	Meissner, W.; Ochsenfeld, R., Ein neuer effekt bei eintritt der supraleitfähigkeit, Naturwissenschaften, 21, 787-788 (1933)
[6]	Schubnikow, L.; de Haas, W. J., Magnetische widerstandsvergrösserung in einkristallen von wismut bei tiefen temperaturen, Proc. Royal Netherlands Acad. Arts and Science, 33, 130-133 (1930)
[7]	Schubnikow, L.; de Haas, W. J., Neue erscheinungen bei der widerstandsänderung von wismuthkristallen im magnetfeld bei der temperatur von flussigem wasserstoff, Proc. Royal Netherlands Acad. Arts and Science, 33, 363-378 (1930)
[8]	Schubnikow, L.; de Haas, W. J., Neue erscheinungen bei der widerstandsänderung von wismuthkristallen im magnetfeld bei der temperatur von flüssigem wasserstoff, Proc. Royal Netherlands Acad. Arts and Science, 33, 418-432 (1930)
[9]	Ando, T.; Matsumoto, Y.; Uemura, Y., Theory of Hall effect in a two-dimensional electron system, J. Phys. Soc. Japan, 39, 279 (1975)
[10]	Klitzing, K. V.; Dorda, G.; Pepper, M., New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett., 45, 494-497 (1980)
[11]	Laughlin, R. B., Quantized Hall conductivity in two dimensions, Phys. Rev., B23, 5632-5633 (1981)
[12]	Bardeen, J.; Cooper, L. N.; Schrieffer, J. R., Theory of superconductivity, Phys. Rev., 108, 1175-1204 (1957) · Zbl 0090.45401
[13]	Bardeen, J.; Cooper, L. N.; Schrieffer, J. R., Microscopic theory of superconductivity, Phys. Rev., 106, 162 (1957) · Zbl 0090.45401
[14]	Vilenkin, A., Equilibrium parity violating current in a magnetic field, Phys. Rev., D22, 3080-3084 (1980)
[15]	Vachaspati, T., Magnetic fields from cosmological phase transitions, Phys. Lett., B265, 258-261 (1991)
[16]	Enqvist, K.; Olesen, P., On primordial magnetic fields of electroweak origin, Phys. Lett., B319, 178-185 (1993)
[17]	Cheng, B.-L.; Olinto, A. V., Primordial magnetic fields generated in the quark-hadron transition, Phys. Rev., D50, 2421-2424 (1994)
[18]	Baym, G.; Bodeker, D.; McLerran, L. D., Magnetic fields produced by phase transition bubbles in the electroweak phase transition, Phys. Rev., D53, 662-667 (1996)
[19]	Grasso, D.; Rubinstein, H. R., Magnetic fields in the early universe, Phys. Rept., 348, 163-266 (2001)
[20]	Rafelski, J.; Müller, B., Magnetic splitting of quasimolecular electronic states in strong fields, Phys. Rev. Lett., 36, 517-520 (1976)
[21]	Kharzeev, D. E.; McLerran, L. D.; Warringa, H. J., The Effects of topological charge change in heavy ion collisions: “Event by event P and CP violation”, Nuclear Phys., A803, 227-253 (2008)
[22]	Skokov, V.; Illarionov, A. Y.; Toneev, V., Estimate of the magnetic field strength in heavy-ion collisions, Internat. J. Modern Phys., A24, 5925-5932 (2009)
[23]	Bzdak, A.; Skokov, V., Event-by-event fluctuations of magnetic and electric fields in heavy ion collisions, Phys. Lett., B710, 171-174 (2012)
[24]	Voronyuk, V.; Toneev, V.; Cassing, W.; Bratkovskaya, E.; Konchakovski, V., (Electro-)magnetic field evolution in relativistic heavy-ion collisions, Phys. Rev., C83, 054911 (2011)
[25]	Deng, W.-T.; Huang, X.-G., Event-by-event generation of electromagnetic fields in heavy-ion collisions, Phys. Rev., C85, 044907 (2012)
[26]	Kouveliotou, C.; Dieters, S.; Strohmayer, T.; Van paradijs, J.; Fishman, G. J., An X-ray pulsar with a superstrong magnetic field in the soft gamma-ray repeater SGR 1806-20., Nature, 393, 235-237 (1998)
[28]	Olausen, S.; Kaspi, V., The McGill magnetar catalog, Astrophys. J. Suppl., 212, 6 (2014)
[29]	Thompson, C.; Duncan, R. C., Neutron star dynamos and the origins of pulsar magnetism, Astrophys. J., 408, 194 (1993)
[30]	Duncan, R. C.; Thompson, C., Formation of very strongly magnetized neutron stars-implications for gamma-ray bursts, Astrophys. J., 392, L9 (1992)
[31]	Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y., Electric field effect in atomically thin carbon films, Science, 306, 666-669 (2004)
[32]	Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A., Two-dimensional gas of massless Dirac fermions in graphene, Nature, 438, 197-200 (2005)
[33]	Zhang, Y.; Tan, Y.-W.; Stormer, H. L.; Kim, P., Experimental observation of the quantum Hall effect and Berry’s phase in graphene, Nature, 438, 201-204 (2005)
[34]	Gusynin, V. P.; Miransky, V. A.; Shovkovy, I. A., Catalysis of dynamical flavor symmetry breaking by a magnetic field in \((2 + 1)\)-dimensions, Phys. Rev. Lett., 73, 3499-3502 (1994)
[35]	Gusynin, V. P.; Miransky, V. A.; Shovkovy, I. A., Dynamical flavor symmetry breaking by a magnetic field in \((2 + 1)\)-dimensions, Phys. Rev., D52, 4718-4735 (1995)
[36]	Gusynin, V. P.; Miransky, V. A.; Shovkovy, I. A., Dimensional reduction and dynamical chiral symmetry breaking by a magnetic field in \((3 + 1)\)-dimensions, Phys. Lett., B349, 477-483 (1995)
[37]	Kharzeev, D.; Zhitnitsky, A., Charge separation induced by P-odd bubbles in QCD matter, Nuclear Phys., A797, 67-79 (2007)
[38]	Fukushima, K.; Kharzeev, D. E.; Warringa, H. J., The chiral magnetic effect, Phys. Rev., D78, 074033 (2008)
[39]	Metlitski, M. A.; Zhitnitsky, A. R., Anomalous axion interactions and topological currents in dense matter, Phys. Rev., D72, 045011 (2005)
[40]	Newman, G. M.; Son, D. T., Response of strongly-interacting matter to magnetic field: Some exact results, Phys. Rev., D73, 045006 (2006)
[41]	Heisenberg, W.; Euler, H., Consequences of Dirac’s theory of positrons, Z. Phys., 98, 714-732 (1936) · Zbl 0013.18503
[42]	Schwinger, J. S., On gauge invariance and vacuum polarization, Phys. Rev., 82, 664-679 (1951) · Zbl 0043.42201
[43]	Dunne, G. V., The Heisenberg-Euler effective action: 75 years on, Internat. J. Modern Phys., A27, 1260004 (2012), http://dx.doi.org/10.1142/S2010194512007222, http://dx.doi.org/10.1142/S0217751X12600044, arXiv:1202.1557 · Zbl 1247.81595
[44]	Klevansky, S. P.; Lemmer, R. H., Chiral symmetry restoration in the Nambu-Jona-Lasinio model with a constant electromagnetic field, Phys. Rev., D39, 3478-3489 (1989)
[45]	Suganuma, H.; Tatsumi, T., On the behavior of symmetry and phase transitions in a strong electromagnetic field, Ann. Physics, 208, 470-508 (1991)
[46]	Klimenko, K. G., Three-dimensional Gross-Neveu model at nonzero temperature and in an external magnetic field, Z. Phys., C54, 323-330 (1992)
[47]	Klimenko, K. G., Three-dimensional Gross-Neveu model at nonzero temperature and in an external magnetic field, Theoret. Math. Phys., 90, 1-6 (1992)
[48]	Krive, I. V.; Naftulin, S. A., Dynamical symmetry breaking and phase transitions in a three-dimensional Gross-Neveu model in a strong magnetic field, Phys. Rev., D46, 2737-2740 (1992)
[49]	Krive, I. V.; Naftulin, S. A., Electrodynamics of systems with dynamical generation of mass in \((2 + 1)\)-dimensional space-time, Sov. J. Nuclear Phys., 54, 897-902 (1991)
[50]	Klevansky, S. P., The nambu-jona-lasinio model of quantum chromodynamics, Rev. Modern Phys., 64, 649-708 (1992)
[51]	Babansky, A. Y.; Gorbar, E. V.; Shchepanyuk, G., Chiral symmetry breaking in the Nambu-Jona-Lasinio model in external constant electromagnetic field, Phys. Lett., B419, 272-278 (1998)
[53]	Ebert, D.; Klimenko, K. G.; Vdovichenko, M. A.; Vshivtsev, A. S., Magnetic oscillations in dense cold quark matter with four fermion interactions, Phys. Rev., D61, 025005 (2000)
[54]	Vdovichenko, M. A.; Vshivtsev, A. S.; Klimenko, K. G., Magnetic catalysis and magnetic oscillations in the Nambu-Jona-Lasinio model, Phys. Atom. Nucl., 63, 470-479 (2000)
[55]	Zhukovsky, V. C.; Klimenko, K. G.; Khudyakov, V. V., Magnetic catalysis in a P-even, chiral invariant three-dimensional model with four-fermion interaction, Theoret. Math. Phys., 124, 1132 (2000) · Zbl 1112.81356
[56]	Ishi-i, M.; Kashiwa, T.; Tanimura, N., Effect of dynamical SU(2) gluons to the gap equation of Nambu-Jona-Lasinio model in constant background magnetic field, Phys. Rev., D65, 065025 (2002)
[57]	Inagaki, T.; Kimura, D.; Murata, T., Four-fermion interaction model in a constant magnetic field at finite temperature and chemical potential, Progr. Theoret. Phys., 111, 371-386 (2004) · Zbl 1057.81563
[58]	Ebert, D.; Klimenko, K., Quark droplets stability induced by external magnetic field, Nuclear Phys., A728, 203-225 (2003) · Zbl 1058.81754
[59]	Inagaki, T.; Kimura, D.; Murata, T., NJL model at finite chemical potential in a constant magnetic field, Progr. Theoret. Phys. Suppl., 153, 321-324 (2004)
[60]	Ghosh, S.; Mandal, S.; Chakrabarty, S., Chiral properties of QCD vacuum in magnetars: A Nambu-Jona-Lasinio model with semi-classical approximation, Phys. Rev., C75, 015805 (2007)
[61]	Osipov, A. A.; Hiller, B.; Blin, A. H.; da Providencia, J., Dynamical chiral symmetry breaking by a magnetic field and multi-quark interactions, Phys. Lett., B650, 262-267 (2007)
[62]	Hiller, B.; Osipov, A. A.; Blin, A. H.; da Providencia, J., Effects of quark interactions on dynamical chiral symmetry breaking by a magnetic field, SIGMA, 4, 024 (2008) · Zbl 1192.81201
[63]	Klimenko, K. G.; Zhukovsky, V. C., Does there arise a significant enhancement of the dynamical quark mass in a strong magnetic field?, Phys. Lett., B665, 352-355 (2008)
[64]	Menezes, D. P.; Benghi pinto, M.; Avancini, S. S.; Perez martinez, A.; Providencia, C., Quark matter under strong magnetic fields in the Nambu-Jona-Lasinio Model, Phys. Rev., C79, 035807 (2009)
[65]	Menezes, D. P.; Benghi pinto, M.; Avancini, S. S.; Providencia, C., Quark matter under strong magnetic fields in the su(3) Nambu-Jona-Lasinio Model, Phys. Rev., C80, 065805 (2009)
[66]	Boomsma, J. K.; Boer, D., The Influence of strong magnetic fields and instantons on the phase structure of the two-flavor NJL model, Phys. Rev., D81, 074005 (2010)
[67]	Fayazbakhsh, S.; Sadooghi, N., Phase diagram of hot magnetized two-flavor color superconducting quark matter, Phys. Rev., D83, 025026 (2011)
[68]	Chatterjee, B.; Mishra, H.; Mishra, A., Chiral symmety breaking in 3-flavor Nambu-Jona Lasinio model in magnetic background, Nuclear Phys., A862-863, 312-315 (2011)
[69]	Chatterjee, B.; Mishra, H.; Mishra, A., Vacuum structure and chiral symmetry breaking in strong magnetic fields for hot and dense quark matter, Phys. Rev., D84, 014016 (2011)
[70]	Avancini, S. S.; Menezes, D. P.; Pinto, M. B.; Providencia, C., The QCD critical end point under strong magnetic fields, Phys. Rev., D85, 091901 (2012)
[71]	Ferrari, G. N.; Garcia, A. F.; Pinto, M. B., Chiral transition within effective quark models under magnetic fields, Phys. Rev., D86, 096005 (2012)
[72]	Allen, P. G.; Scoccola, N. N., Quark matter under strong magnetic fields in SU(2) NJL-type models: parameter dependence of the cold dense matter phase diagram, Phys. Rev., D88, 094005 (2013)
[73]	Fayazbakhsh, S.; Sadooghi, N., Anomalous magnetic moment of hot quarks, inverse magnetic catalysis and reentrance of chiral symmetry broken phase, Phys. Rev. D, 90, 105030 (2014)
[74]	Gorbar, E. V., On chiral symmetry breaking in a constant magnetic field in higher dimension, Phys. Lett., B491, 305-310 (2000)
[75]	Gatto, R.; Ruggieri, M., Dressed Polyakov loop and phase diagram of hot quark matter under magnetic field, Phys. Rev., D82, 054027 (2010)
[76]	Gatto, R.; Ruggieri, M., Deconfinement and chiral symmetry restoration in a strong magnetic background, Phys. Rev., D83, 034016 (2011)
[77]	Gatto, R.; Ruggieri, M., Quark Matter in a Strong Magnetic Background, Lect. Notes Phys., 871, 87-119 (2013)
[78]	Ferreira, M.; Costa, P.; Menezes, D. P.; Providência, C.; Scoccola, N., Deconfinement and chiral restoration within the SU(3) Polyakov-Nambu-Jona-Lasinio and entangled Polyakov-Nambu-Jona-Lasinio models in an external magnetic field, Phys. Rev., D89, 016002 (2014)
[79]	Ferreira, M.; Costa, P.; Lourenço, O.; Frederico, T.; Providência, C., Inverse magnetic catalysis in the \((2 + 1)\)-flavor Nambu-Jona-Lasinio and Polyakov-Nambu-Jona-Lasinio models, Phys. Rev., D89, 116011 (2014)
[80]	Andersen, J. O.; Naylor, W. R.; Tranberg, A., Chiral and deconfinement transitions in a magnetic background using the functional renormalization group with the Polyakov loop, J. High Energy Phys., 1404, 187 (2014)
[81]	Andersen, J. O.; Naylor, W. R.; Tranberg, A., Inverse magnetic catalysis and regularization in the quark-meson model, J. High Energy Phys., 1502, 042 (2015)
[82]	Mizher, A. J.; Chernodub, M. N.; Fraga, E. S., Phase diagram of hot QCD in an external magnetic field: possible splitting of deconfinement and chiral transitions, Phys. Rev. D, 82, 105016 (2010)
[83]	Elias, V.; Mckeon, D.; Miransky, V. A.; Shovkovy, I. A., The Gross-Neveu model and the supersymmetric and nonsupersymmetric Nambu-Jona-Lasinio model in a magnetic field, Phys. Rev., D54, 7884-7893 (1996)
[84]	Andersen, J. O.; Khan, R., Chiral transition in a magnetic field and at finite baryon density, Phys. Rev., D85, 065026 (2012)
[85]	Andersen, J. O.; Tranberg, A., The Chiral transition in a magnetic background: Finite density effects and the functional renormalization group, J. High Energy Phys., 1208, 002 (2012)
[86]	Fraga, E.; Mintz, B.; Schaffner-Bielich, J., A search for inverse magnetic catalysis in thermal quark-meson models, Phys. Lett., B731, 154-158 (2014)
[87]	Ruggieri, M.; Tachibana, M.; Greco, V., Renormalized vs. nonrenormalized chiral transition in a magnetic background, J. High Energy Phys., 1307, 165 (2013) · Zbl 1342.81698
[88]	Ruggieri, M.; Oliva, L.; Castorina, P.; Gatto, R.; Greco, V., Critical endpoint and inverse magnetic catalysis for finite temperature and density quark matter in a magnetic background, Phys. Lett., B734, 255 (2014)
[89]	Fraga, E. S.; Mizher, A. J., Chiral transition in a strong magnetic background, Phys. Rev. D, 78, 025016 (2008)
[90]	Fraga, E.; Mintz, B.; Schaffner-Bielich, J., A search for inverse magnetic catalysis in thermal quark-meson models, Phys. Lett. B, 731, 154-158 (2014)
[91]	Geyer, B.; Granda, L. N.; Odintsov, S. D., Nambu-Jona-Lasinio model in curved space-time with magnetic field, Modern Phys. Lett., A11, 2053-2064 (1996)
[92]	Gitman, D. M.; Odintsov, S. D.; Shilnov, Y. I., Chiral symmetry breaking in \(d = 3\) NJL model in external gravitational and magnetic fields, Phys. Rev., D54, 2968-2970 (1996)
[93]	Inagaki, T.; Odintsov, S. D.; Shil’nov, Y. I., Dynamical symmetry breaking in the external gravitational and constant magnetic fields, Internat. J. Modern Phys., A14, 481-504 (1999) · Zbl 0931.81004
[94]	Gorbar, E. V.; Gusynin, V. P., Gap generation for Dirac fermions on Lobachevsky plane in a magnetic field, Ann. Phys., 323, 2132-2146 (2008) · Zbl 1146.81030
[95]	Cohen, T. D.; Mcgady, D. A.; Werbos, E. S., The Chiral condensate in a constant electromagnetic field, Phys. Rev., C76, 055201 (2007)
[96]	Cohen, T. D.; Werbos, E. S., Magnetization of the QCD vacuum at large fields, Phys. Rev., C80, 015203 (2009)
[97]	Shushpanov, I. A.; Smilga, A. V., Quark condensate in a magnetic field, Phys. Lett., B402, 351-358 (1997)
[98]	Agasian, N. O.; Shushpanov, I., The Quark and gluon condensates and low-energy QCD theorems in a magnetic field, Phys. Lett. B, 472, 143-149 (2000)
[99]	Agasian, N. O., Phase structure of the QCD vacuum in a magnetic field at low temperature, Phys. Lett. B, 488, 39-45 (2000)
[100]	Agasian, N. O.; Shushpanov, I., Gell-Mann-Oakes-Renner relation in a magnetic field at finite temperature, J. High Energy Phys., 0110, 006 (2001)
[101]	Agasian, N. O., Chiral thermodynamics in a magnetic field, Phys. Atom. Nucl., 64, 554-560 (2001) · Zbl 0972.81670
[102]	Elizalde, E.; Ferrer, E. J.; de la Incera, V., Beyond constant mass approximation magnetic catalysis in the gauge Higgs-Yukawa model, Phys. Rev., D68, 096004 (2003)
[103]	Ferrer, E. J.; de la Incera, V., Yukawa interactions and dynamical generation of mass in an external magnetic field, AIP Conf. Proc., 444, 452-457 (1998)
[104]	Ferrer, E. J.; de la Incera, V., Yukawa coupling contribution to magnetic field induced dynamical mass, Internat. J. Modern Phys., 14, 3963 (1999)
[105]	Ferrer, E. J.; de la Incera, V., Magnetic catalysis in the presence of scalar fields, Phys. Lett., B481, 287-294 (2000)
[106]	Hong, D. K.; Kim, Y.; Sin, S.-J., RG analysis of magnetic catalysis in dynamical symmetry breaking, Phys. Rev., D54, 7879-7883 (1996)
[107]	Semenoff, G. W.; Shovkovy, I. A.; Wijewardhana, L. C.R., Universality and the magnetic catalysis of chiral symmetry breaking, Phys. Rev., D60, 105024 (1999)
[108]	Fukushima, K.; Pawlowski, J. M., Magnetic catalysis in hot and dense quark matter and quantum fluctuations, Phys. Rev., D86, 076013 (2012)
[109]	Scherer, D. D.; Gies, H., Renormalization group study of magnetic catalysis in the 3d Gross-Neveu model, Phys. Rev., B85, 195417 (2012)
[110]	Kamikado, K.; Kanazawa, T., Chiral dynamics in a magnetic field from the functional renormalization group, J. High Energy Phys., 1403, 009 (2014)
[111]	Kojo, T.; Su, N., A renormalization group approach for QCD in a strong magnetic field, Phys. Lett., B726, 839-845 (2013) · Zbl 1331.81316
[113]	Gusynin, V. P.; Miransky, V. A.; Shovkovy, I. A., Dynamical chiral symmetry breaking by a magnetic field in QED, Phys. Rev., D52, 4747-4751 (1995)
[114]	Gusynin, V. P.; Miransky, V. A.; Shovkovy, I. A., Dimensional reduction and catalysis of dynamical symmetry breaking by a magnetic field, Nuclear Phys., B462, 249-290 (1996)
[115]	Parwani, R. R., On chiral symmetry breaking by external magnetic fields in QED in three-dimensions, Phys. Lett., B358, 101-105 (1995)
[116]	Parwani, R. R., Spin polarization by external magnetic fields, Aharonov-Bohm flux strings, and chiral symmetry breaking in QED in three-dimensions, Internat. J. Modern Phys., A11, 1715-1732 (1996)
[118]	Gusynin, V. P.; Shovkovy, I. A., Chiral symmetry breaking in QED in a magnetic field at finite temperature, Phys. Rev., D56, 5251-5253 (1997)
[119]	Gusynin, V. P.; Smilga, A. V., Electron selfenergy in strong magnetic field: Summation of double logarithmic terms, Phys. Lett., B450, 267-274 (1999)
[120]	Gusynin, V. P.; Miransky, V. A.; Shovkovy, I. A., Dynamical chiral symmetry breaking in QED in a magnetic field: Toward exact results, Phys. Rev. Lett., 83, 1291-1294 (1999)
[121]	Lee, D. S.; Mcgraw, P. N.; Ng, Y. J.; Shovkovy, I. A., The effective potential of composite fields in weakly coupled QED in a uniform external magnetic field, Phys. Rev., D59, 085008 (1999)
[122]	Gusynin, V. P.; Miransky, V. A.; Shovkovy, I. A., Theory of the magnetic catalysis of chiral symmetry breaking in QED, Nuclear Phys., B563, 361-389 (1999)
[123]	Farakos, K.; Koutsoumbas, G.; Mavromatos, N. E.; Momen, A., On magnetic catalysis in even flavor QED(3), Phys. Rev., D61, 045005 (2000)
[124]	Gusynin, V. P.; Miransky, V. A.; Shovkovy, I. A., Physical gauge in the problem of dynamical chiral symmetry breaking in QED in a magnetic field, Found. Phys., 30, 349-357 (2000)
[125]	Alexandre, J.; Farakos, K.; Koutsoumbas, G., Magnetic catalysis in QED(3) at finite temperature: Beyond the constant mass approximation, Phys. Rev., D63, 065015 (2001)
[126]	Alexandre, J.; Farakos, K.; Koutsoumbas, G., Remark on the momentum dependence of the magnetic catalysis in QED, Phys. Rev., D64, 067702 (2001)
[127]	Kabat, D. N.; Lee, K.-M.; Weinberg, E. J., QCD vacuum structure in strong magnetic fields, Phys. Rev., D66, 014004 (2002)
[128]	Miransky, V. A.; Shovkovy, I. A., Magnetic catalysis and anisotropic confinement in QCD, Phys. Rev., D66, 045006 (2002)
[129]	Gusynin, V. P.; Miransky, V. A.; Shovkovy, I. A., Large \(N\) dynamics in QED in a magnetic field, Phys. Rev., D67, 107703 (2003)
[130]	Leung, C. N.; Wang, S.-Y., Gauge independence and chiral symmetry breaking in a strong magnetic field, Ann. Physics, 322, 701-708 (2007) · Zbl 1114.81082
[131]	Leung, C. N.; Wang, S.-Y., Gauge independent approach to chiral symmetry breaking in a strong magnetic field, Nuclear Phys., B747, 266-293 (2006) · Zbl 1178.81289
[132]	Sadooghi, N.; Sodeiri jalili, A., New look at the modified Coulomb potential in a strong magnetic field, Phys. Rev., D76, 065013 (2007)
[133]	Ayala, A.; Bashir, A.; Raya, A.; Sanchez, A., Impact of a uniform magnetic field and nonzero temperature on explicit chiral symmetry breaking in QED: Arbitrary hierarchy of energy scales, J. Phys., G37, 015001 (2010)
[134]	Ayala, A.; Bashir, A.; Gutierrez, E.; Raya, A.; Sanchez, A., Chiral and parity symmetry breaking for planar fermions: Effects of a heat bath and uniform external magnetic field, Phys. Rev., D82, 056011 (2010)
[135]	Mueller, N.; Bonnet, J. A.; Fischer, C. S., Dynamical quark mass generation in a strong external magnetic field, Phys. Rev., D89, 094023 (2014)
[136]	Filev, V. G.; Johnson, C. V.; Rashkov, R.; Viswanathan, K., Flavoured large N gauge theory in an external magnetic field, J. High Energy Phys., 0710, 019 (2007)
[137]	Filev, V. G., Criticality, scaling and chiral symmetry breaking in external magnetic field, J. High Energy Phys., 0804, 088 (2008)
[138]	Erdmenger, J.; Meyer, R.; Shock, J. P., AdS/CFT with flavour in electric and magnetic Kalb-Ramond fields, J. High Energy Phys., 0712, 091 (2007) · Zbl 1246.81237
[139]	Zayakin, A., QCD vacuum properties in a magnetic field from AdS/CFT: Chiral condensate and goldstone mass, J. High Energy Phys., 0807, 116 (2008)
[140]	Argyres, P. C.; Edalati, M.; Leigh, R. G.; Vazquez-Poritz, J. F., Open Wilson lines and chiral condensates in thermal holographic QCD, Phys. Rev., D79, 045022 (2009)
[141]	Filev, V. G.; Johnson, C. V.; Shock, J. P., Universal holographic chiral dynamics in an external magnetic field, J. High Energy Phys., 0908, 013 (2009)
[142]	Filev, V. G.; Raskov, R. C., Magnetic catalysis of chiral symmetry breaking. A holographic prospective, Adv. High Energy Phys., 2010, 473206 (2010) · Zbl 1216.81116
[143]	Filev, V. G.; Zoakos, D., Towards unquenched holographic magnetic catalysis, J. High Energy Phys., 1108, 022 (2011) · Zbl 1298.81277
[144]	Evans, N.; Gebauer, A.; Kim, K.-Y.; Magou, M., Holographic description of the phase diagram of a chiral symmetry breaking gauge theory, J. High Energy Phys., 1003, 132 (2010) · Zbl 1271.81174
[145]	Evans, N.; Gebauer, A.; Kim, K.-Y.; Magou, M., Phase diagram of the D3/D5 system in a magnetic field and a BKT transition, Phys. Lett., B698, 91-95 (2011)
[146]	Evans, N.; Kalaydzhyan, T.; Kim, K.-Y.; Kirsch, I., Non-equilibrium physics at a holographic chiral phase transition, J. High Energy Phys., 1101, 050 (2011) · Zbl 1214.81153
[147]	Evans, N.; Gebauer, A.; Kim, K.-Y., \(E, B, \mu, T\) phase structure of the D3/D7 holographic dual, J. High Energy Phys., 1105, 067 (2011) · Zbl 1296.81135
[148]	Evans, N.; Kim, K.-Y.; Shock, J. P., Chiral phase transitions and quantum critical points of the D3/D7(D5) system with mutually perpendicular E and B fields at finite temperature and density, J. High Energy Phys., 1109, 021 (2011) · Zbl 1301.81123
[149]	Preis, F.; Rebhan, A.; Schmitt, A., Inverse magnetic catalysis in dense holographic matter, J. High Energy Phys., 1103, 033 (2011) · Zbl 1301.81310
[150]	Preis, F.; Rebhan, A.; Schmitt, A., Holographic baryonic matter in a background magnetic field, J. Phys., G39, 054006 (2012)
[151]	Erdmenger, J.; Filev, V. G.; Zoakos, D., Magnetic catalysis with massive dynamical flavours, J. High Energy Phys., 1208, 004 (2012)
[152]	Preis, F.; Rebhan, A.; Schmitt, A., Inverse magnetic catalysis in field theory and gauge-gravity duality, Lect. Notes Phys., 871, 51-86 (2013)
[153]	Bolognesi, S.; Tong, D., Magnetic catalysis in AdS4, Class. Quant. Grav., 29, 194003 (2012) · Zbl 1254.83028
[154]	Bolognesi, S.; Laia, J. N.; Tong, D.; Wong, K., A gapless hard wall: Magnetic catalysis in bulk and boundary, J. High Energy Phys., 1207, 162 (2012)
[155]	Alam, M. S.; Kaplunovsky, V. S.; Kundu, A., Chiral symmetry breaking and external fields in the Kuperstein-Sonnenschein Model, J. High Energy Phys., 1204, 111 (2012) · Zbl 1348.81306
[158]	Farakos, K.; Koutsoumbas, G.; Mavromatos, N. E., Dynamical flavor symmetry breaking by a magnetic field in lattice QED in three-dimensions, Phys. Lett., B431, 147-160 (1998)
[159]	Alexandre, J.; Farakos, K.; Hands, S.; Koutsoumbas, G.; Morrison, S., QED(3) with dynamical fermions in an external magnetic field, Phys. Rev., D64, 034502 (2001)
[160]	Cea, P.; Cosmai, L.; Giudice, P.; Papa, A., Lattice planar QED in external magnetic field, PoS LATTICE2011, 307 (2011)
[161]	Cea, P.; Cosmai, L.; Giudice, P.; Papa, A., Chiral symmetry breaking in planar QED in external magnetic fields, Phys. Rev., D85, 094505 (2012)
[162]	Buividovich, P.; Chernodub, M. N.; Luschevskaya, E. V.; Polikarpov, M. I., Numerical study of chiral symmetry breaking in non-Abelian gauge theory with background magnetic field, Phys. Lett., B682, 484-489 (2010)
[163]	Buividovich, P.; Chernodub, M.; Luschevskaya, E.; Polikarpov, M., Lattice QCD in strong magnetic fields, eCONF C0906083, 25 (2009)
[164]	Braguta, V. V.; Buividovich, P. V.; Kalaydzhyan, T.; Kuznetsov, S. V.; Polikarpov, M. I., The chiral magnetic effect and chiral symmetry breaking in SU(3) quenched lattice gauge theory, PoS LATTICE2010, 190 (2010)
[165]	D’elia, M.; Mukherjee, S.; Sanfilippo, F., QCD phase transition in a strong magnetic background, Phys. Rev., D82, 051501 (2010)
[166]	D’elia, M.; Negro, F., Chiral properties of strong interactions in a magnetic background, Phys. Rev., D83, 114028 (2011)
[167]	Bali, G. S.; Bruckmann, F.; Endrődi, G.; Fodor, Z.; Katz, S. D., The QCD phase diagram for external magnetic fields, J. High Energy Phys., 1202, 044 (2012) · Zbl 1309.81258
[168]	Bali, G. S.; Bruckmann, F.; Endrödi, G.; Fodor, Z.; Katz, S. D., The finite temperature QCD transition in external magnetic fields, PoS LATTICE2011, 192 (2011)
[169]	Bali, G.; Bruckmann, F.; Endrödi, G.; Fodor, Z.; Katz, S., QCD quark condensate in external magnetic fields, Phys. Rev., D86, 071502 (2012)
[170]	D’Elia, M., Lattice QCD simulations in external background fields, Lect. Notes Phys., 871, 181-208 (2013)
[171]	Ilgenfritz, E.-M.; Kalinowski, M.; Müller-Preussker, M.; Petersson, B.; Schreiber, A., Two-color QCD with staggered fermions at finite temperature under the influence of a magnetic field, Phys. Rev., D85, 114504 (2012)
[172]	Ilgenfritz, E. M.; Müller-Preussker, M.; Petersson, B.; Schreiber, A., Magnetic catalysis (and inverse catalysis) at finite temperature in two-color lattice QCD, Phys. Rev., D89, 054512 (2014)
[173]	D’Elia, M., Lattice QCD in background fields, J. Phys. Conf. Ser., 432, 012004 (2013)
[174]	Bruckmann, F.; Endrődi, G.; Kovacs, T. G., Inverse magnetic catalysis and the Polyakov loop, J. High Energy Phys., 1304, 112 (2013)
[176]	Gorbar, E. V.; Gusynin, V. P.; Miransky, V. A., Toward theory of quantum Hall effect in graphene, Low Temp. Phys., 34, 790 (2008)
[177]	Gorbar, E. V.; Gusynin, V. P.; Miransky, V. A.; Shovkovy, I. A., Dynamics in the quantum Hall effect and the phase diagram of graphene, Phys. Rev., B78, 085437 (2008)
[179]	Gusynin, V. P.; Miransky, V. A.; Sharapov, S. G.; Shovkovy, I. A., Excitonic gap, phase transition, and quantum Hall effect in graphene, Phys. Rev., B74, 195429 (2006)
[180]	Herbut, I. F.; Roy, B., Quantum critical scaling in magnetic field near the Dirac point in graphene, Phys. Rev., B77, 245438 (2008)
[181]	Semenoff, G. W., Electronic zero modes of vortices in Hall states of gapped graphene, Phys. Rev. B83, 115450 (2011)
[182]	Semenoff, G. W.; Zhou, F., Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene, J. High Energy Phys., 1107, 037 (2011) · Zbl 1298.82086
[183]	Ferrer, E. J.; Gusynin, V. P.; de la Incera, V., Magnetic field induced gap and kink behavior of thermal conductivity in cuprates, Modern Phys. Lett., B16, 107-116 (2002)
[184]	Ferrer, E. J.; Gusynin, V. P.; de la Incera, V., Thermal conductivity in 3-D NJL model under external magnetic field, Eur. Phys. J. B33, 397 (2003)
[185]	Liu, W. V., Parity breaking and phase transition induced by a magnetic field in high \(T_c\) superconductors, Nuclear Phys., B556, 563-572 (1999)
[186]	Semenoff, G. W.; Shovkovy, I. A.; Wijewardhana, L. C.R., Phase transition induced by a magnetic field, Modern Phys. Lett., A13, 1143-1154 (1998)
[187]	Zhukovsky, V. C.; Klimenko, K. G., Magnetic catalysis of the P-parity-breaking phase transition of the first order and high-temperature superconductivity, Theoret. Math. Phys., 134, 254-270 (2003) · Zbl 1178.82094
[188]	Zhukovsky, V. C.; Klimenko, K. G.; Khudyakov, V. V.; Ebert, D., Magnetic catalysis of parity breaking in a massive Gross-Neveu model and high temperature superconductivity, JETP Lett., 73, 121-125 (2001)
[189]	Gorbar, E. V.; Gusynin, V. P.; Miransky, V. A.; Shovkovy, I. A., Magnetic field driven metal insulator phase transition in planar systems, Phys. Rev., B66, 045108 (2002)
[190]	Khveshchenko, D. V., Ghost excitonic insulator transition in layered graphite, Phys. Rev. Lett., 87, 246802 (2001)
[191]	Khveshchenko, D. V., Magnetic-field-induced insulating behavior in highly oriented pyrolitic graphite, Phys. Rev. Lett., 87, 206401 (2001)
[192]	Ebert, D.; Klimenko, K. G.; Toki, H.; Zhukovsky, V. C., Chromomagnetic catalysis of color superconductivity and dimensional reduction, Progr. Theoret. Phys., 106, 835-849 (2001) · Zbl 0990.81771
[193]	Ebert, D.; Zhukovsky, V. C., Chiral phase transitions in strong chromomagnetic fields at finite temperature and dimensional reduction, Modern Phys. Lett., A12, 2567-2576 (1997) · Zbl 0908.58076
[194]	Gusynin, V. P.; Hong, D.; Shovkovy, I. A., Chiral symmetry breaking by a non-Abelian external field in (2+1)-dimensions, Phys. Rev., D57, 5230-5235 (1998)
[195]	Klimenko, K. G.; Magnitsky, B.; Vshivtsev, A. S., Three-dimensional \((\psi \overline{\psi})^2\) model with an external non-Abelian field, temperature and chemical potential, Nuovo Cimento, A107, 439-452 (1994)
[196]	Shovkovy, I. A.; Turkowski, V. M., Dimensional reduction in Nambu-Jona-Lasinio model in external chromomagnetic field, Phys. Lett., B367, 213-218 (1996)
[197]	Vshivtsev, A. S.; Klimenko, K. G.; Magnitsky, B., Three-dimensional Gross-Neveu model in the external chromomagnetic fields at finite temperature, Theoret. Math. Phys., 101, 1436-1442 (1994)
[198]	Zhukovsky, V. C.; Khudyakov, V. V.; Klimenko, K. G.; Ebert, D., Chromomagnetic catalysis of color superconductivity, JETP Lett., 74, 523-528 (2001) · Zbl 0990.81771
[199]	Fomin, P. I.; Gusynin, V. P.; Miransky, V. A.; Sitenko, Y. A., Dynamical symmetry breaking and particle mass generation in gauge field theories, Riv. Nuovo Cimento, 6N5, 1-90 (1983)
[200]	Miransky, V.; Fomin, P., Dynamical mechanism of symmetry breaking and particle mass generation in gauge field theories, Sov. J. Part. Nucl., 16, 203 (1985)
[201]	Miransky, V. A., Dynamical Symmetry Breaking in Quantum Field Theories (1994), World Scientific: World Scientific Singapore
[202]	Gorbar, E.; Gusynin, V.; Miransky, V., Dynamical chiral symmetry breaking on a brane in reduced QED, Phys. Rev., D64, 105028 (2001)
[203]	Alexandre, J.; Farakos, K.; Koutsoumbas, G.; Mavromatos, N. E., Spatially anisotropic four-dimensional gauge interactions, planar fermions and magnetic catalysis, Phys. Rev., D64, 125007 (2001)
[204]	Bogolyubov, N., On the theory of superfluidity, J. Phys. (USSR), 11, 23-32 (1947)
[205]	Akhiezer, A. I.; Berestetsky, V. B., Quantum Electrodynamics, Interscience (1965), New: New York · Zbl 0084.45005
[206]	Gradshteyn, I. S.; Ryzhik, I. M., Table of Integrals, Series and Products (1980), Academic Press: Academic Press Orlando · Zbl 0521.33001
[207]	Pisarski, R. D., Chiral symmetry breaking in three-dimensional electrodynamics, Phys. Rev., D29, 2423 (1984)
[208]	Appelquist, T. W.; Bowick, M. J.; Karabali, D.; Wijewardhana, L., Spontaneous chiral symmetry breaking in three-dimensional QED, Phys. Rev., D33, 3704 (1986)
[209]	Appelquist, T.; Nash, D.; Wijewardhana, L., Critical behavior in \((2 + 1)\)-dimensional QED, Phys. Rev. Lett., 60, 2575 (1988)
[210]	Dagotto, E.; Kogut, J. B.; Kocic, A., A computer simulation of chiral symmetry breaking in \((2 + 1)\)-dimensional QED with N flavors, Phys. Rev. Lett., 62, 1083 (1989)
[211]	Hands, S.; Kogut, J. B., Finite size effects and chiral symmetry breaking in quenched three-dimensional QED, Nuclear Phys., B335, 455 (1990)
[212]	Pisarski, R. D., Fermion mass in three-dimensions and the renormalization group, Phys. Rev., D44, 1866-1872 (1991)
[213]	Pennington, M.; Walsh, D., Masses from nothing: A nonperturbative study of QED in three-dimensions, Phys. Lett., B253, 246-251 (1991)
[214]	Gusynin, V.; Miransky, V.; Shpagin, A., Effective action and conformal phase transition in QED(3), Phys. Rev., D58, 085023 (1998)
[215]	Chodos, A.; Everding, K.; Owen, D. A., QED with a chemical potential: 1. The case of a constant magnetic field, Phys. Rev., D42, 2881-2892 (1990)
[216]	Atiyah, M.; Singer, I., The index of elliptic operators. 1, Ann. Math., 87, 484-530 (1968) · Zbl 0164.24001
[217]	Haag, R., The mathematical structure of the Bardeen-Cooper-Schrieffer model, Nuovo Cimento, 25, 287-299 (1962) · Zbl 0113.46210
[218]	Niemi, A. J.; Semenoff, G. W., Axial anomaly induced fermion fractionization and effective gauge theory actions in odd dimensional space-times, Phys. Rev. Lett., 51, 2077 (1983)
[219]	Kovner, A.; Rosenstein, B.; Eliezer, D., Photon as a Goldstone boson in (2+1)-dimensional Abelian gauge theories, Nuclear Phys., B350, 325-354 (1991)
[220]	Goldstone, J.; Salam, A.; Weinberg, S., Broken symmetries, Phys. Rev., 127, 965-970 (1962) · Zbl 0106.20601
[221]	Stratonovich, R. L., On a method of calculating quantum distribution functions, Sov. Phys. Dokl., 2, 416 (1957) · Zbl 0080.19804
[222]	Hubbard, J., Calculation of partition functions, Phys. Rev. Lett., 3, 77-78 (1959)
[223]	Gross, D. J.; Neveu, A., Dynamical symmetry breaking in asymptotically free field theories, Phys. Rev., D10, 3235 (1974)
[224]	Witten, E., Chiral symmetry, the \(1 / N\) expansion, and the SU(N) Thirring model, Nuclear Phys., B145, 110 (1978)
[225]	Mermin, N.; Wagner, H., Absence of ferromagnetism or antiferromagnetism in one-dimensional or two-dimensional isotropic Heisenberg models, Phys. Rev. Lett., 17, 1133-1136 (1966)
[226]	Coleman, S. R., There are no Goldstone bosons in two-dimensions, Commun. Math. Phys., 31, 259-264 (1973) · Zbl 1125.81321
[227]	Zak, J., Magnetic translation group, Phys. Rev., 134, A1602-A1606 (1964) · Zbl 0131.45404
[228]	Avron, J. E.; Herbst, I. W.; Simon, B., Separation of center of mass in homogeneous magnetic fields, Ann. Physics, 114, 431-451 (1978) · Zbl 0409.35027
[229]	Rosenstein, B.; Warr, B.; Park, S., Dynamical symmetry breaking in four Fermi interaction models, Phys. Rep., 205, 59-108 (1991)
[230]	Bateman, H.; Erdelyi, A., Higher Transcendental Functions, Vol. 1 (1953), McGraw-Hill: McGraw-Hill New York · Zbl 0051.30303
[232]	(Olver, F. W.J.; Lozier, D. W.; Boisvert, R. F.; Clark, C. W., NIST Handbook of Mathematical Functions (2010), Cambridge University Press: Cambridge University Press New York, NY), print companion to [231] · Zbl 1198.00002
[233]	Gusynin, V.; Miransky, V., On the effective action in field theories with dynamical symmetry breaking, Modern Phys. Lett., A6, 2443-2452 (1991) · Zbl 1020.81689
[234]	Gusynin, V.; Miransky, V., Effective action in the gauged Nambu-Jona-Lasinio model, Sov. Phys. JETP, 74, 216-223 (1992)
[235]	Miransky, V., On the generating functional for proper vertices of local composite operators in theories with dynamical symmetry breaking, Internat. J. Modern Phys., A8, 135-151 (1993)
[236]	Kondo, K.-i.; Tanabashi, M.; Yamawaki, K., Renormalization in the gauged Nambu-Jona-Lasinio model, Progr. Theoret. Phys., 89, 1249-1302 (1993)
[237]	Hands, S.; Kocic, A.; Kogut, J. B., Four Fermi theories in fewer than four-dimensions, Ann. Physics, 224, 29-89 (1993)
[238]	Andersen, J.; Haugset, T., Magnetization in (2+1)-dimensional QED at finite temperature and density, Phys. Rev., D51, 3073-3080 (1995)
[239]	Cangemi, D.; Dunne, G. V., Temperature expansions for magnetic systems, Ann. Physics, 249, 582-602 (1996)
[240]	Elmfors, P.; Persson, D.; Skagerstam, B.-S., QED effective action at finite temperature and density, Phys. Rev. Lett., 71, 480-483 (1993)
[241]	Elmfors, P.; Persson, D.; Skagerstam, B.-S., Real time thermal propagators and the QED effective action for an external magnetic field, Astropart. Phys., 2, 299-326 (1994)
[242]	Elmfors, P.; Liljenberg, P.; Persson, D.; Skagerstam, B.-S., Thermal versus vacuum magnetization in QED, Phys. Rev., D51, 5885-5888 (1995)
[243]	Persson, D.; Zeitlin, V., A Note on QED with magnetic field and chemical potential, Phys. Rev., D51, 2026-2029 (1995)
[244]	Dolan, L.; Jackiw, R., Symmetry behavior at finite temperature, Phys. Rev., D9, 3320-3341 (1974)
[245]	Polyakov, A. M.; Wiegmann, P., Theory of nonabelian Goldstone bosons, Phys. Lett., B131, 121-126 (1983)
[246]	Cao, G.; He, L.; Zhuang, P., Collective modes and Kosterlitz-Thouless transition in a magnetic field in the planar Nambu-Jona-Lasino model, Phys. Rev., D90, 056005 (2014)
[247]	Berezinskii, V. L., Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group i. Classical systems, Sov. Phys. JETP. Sov. Phys. JETP, Zh. Eksp. Teor. Fiz., 59, 907 (1970)
[248]	Kosterlitz, J. M.; Thouless, D. J., Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C, 6, 1181-1203 (1973)
[249]	Goldstone, J., Field theories with superconductor solutions, Nuovo Cimento, 19, 154-164 (1961) · Zbl 0099.23006
[250]	Nambu, Y., Axial vector current conservation in weak interactions, Phys. Rev. Lett., 4, 380-382 (1960)
[251]	Simon, B., The bound state of weakly coupled Schrodinger operators in one and two-dimensions, Ann. Physics, 97, 279-288 (1976) · Zbl 0325.35029
[252]	Simon, B., On the Number of Bound States of Two-Body Schrodinger Operators—A Review (1976), Princeton University Press, Princeton: Princeton University Press, Princeton NJ · Zbl 0349.35022
[253]	Banks, T.; Casher, A., Chiral symmetry breaking in confining theories, Nuclear Phys., B169, 103 (1980)
[255]	Leung, C. N.; Ng, Y. J.; Ackley, A. W., Schwinger-Dyson equation approach to chiral symmetry breaking in an external magnetic field, Phys. Rev., D54, 4181-4184 (1996)
[256]	Dittrich, W.; Reuter, M., (Effective Lagrangians In Quantum Electrodynamics. Effective Lagrangians In Quantum Electrodynamics, Lecture Notes in Physics, vol. 220 (1985), Springer: Springer Berlin)
[257]	Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (1972), Dover, New: Dover, New York · Zbl 0543.33001
[258]	Perelomov, A.; Popov, V., Collapse onto scattering centre in quantum mechanics, Teor. Mat. Fiz., 4, 48-65 (1970)
[259]	Fradkin, E.; Gitman, D.; Shvartsman, S., Quantum Electrodynamics with Unstable Vacuum (1991), Springer-Verlag: Springer-Verlag Berlin
[260]	Batalin, I. A.; Shabad, A. E., Photon green function in a stationary homogeneous field of the most general form, Zh. Eksp. Teor. Fiz.. Zh. Eksp. Teor. Fiz., Sov. Phys. JETP, 33, 483-486 (1971)
[261]	Tsai, W.-Y., Vacuum polarization in homogeneous magnetic fields, Phys. Rev. D 10, 8, 2699-2702 (1974)
[262]	Shabad, A. E., Photon dispersion in a strong magnetic field, Ann. Physics, 90, 166-195 (1975)
[263]	Loskutov, Y. M.; Skobelev, V. V., Nonlinear electrodynamics in a superstrong magnetic field, Phys. Lett., A56, 151-152 (1976)
[264]	Calucci, G.; Ragazzon, R., Nonlogarithmic terms in the strong field dependence of the photon propagator, J. Phys., A27, 2161-2166 (1994)
[265]	Hattori, K.; Itakura, K., Vacuum birefringence in strong magnetic fields: (I) Photon polarization tensor with all the Landau levels, Ann. Physics, 330, 23-54 (2013) · Zbl 1266.81165
[266]	Hattori, K.; Itakura, K., Vacuum birefringence in strong magnetic fields: (II) Complex refractive index from the lowest Landau level, Ann. Physics, 334, 58-82 (2013)
[267]	Karbstein, F., Photon polarization tensor in a homogeneous magnetic or electric field, Phys. Rev. D88, 8, 085033 (2013)
[268]	Chao, J.; Yu, L.; Huang, M., Zeta function regularization of photon polarization tensor for a magnetized vacuum, Phys. Rev., D90, 045033 (2014)
[269]	Schwinger, J. S., Gauge invariance mass, Phys. Rev., 125, 397-398 (1962) · Zbl 0099.23002
[270]	Coleman, S. R., More about the massive Schwinger model, Ann. Physics, 101, 239 (1976)
[271]	Frishman, Y., (Particles Quantum Fields and Statistical Particles, Quantum Fields and Statistical Mechanics. Particles Quantum Fields and Statistical Particles, Quantum Fields and Statistical Mechanics, Lecture Notes in Physics, vol. 32 (1975), Springer: Springer Berlin)
[272]	Cornwall, J. M.; Jackiw, R.; Tomboulis, E., Effective action for composite operators, Phys. Rev., D10, 2428-2445 (1974) · Zbl 1110.81324
[273]	Fradkin, E. H., Field Theories of Condensed Matter Systems (1991), Addison-Wesley, Redwood City: Addison-Wesley, Redwood City CA · Zbl 0984.82504
[274]	Semenoff, G. W., Condensed matter simulation of a three-dimensional anomaly, Phys. Rev. Lett., 53, 2449 (1984)
[275]	Marston, J. B.; Affleck, I., Large-\(N\) limit of the Hubbard-Heisenberg model, Phys. Rev., B39, 11538-11558 (1989)
[276]	Marston, J., Instantons and massless fermions in \((2 + 1)\) -dimensional lattice QED and antiferromagnets, Phys. Rev. Lett., 64, 1166-1169 (1990)
[277]	Kovner, A.; Rosenstein, B., Kosterlitz-Thouless mechanism of two-dimensional superconductivity, Phys. Rev., B42, 4748-4751 (1990)
[278]	Dorey, N.; Mavromatos, N., QED in three-dimension and two-dimensional superconductivity without parity violation, Nuclear Phys., B386, 614-682 (1992)
[279]	Aitchison, I. J.R.; Mavromatos, N. E., Deviations from fermi-liquid behavior in \((2 + 1)\)-dimensional quantum electrodynamics and the normal phase of high-\(T_c\) superconductors, Phys. Rev., B53, 9321-9336 (1996)
[280]	González, J.; Guinea, F.; Vozmediano, M. A.H., Marginal-Fermi-liquid behavior from two-dimensional Coulomb interaction, Phys. Rev., B59, R2474-R2477 (1999)
[281]	González, J. J.; Guinea, F.; Vozmediano, M. A.H., Electron-electron interactions in graphene sheets, Phys. Rev., B63, 134421 (2001)
[282]	Marinelli, L.; Halperin, B. I.; Simon, S. H., Quasiparticle spectrum of \(d\)-wave superconductors in the mixed state, Phys. Rev., B62, 3488-3501 (2000)
[283]	Franz, M.; Tešanović, Z., Quasiparticles in the vortex lattice of unconventional superconductors: Bloch waves or Landau levels?, Phys. Rev. Lett., 84, 554-557 (2000)
[284]	Vafek, O.; Melikyan, A.; Franz, M.; Tešanović, Z., Quasiparticles and vortices in unconventional superconductors, Phys. Rev., B63, 134509 (2001)
[285]	Ye, J., Random magnetic field and quasiparticle transport in the mixed state of high-\(T_c\) cuprates, Phys. Rev. Lett., 86, 316-319 (2001)
[286]	Vishwanath, A., Quantized thermal Hall effect in the mixed state of \(d\)-wave superconductors, Phys. Rev. Lett., 87, 217004 (2001)
[287]	Farakos, K.; Koutsoumbas, G.; Mavromatos, N., Probing the gauge structure of high temperature superconductors, Internat. J. Modern Phys., B12, 2475-2494 (1998)
[288]	Teber, S., Electromagnetic current correlations in reduced quantum electrodynamics, Phys. Rev., D86, 025005 (2012)
[289]	Kotikov, A.; Teber, S., Two-loop fermion self-energy in reduced quantum electrodynamics and application to the ultra-relativistic limit of graphene, Phys. Rev., D89, 065038 (2014)
[290]	Wallace, P., The band theory of graphite, Phys. Rev., 71, 622-634 (1947) · Zbl 0033.14304
[291]	Mcclure, J., Band structure of graphite and de Haas-van Alphen effect, Phys. Rev., 108, 612-618 (1957)
[292]	Deser, S.; Jackiw, R.; Templeton, S., Topologically massive gauge theories, Ann. Physics, 140, 372-411 (1982)
[293]	Jackiw, R.; Templeton, S., How superrenormalizable interactions cure their infrared divergences, Phys. Rev., D23, 2291 (1981)
[294]	Appelquist, T.; Bowick, M. J.; Karabali, D.; Wijewardhana, L., Spontaneous breaking of parity in \((2 + 1)\)-dimensional QED, Phys. Rev., D33, 3774 (1986)
[296]	Schramm, S.; Müller, B.; Schramm, A. J., Quark-anti-quark condensates in strong magnetic fields, Modern Phys. Lett., A7, 973-982 (1992)
[297]	Gross, D. J.; Pisarski, R. D.; Yaffe, L. G., QCD and instantons at finite temperature, Rev. Modern Phys., 53, 43 (1981)
[298]	Collins, J. C.; Perry, M., Superdense matter: Neutrons or asymptotically free quarks?, Phys. Rev. Lett., 34, 1353 (1975)
[299]	Rajagopal, K.; Wilczek, F., The Condensed matter physics of QCD, (Shifman, M., At the Frontier of Particle Physics, vol. 3 (2000), World Scientific: World Scientific Singapore)
[300]	Rischke, D. H., The quark gluon plasma in equilibrium, Progr. Part. Nuclear Phys., 52, 197-296 (2004)
[301]	Schwinger, J. S., Gauge invariance mass. 2, Phys. Rev., 128, 2425-2429 (1962) · Zbl 0118.44001
[302]	Pagels, H.; Stokar, S., The pion decay constant electromagnetic form-factor and quark electromagnetic selfenergy in QCD, Phys. Rev., D20, 2947 (1979)
[303]	Miransky, V. A.; Shovkovy, I. A.; Wijewardhana, L. C.R., Diquarks in cold dense QCD with two flavors, Phys. Rev., D62, 085025 (2000)
[304]	Miransky, V. A.; Shovkovy, I. A.; Wijewardhana, L. C.R., Bethe-Salpeter equation for diquarks in color flavor locked phase of cold dense QCD, Phys. Rev., D63, 056005 (2001) · Zbl 1006.81542
[305]	Beane, S. R.; Bedaque, P. F.; Savage, M. J., Meson masses in high density QCD, Phys. Lett., B483, 131-138 (2000)
[306]	Son, D.; Stephanov, M. A., Inverse meson mass ordering in color flavor locking phase of high density QCD, Phys. Rev., D61, 074012 (2000)
[307]	Son, D.; Stephanov, M. A., Inverse meson mass ordering in color flavor locking phase of high density QCD: Erratum, Phys. Rev., D62, 059902 (2000)
[308]	Zarembo, K., Dispersion laws for Goldstone bosons in a color superconductor, Phys. Rev., D62, 054003 (2000)
[309]	Landau, L. D.; Lifshitz, E. M.; Pitaevskii, L. P., Electrodynamics of Continuous Media (1984), Pergamon Press: Pergamon Press Oxford
[310]	Bonati, C.; D’Elia, M.; Mariti, M.; Mesiti, M.; Negro, F., Anisotropy of the quark-antiquark potential in a magnetic field, Phys. Rev., D89, 114502 (2014)
[311]	Shovkovy, I. A., Two lectures on color superconductivity, Found. Phys., 35, 1309-1358 (2005) · Zbl 1102.81321
[312]	Alford, M. G.; Schmitt, A.; Rajagopal, K.; Schäfer, T., Color superconductivity in dense quark matter, Rev. Modern Phys., 80, 1455-1515 (2008)
[313]	Son, D., Superconductivity by long range color magnetic interaction in high density quark matter, Phys. Rev., D59, 094019 (1999)
[314]	Schäfer, T.; Wilczek, F., Superconductivity from perturbative one gluon exchange in high density quark matter, Phys. Rev., D60, 114033 (1999)
[315]	Hong, D. K.; Miransky, V. A.; Shovkovy, I. A.; Wijewardhana, L. C.R., Schwinger-Dyson approach to color superconductivity in dense QCD, Phys. Rev., D61, 056001 (2000), http://dx.doi.org/10.1103/PhysRevD.61.056001, http://dx.doi.org/10.1103/PhysRevD.62.059903, arXiv:hep-ph/9906478
[316]	Hsu, S. D.; Schwetz, M., Magnetic interactions, the renormalization group and color superconductivity in high density QCD, Nuclear Phys., B572, 211-226 (2000)
[317]	Pisarski, R. D.; Rischke, D. H., Color superconductivity in weak coupling, Phys. Rev., D61, 074017 (2000)
[318]	Shovkovy, I. A.; Wijewardhana, L. C.R., On gap equations and color flavor locking in cold dense QCD with three massless flavors, Phys. Lett., B470, 189-199 (1999)
[319]	Alford, M. G.; Rajagopal, K.; Wilczek, F., Color flavor locking and chiral symmetry breaking in high density QCD, Nuclear Phys., B537, 443-458 (1999)
[320]	Rischke, D.; Son, D.; Stephanov, M. A., Asymptotic deconfinement in high density QCD, Phys. Rev. Lett., 87, 062001 (2001)
[321]	Bornyakov, V. G.; Buividovich, P. V.; Cundy, N.; Kochetkov, O. A.; Schäfer, A., Deconfinement transition in two-flavor lattice QCD with dynamical overlap fermions in an external magnetic field, Phys. Rev. D, 90, 034501 (2014)
[322]	Farias, R.; Gomes, K.; Krein, G.; Pinto, M., Importance of asymptotic freedom for the pseudocritical temperature in magnetized quark matter, Phys. Rev. C, 90, 025203 (2014)
[323]	Ayala, A.; Loewe, M.; Mizher, A. J.; Zamora, R., Inverse magnetic catalysis for the chiral transition induced by thermo-magnetic effects on the coupling constant, Phys. Rev., D90, 036001 (2014)
[325]	Ferrer, E.; de la Incera, V.; Wen, X., Quark antiscreening at strong magnetic field and inverse magnetic catalysis, Phys. Rev. D, 91, 054006 (2015)
[326]	Fraga, E. S.; Palhares, L. F., Deconfinement in the presence of a strong magnetic background: an exercise within the MIT bag model, Phys. Rev. D, 86, 016008 (2012)
[327]	Chao, J.; Chu, P.; Huang, M., Inverse magnetic catalysis induced by sphalerons, Phys. Rev., D88, 054009 (2013)
[328]	Yu, L.; Liu, H.; Huang, M., Spontaneous generation of local CP violation and inverse magnetic catalysis, Phys. Rev., D90, 074009 (2014)
[330]	Bali, G.; Bruckmann, F.; Endrődi, G.; Gruber, F.; Schaefer, A., Magnetic field-induced gluonic (inverse) catalysis and pressure (an)isotropy in QCD, J. High Energy Phys., 1304, 130 (2013) · Zbl 1342.81659
[331]	Ozaki, S., QCD effective potential with strong \(U(1){}_{em}\) magnetic fields, Phys. Rev., D89, 054022 (2014)
[332]	Fukushima, K.; Hidaka, Y., Magnetic catalysis vs magnetic inhibition, Phys. Rev. Lett., 110, 031601 (2013)
[333]	Kojo, T.; Su, N., The quark mass gap in a magnetic field, Phys. Lett., B720, 192-197 (2013) · Zbl 1372.81150
[334]	Kojo, T.; Su, N., The quark mass gap in strong magnetic fields, Nuclear Phys. A., 931, 763-768 (2014)
[335]	Cohen, T. D.; Yamamoto, N., New critical point for QCD in a magnetic field, Phys. Rev., D89, 054029 (2014)
[336]	Yaffe, L.; Svetitsky, B., First order phase transition in the SU(3) gauge theory at finite temperature, Phys. Rev., D26, 963 (1982)
[338]	Bali, G.; Bruckmann, F.; Endrődi, G.; Katz, S.; Schäfer, A., The QCD equation of state in background magnetic fields, J. High Energy Phys., 1408, 177 (2014)
[339]	Castro Neto, A. H.; Guinea, F.; Peres, N. M.R.; Novoselov, K. S.; Geim, A. K., The electronic properties of graphene, Rev. Modern Phys., 81, 109-162 (2009)
[340]	Zheng, Y.; Ando, T., Hall conductivity of a two-dimensional graphite system, Phys. Rev., B65, 245420 (2002)
[341]	Gusynin, V. P.; Sharapov, S. G., Unconventional integer quantum Hall effect in graphene, Phys. Rev. Lett., 95, 146801 (2005)
[342]	Gusynin, V. P.; Sharapov, S. G., Transport of Dirac quasiparticles in graphene: Hall and optical conductivities, Phys. Rev., B73, 245411 (2006)
[343]	Peres, N. M.R.; Guinea, F.; Castro Neto, A. H., Electronic properties of disordered two-dimensional carbon, Phys. Rev., B73, 125411 (2006)
[344]	Haldane, F. D.M., Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the ’Parity anomaly’, Phys. Rev. Lett., 61, 2015-2018 (1988)
[345]	Sharapov, S.; Gusynin, V.; Beck, H., Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations, Phys. Rev., B69, 075104 (2004)
[346]	Zhang, Y.; Jiang, Z.; Small, J. P.; Purewal, M. S.; Tan, Y.-W.; Fazlollahi, M.; Chudow, J. D.; Jaszczak, J. A.; Stormer, H. L.; Kim, P., Landau-level splitting in graphene in high magnetic fields, Phys. Rev. Lett., 96, 136806 (2006)
[347]	Jiang, Z.; Zhang, Y.; Stormer, H. L.; Kim, P., Quantum Hall states near the charge-neutral Dirac point in graphene, Phys. Rev. Lett., 99, 106802 (2007)
[348]	Du, X.; Skachko, I.; Duerr, F.; Luican, A.; Andrei, E. Y., Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene, Nature, 462, 192-195 (2009)
[349]	Bolotin, K. I.; Ghahari, F.; Shulman, M. D.; Stormer, H. L.; Kim, P., Observation of the fractional quantum Hall effect in graphene, Nature, 462, 196-199 (2009)
[350]	Nomura, K.; MacDonald, A. H., Quantum Hall ferromagnetism in graphene, Phys. Rev. Lett., 96, 256602 (2006)
[351]	Yang, K.; Das sarma, S.; MacDonald, A. H., Collective modes and skyrmion excitations in graphene SU(4) quantum Hall ferromagnets, Phys. Rev., B74, 075423 (2006)
[352]	Goerbig, M. O.; Moessner, R.; Douçot, B., Electron interactions in graphene in a strong magnetic field, Phys. Rev., B74, 161407 (2006)
[353]	Alicea, J.; Fisher, M. P.A., Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes, Phys. Rev., B74, 075422 (2006)
[354]	Sheng, L.; Sheng, D. N.; Haldane, F. D.M.; Balents, L., Odd-integer quantum Hall effect in graphene: Interaction and disorder effects, Phys. Rev. Lett., 99, 196802 (2007)
[355]	Abanin, D. A.; Lee, P. A.; Levitov, L. S., Spin-filtered edge states and quantum Hall effect in graphene, Phys. Rev. Lett., 96, 176803 (2006)
[356]	Abanin, D. A.; Lee, P. A.; Levitov, L. S., Charge and spin transport at the quantum Hall edge of graphene, Solid State Commun., 143, 77-85 (2007)
[357]	Fogler, M. M.; Shklovskii, B. I., Collapse of spin splitting in the quantum Hall effect, Phys. Rev., B52, 17366-17378 (1995) · Zbl 1020.82584
[358]	Herbut, I. F., Interactions and phase transitions on graphene’s honeycomb lattice, Phys. Rev. Lett., 97, 146401 (2006)
[359]	Herbut, I. F., Theory of integer quantum Hall effect in graphene, Phys. Rev., B75, 165411 (2007)
[360]	Herbut, I. F., SO(3) symmetry between Néel and ferromagnetic order parameters for graphene in a magnetic field, Phys. Rev., B76, 085432 (2007)
[361]	Fuchs, J.-N.; Lederer, P., Spontaneous parity breaking of graphene in the quantum Hall regime, Phys. Rev. Lett., 98, 016803 (2007)
[362]	Ezawa, M., Intrinsic Zeeman effect in graphene, J. Phys. Soc. Japan, 76, 094701 (2007)
[363]	Ezawa, M., Supersymmetry and unconventional quantum Hall effect in monolayer, bilayer and trilayer graphene, Physica E, 40, 269-272 (2007)
[364]	Koshino, M.; Ando, T., Splitting of the quantum Hall transition in disordered graphenes, Phys. Rev., B75, 033412 (2007)
[365]	Giesbers, A. J.M.; Zeitler, U.; Katsnelson, M. I.; Ponomarenko, L. A.; Mohiuddin, T. M.; Maan, J. C., Quantum-Hall activation gaps in graphene, Phys. Rev. Lett., 99, 206803 (2007)
[366]	Goswami, P.; Jia, X.; Chakravarty, S., Quantum Hall plateau transition in the lowest Landau level of disordered graphene, Phys. Rev., B76, 205408 (2007)
[367]	Nomura, K.; Ryu, S.; Koshino, M.; Mudry, C.; Furusaki, A., Quantum Hall effect of massless Dirac fermions in a vanishing magnetic field, Phys. Rev. Lett., 100, 246806 (2008)
[368]	Jia, X.; Goswami, P.; Chakravarty, S., Dissipation and criticality in the lowest Landau level of graphene, Phys. Rev. Lett., 101, 036805 (2008)
[369]	Bolotin, K. I.; Sikes, K. J.; Jiang, Z.; Klima, M.; Fudenberg, G.; Hone, J.; Kim, P.; Stormer, H. L., Ultrahigh electron mobility in suspended graphene, Solid State Commun., 146, 351-355 (2008)
[370]	Li, G.; Luican, A.; Andrei, E. Y., Scanning tunneling spectroscopy of graphene on graphite, Phys. Rev. Lett., 102, 176804 (2009)
[371]	Aleiner, I. L.; Kharzeev, D. E.; Tsvelik, A. M., Spontaneous symmetry breaking in graphene subjected to an in-plane magnetic field, Phys. Rev., B76, 195415 (2007)
[372]	Kharitonov, M., Phase diagram for the \(\nu = 0\) quantum Hall state in monolayer graphene, Phys. Rev., B85, 155439 (2012)
[373]	Gusynin, V. P.; Sharapov, S. G.; Carbotte, J. P., AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics, Internat. J. Modern Phys., B21, 4611-4658 (2007) · Zbl 1141.81345
[375]	Sinner, A.; Ziegler, K., Effect of the Coulomb interaction on the gap in monolayer and bilayer graphene, Phys. Rev., B82, 165453 (2010)
[376]	Pyatkovskiy, P.; Gusynin, V. P., Dynamical polarization of monolayer graphene in a magnetic field, Phys. Rev., B83, 075422 (2011)
[377]	Gamayun, O.; Gorbar, E. V.; Gusynin, V. P., Gap generation and semimetal-insulator phase transition in graphene, Phys. Rev., B81, 075429 (2010)
[379]	Sadowski, M. L.; Martinez, G.; Potemski, M.; Berger, C.; de Heer, W. A., Landau level spectroscopy of ultrathin graphite layers, Phys. Rev. Lett., 97, 266405 (2006)
[380]	Jiang, Z.; Henriksen, E. A.; Tung, L. C.; Wang, Y.-J.; Schwartz, M. E.; Han, M. Y.; Kim, P.; Stormer, H. L., Infrared spectroscopy of Landau levels of graphene, Phys. Rev. Lett., 98, 197403 (2007)
[381]	Orlita, M.; Potemski, M., Dirac electronic states in graphene systems: optical spectroscopy studies, Semicond. Sci. Technol., 25, 063001 (2010)
[382]	Roldan, R.; Fuchs, J.-N.; Goerbig, M. O., Collective modes of doped graphene and a standard two-dimensional electron gas in a strong magnetic field: Linear magnetoplasmons versus magnetoexcitons, Phys. Rev., B80, 085408 (2009)
[383]	Iyengar, A.; Wang, J.; Fertig, H. A.; Brey, L., Excitations from filled Landau levels in graphene, Phys. Rev., B75, 125430 (2007)
[384]	Jung, J.; MacDonald, A. H., Theory of the magnetic-field-induced insulator in neutral graphene sheets, Phys. Rev., B80, 235417 (2009)
[385]	Kharitonov, M., Edge excitations of the canted antiferromagnetic phase of the \(\nu =0\) quantum Hall state in graphene: A simplified analysis, Phys. Rev., B86, 075450 (2012)
[386]	Roy, B.; Kennett, M. P.; Das Sarma, S., Chiral symmetry breaking and the quantum Hall effect in monolayer graphene, Phys. Rev. B, 90, 201409(R) (2014)
[387]	Nomura, K.; Ryu, S.; Lee, D.-H., Field-induced Kosterlitz-Thouless transition in the N=0 Landau level of graphene, Phys. Rev. Lett., 103, 216801 (2009)
[388]	Hou, C.-Y.; Chamon, C.; Mudry, C., Deconfined fractional electric charges in graphene at high magnetic fields, Phys. Rev., B81, 075427 (2010)
[389]	Abanin, D. A.; Novoselov, K. S.; Zeitler, U.; Lee, P. A.; Geim, A. K.; Levitov, L. S., Dissipative quantum Hall effect in graphene near the Dirac point, Phys. Rev. Lett., 98, 196806 (2007)
[390]	Checkelsky, J. G.; Li, L.; Ong, N. P., Zero-energy state in graphene in a high magnetic field, Phys. Rev. Lett., 100, 206801 (2008)
[391]	Checkelsky, J. G.; Li, L.; Ong, N. P., Divergent resistance at the Dirac point in graphene: Evidence for a transition in a high magnetic field, Phys. Rev., B79, 115434 (2009)
[392]	Zhao, Y.; Cadden-Zimansky, P.; Ghahari, F.; Kim, P., Magnetoresistance measurements of graphene at the charge neutrality point, Phys. Rev. Lett., 108, 106804 (2012)
[393]	Young, A. F.; Dean, C. R.; Wang, L.; Ren, H.; Cadden-Zimansky, P.; Watanabe, K.; Taniguchi, T.; Hone, J.; Shepard, K. L.; Kim, P., Spin and valley quantum Hall ferromagnetism in graphene, Nat. Phys., 8, 550-556 (2012)
[394]	Abanin, D. A.; Feldman, B. E.; Yacoby, A.; Halperin, B. I., Fractional and integer quantum Hall effects in the zeroth Landau level in graphene, Phys. Rev., B88, 115407 (2013)
[395]	Young, A. F.; Sanchez-Yamagishi, J. D.; Hunt, B.; Choi, S. H.; Watanabe, K.; Taniguchi, T.; Ashoori, R. C.; Jarillo-Herrero, P., Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state, Nature, 505, 7484, 528-532 (2014)
[396]	McCann, E.; Fal’ko, V. I., Landau-level degeneracy and quantum Hall effect in a graphite bilayer, Phys. Rev. Lett., 96, 086805 (2006)
[397]	Novoselov, K. S.; McCann, E.; Morozov, S. V.; Fal’ko, V. I.; Katsnelson, M. I.; Zeitler, U.; Jiang, D.; Schedin, F.; Geim, A. K., Unconventional quantum Hall effect and Berry’s phase of \(2 \pi\) in bilayer graphene, Nat. Phys., 2, 177-180 (2006)
[398]	Henriksen, E. A.; Jiang, Z.; Tung, L.-C.; Schwartz, M. E.; Takita, M.; Wang, Y.-J.; Kim, P.; Stormer, H. L., Cyclotron resonance in bilayer graphene, Phys. Rev. Lett., 100, 087403 (2008)
[399]	McCann, E.; Koshino, M., The electronic properties of bilayer graphene, Rep. Progr. Phys., 76, 056503 (2013), arXiv:1205.6953, http://arxiv.org/abs/1205.6953
[400]	Killi, M.; Wu, S.; Paramekanti, A., Graphene: kinks, superlattices Landau levels magnetotransport, Internat. J. Modern Phys., B26, 1242007 (2012), arXiv:1205.6813, http://arxiv.org/abs/1205.6813
[401]	Feldman, B. E.; Martin, J.; Yacoby, A., Broken-symmetry states and divergent resistance in suspended bilayer graphene, Nat. Phys., 5, 889-893 (2009)
[402]	Zhao, Y.; Cadden-Zimansky, P.; Jiang, Z.; Kim, P., Symmetry breaking in the zero-energy Landau level in bilayer graphene, Phys. Rev. Lett., 104, 066801 (2010)
[403]	Barlas, Y.; Cote, R.; Nomura, K.; MacDonald, A. H., Intra-Landau level cyclotron resonance in bilayer graphene, Phys. Rev. Lett., 101, 097601 (2008)
[404]	Shizuya, K., Pseudo-zero-mode Landau levels and collective excitations in bilayer graphene, Phys. Rev. B79, 165402 (2009)
[405]	Nakamura, M.; Castro, E. V.; Dora, B., Valley symmetry breaking in bilayer graphene: a test to the minimal model, Phys. Rev. Lett., 103, 266804 (2009)
[406]	Nandkishore, R.; Levitov, L., Dynamical screening and ferroelectric-type excitonic instability in bilayer graphene, Phys. Rev. Lett., 104, 156803 (2010)
[407]	Gorbar, E. V.; Gusynin, V. P.; Miransky, V. A., Energy gaps at neutrality point in bilayer graphene in a magnetic field, JETP Lett., 91, 314-318 (2010)
[408]	Gorbar, E. V.; Gusynin, V. P.; Miransky, V. A., Dynamics and phase diagram of the \(\nu =0\) quantum Hall state in bilayer graphene, Phys. Rev., B81, 155451 (2010)
[409]	Baym, G.; Kadanoff, L. P., Conservation laws and correlation functions, Phys. Rev., 124, 287-299 (1961) · Zbl 0111.44002
[410]	Gorbar, E. V.; Gusynin, V. P.; Miransky, V. A.; Shovkovy, I. A., Broken-symmetry \(\nu = 0\) quantum Hall states in bilayer graphene: Landau level mixing and dynamical screening, Phys. Rev., B85, 235460 (2012)
[411]	Gorbar, E. V.; Gusynin, V. P.; Jia, J.; Miransky, V. A., Broken-symmetry states and phase diagram of the lowest Landau level in bilayer graphene, Phys. Rev. B84, 235449 (2011)
[412]	Weitz, R. T.; Allen, M. T.; Feldman, B. E.; Martin, J.; Yacoby, A., Broken-symmetry states in doubly gated suspended bilayer graphene, Science, 330, 812 (2010)
[413]	Kharitonov, M., Canted antiferromagnetic phase of the \(\nu = 0\) quantum Hall state in bilayer graphene, Phys. Rev. Lett., 109, 046803 (2012)
[414]	Kharitonov, M., Antiferromagnetic state in bilayer graphene, Phys. Rev. B86, 195435 (2012)
[415]	Kim, S.; Lee, K.; Tutuc, E., Spin-polarized to valley-polarized transition in graphene bilayers at \(\nu = 0\) in high magnetic fields, Phys. Rev. Lett., 107, 016803 (2011)
[416]	Velasco, J.; Jing, L.; Bao, W.; Lee, Y.; Kratz, P., Transport spectroscopy of symmetry-broken insulating states in bilayer graphene, Nat. Nanotech., 7, 156-160 (2012)
[417]	Maher, P.; Dean, C. R.; Young, A. F.; Taniguchi, T.; Watanabe, K.; Shepard, K. L.; Hone, J.; Kim, P., Evidence for a spin phase transition at charge neutrality in bilayer graphene, Nat. Phys, 9, 3, 154-158 (2013), arXiv:arXiv:1212.3846, http://dx.doi.org/10.1038/nphys2528
[418]	Freitag, F.; Trbovic, J.; Weiss, M.; Schönenberger, C., Spontaneously gapped ground state in suspended bilayer graphene, Phys. Rev. Lett., 108, 076602 (2012)
[419]	Bernstein, A.; Holstein, B. R., Neutral pion lifetime measurements and the QCD chiral anomaly, Rev. Modern Phys., 85, 49 (2013)
[420]	Bell, J.; Jackiw, R., A PCAC puzzle: \(p i^0 \to \gamma \gamma\) in the \(\sigma \)-model, Nuovo Cimento, A60, 47-61 (1969)
[421]	Adler, S. L., Axial vector vertex in spinor electrodynamics, Phys. Rev., 177, 2426-2438 (1969)
[422]	Veneziano, G., U(1) Without instantons, Nuclear Phys., B159, 213-224 (1979)
[423]	Witten, E., Current algebra theorems for the U(1) Goldstone Boson, Nuclear Phys., B156, 269 (1979)
[424]	Adler, S. L.; Bardeen, W. A., Absence of higher order corrections in the anomalous axial vector divergence equation, Phys. Rev., 182, 1517-1536 (1969)
[425]	Peskin, M. E.; Schroeder, D. V., An Introduction to Quantum Field Theory (1995), Addison-Wesley, Reading: Addison-Wesley, Reading MA
[426]	Weinberg, S., The Quantum Theory of Fields. Vol. 2: Modern Applications (1996), Cambridge University Press, Cambridge: Cambridge University Press, Cambridge UK · Zbl 0885.00020
[427]	Bertlmann, R. A., Anomalies in Quantum Field Theory, Oxford University Press (2001), Oxford: Oxford UK
[428]	Fujikawa, K.; Suzuki, H., Path Integrals and Quantum Anomalies (2004), Oxford University Press: Oxford University Press USA, URL: http://researchbooks.org/0198529139 · Zbl 1276.81091
[429]	Kharzeev, D. E., The chiral magnetic effect and anomaly-induced transport, Progr. Part. Nuclear Phys., 75, 133-151 (2014)
[431]	Abelev, B. I.; Aggarwal, M. M.; Ahammed, Z.; Alakhverdyants, A. V.; Anderson, B. D., Azimuthal charged-particle correlations and possible local strong parity violation, Phys. Rev. Lett., 103, 251601 (2009)
[432]	Abelev, B., Charge separation relative to the reaction plane in Pb-Pb collisions at \(\sqrt{s_{N N}} = 2.76\) TeV, Phys. Rev. Lett., 110, 012301 (2013)
[433]	Adamczyk, L., Beam-energy dependence of charge separation along the magnetic field in Au+Au collisions at RHIC, Phys. Rev. Lett., 113, 052302 (2014)
[434]	Charbonneau, J.; Hoffman, K.; Heyl, J., Large pulsar kicks from topological currents, Mon. Not. R. Astron. Soc. Lett., 404, L119-L123 (2010)
[435]	Charbonneau, J.; Zhitnitsky, A., Topological currents in neutron stars: kicks, precession, toroidal fields, and magnetic helicity, J. Cosmol. Astropart. Phys., 1008, 010 (2010)
[437]	Giovannini, M.; Shaposhnikov, M., Primordial hypermagnetic fields and triangle anomaly, Phys. Rev., D57, 2186-2206 (1998)
[438]	Boyarsky, A.; Fröhlich, J.; Ruchayskiy, O., Self-consistent evolution of magnetic fields and chiral asymmetry in the early Universe, Phys. Rev. Lett., 108, 031301 (2012)
[439]	Tashiro, H.; Vachaspati, T.; Vilenkin, A., Chiral effects and cosmic magnetic fields, Phys. Rev., D86, 105033 (2012)
[441]	Vafek, O.; Vishwanath, A., Dirac fermions in solids—from high \(T_c\) cuprates and graphene to topological insulators and Weyl semimetals, Ann. Rev. Cond. Mat. Phys., 5, 83-112 (2014)
[443]	Son, D.; Zhitnitsky, A. R., Quantum anomalies in dense matter, Phys. Rev., D70, 074018 (2004)
[444]	Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A., Chiral asymmetry of the Fermi surface in dense relativistic matter in a magnetic field, Phys. Rev., C80, 032801 (2009)
[445]	Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A., Normal ground state of dense relativistic matter in a magnetic field, Phys. Rev., D83, 085003 (2011)
[446]	Gorbar, E.; Miransky, V.; Shovkovy, I.; Wang, X., Radiative corrections to chiral separation effect in QED, Phys. Rev., D88, 025025 (2013)
[447]	Kharzeev, D., Parity violation in hot QCD: Why it can happen, and how to look for it, Phys. Lett., B633, 260-264 (2006)
[448]	Vilenkin, A., Macroscopic parity violating effects: neutrino fluxes from rotating black holes and in rotating thermal radiation, Phys. Rev., D20, 1807-1812 (1979)
[449]	Erdmenger, J.; Haack, M.; Kaminski, M.; Yarom, A., Fluid dynamics of R-charged black holes, J. High Energy Phys., 0901, 055 (2009) · Zbl 1243.83037
[450]	Banerjee, N.; Bhattacharya, J.; Bhattacharyya, S.; Dutta, S.; Loganayagam, R., Hydrodynamics from charged black branes, J. High Energy Phys., 1101, 094 (2011) · Zbl 1214.83014
[451]	Son, D. T.; Surowka, P., Hydrodynamics with triangle anomalies, Phys. Rev. Lett., 103, 191601 (2009)
[452]	Neiman, Y.; Oz, Y., Anomalies in superfluids and a chiral electric effect, J. High Energy Phys., 1109, 011 (2011) · Zbl 1301.81153
[453]	Huang, X.-G.; Liao, J., Axial current generation from electric field: chiral electric separation effect, Phys. Rev. Lett. 110, 23, 232302 (2013)
[454]	Pu, S.; Wu, S.-Y.; Yang, D.-L., Holographic chiral electric separation effect, Phys. Rev., D89, 085024 (2014)
[455]	Bhattacharyya, S.; Jain, S.; Minwalla, S.; Sharma, T., Constraints on superfluid hydrodynamics from equilibrium partition functions, J. High Energy Phys., 1301, 040 (2013) · Zbl 1342.83066
[456]	Jimenez-Alba, A.; Melgar, L., Anomalous transport in holographic chiral superfluids via Kubo formulae, J. High Energy Phys., 1410, 120 (2014)
[457]	Kharzeev, D. E.; Yee, H.-U., Chiral magnetic wave, Phys. Rev., D83, 085007 (2011)
[458]	Burnier, Y.; Kharzeev, D. E.; Liao, J.; Yee, H.-U., Chiral magnetic wave at finite baryon density and the electric quadrupole moment of quark-gluon plasma in heavy ion collisions, Phys. Rev. Lett., 107, 052303 (2011)
[459]	Pu, S.; Wu, S.-Y.; Yang, D.-L., Chiral Hall effect and chiral electric waves, Phys. Rev. D, 91, 025011 (2015)
[460]	Ambjorn, J.; Greensite, J.; Peterson, C., The axial anomaly and the lattice Dirac sea, Nuclear Phys., B221, 381 (1983)
[461]	Fukushima, K.; Kharzeev, D. E.; Warringa, H. J., Electric-current susceptibility and the chiral magnetic effect, Nuclear Phys., A836, 311-336 (2010)
[462]	Fukushima, K.; Ruggieri, M.; Gatto, R., Chiral magnetic effect in the PNJL model, Phys. Rev., D81, 114031 (2010)
[463]	Fukushima, K.; Ruggieri, M., Dielectric correction to the chiral magnetic effect, Phys. Rev., D82, 054001 (2010)
[465]	Hou, D.; Liu, H.; Ren, H.-c., Some field theoretic issues regarding the chiral magnetic effect, J. High Energy Phys., 1105, 046 (2011) · Zbl 1296.81139
[466]	Fukushima, K., Views of the chiral magnetic effect, Lect. Notes Phys., 871, 241-259 (2013)
[467]	Basar, G.; Dunne, G. V., The chiral magnetic effect and axial anomalies, Lect. Notes Phys., 871, 261-294 (2013)
[468]	Yee, H.-U., Holographic chiral magnetic conductivity, J. High Energy Phys., 0911, 085 (2009)
[469]	Rebhan, A.; Schmitt, A.; Stricker, S. A., Anomalies and the chiral magnetic effect in the Sakai-Sugimoto model, J. High Energy Phys., 1001, 026 (2010) · Zbl 1269.81201
[470]	Gorsky, A.; Kopnin, P.; Zayakin, A., On the chiral magnetic effect in soft-wall AdS/QCD, Phys. Rev., D83, 014023 (2011)
[471]	Gynther, A.; Landsteiner, K.; Pena-Benitez, F.; Rebhan, A., Holographic anomalous conductivities and the chiral magnetic effect, J. High Energy Phys., 1102, 110 (2011) · Zbl 1294.81281
[472]	Hoyos, C.; Nishioka, T.; O’Bannon, A., A chiral magnetic effect from AdS/CFT with flavor, J. High Energy Phys., 1110, 084 (2011) · Zbl 1303.81115
[473]	Kalaydzhyan, T.; Kirsch, I., Fluid/gravity model for the chiral magnetic effect, Phys. Rev. Lett., 106, 211601 (2011)
[474]	Gahramanov, I.; Kalaydzhyan, T.; Kirsch, I., Anisotropic hydrodynamics, holography and the chiral magnetic effect, Phys. Rev., D85, 126013 (2012)
[475]	Jimenez-Alba, A.; Landsteiner, K.; Melgar, L., Anomalous magnetoresponse and the Stückelberg axion in holography, Phys. Rev. D, 90, 126004 (2014)
[476]	Son, D. T.; Yamamoto, N., Berry curvature, triangle anomalies, and the chiral magnetic effect in Fermi liquids, Phys. Rev. Lett., 109, 181602 (2012)
[477]	Son, D. T.; Yamamoto, N., Kinetic theory with Berry curvature from quantum field theories, Phys. Rev. D87, 8, 085016 (2013)
[478]	Stephanov, M.; Yin, Y., Chiral kinetic theory, Phys. Rev. Lett., 109, 162001 (2012)
[479]	Gao, J.-H.; Liang, Z.-T.; Pu, S.; Wang, Q.; Wang, X.-N., Chiral anomaly and local polarization effect from quantum kinetic approach, Phys. Rev. Lett., 109, 232301 (2012)
[480]	Chen, J.-W.; Pu, S.; Wang, Q.; Wang, X.-N., Berry curvature and four-dimensional monopoles in the relativistic chiral kinetic equation, Phys. Rev. Lett. 110, 26, 262301 (2013)
[481]	Satow, D.; Yee, H.-U., Chiral magnetic effect at weak coupling with relaxation dynamics, Phys. Rev., D90, 014027 (2014)
[482]	Buividovich, P. V.; Chernodub, M. N.; Luschevskaya, E. V.; Polikarpov, M. I., Numerical evidence of chiral magnetic effect in lattice gauge theory, Phys. Rev., D80, 054503 (2009)
[483]	Buividovich, P. V.; Chernodub, M. N.; Luschevskaya, E. V.; Polikarpov, M. I., Numerical study of chiral magnetic effect in quenched SU(2) lattice gauge theory, PoS LAT2009, 080 (2009)
[484]	Buividovich, P. V.; Luschevskaya, E. V.; Polikarpov, M. I.; Chernodub, M. N., Chiral magnetic effect in SU(2) lattice gluodynamics at zero temperature, JETP Lett., 90, 412-416 (2009)
[485]	Abramczyk, M.; Blum, T.; Petropoulos, G.; Zhou, R., Chiral magnetic effect in 2+1 flavor QCD+QED, PoS LAT2009, 181 (2009)
[486]	Yamamoto, A., Chiral magnetic effect in lattice QCD with a chiral chemical potential, Phys. Rev. Lett., 107, 031601 (2011)
[487]	Yamamoto, A., Lattice study of the chiral magnetic effect in a chirally imbalanced matter, Phys. Rev., D84, 114504 (2011)
[488]	Yamamoto, A., Chiral magnetic effect on the lattice, Lect. Notes Phys., 871, 387-397 (2013)
[489]	Bali, G.; Bruckmann, F.; Endrödi, G.; Fodor, Z.; Katz, S., Local CP-violation and electric charge separation by magnetic fields from lattice QCD, J. High Energy Phys., 1404, 129 (2014)
[491]	Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A., Chiral asymmetry and axial anomaly in magnetized relativistic matter, Phys. Lett., B695, 354-358 (2011)
[492]	Gorbar, E.; Miransky, V.; Shovkovy, I.; Wang, X., Chiral asymmetry in QED matter in a magnetic field, Phys. Rev., D88, 025043 (2013)
[493]	Redlich, A., Gauge noninvariance and parity violation of three-dimensional fermions, Phys. Rev. Lett., 52, 18 (1984)
[494]	Redlich, A., Parity violation and gauge noninvariance of the efective gauge field action in three-dimensions, Phys. Rev., D29, 2366-2374 (1984)
[495]	Luttinger, J.; Ward, J. C., Ground state energy of a many fermion system. 2, Phys. Rev., 118, 1417-1427 (1960) · Zbl 0098.21705
[496]	Ferrer, E. J.; de la Incera, V., Dynamically induced Zeeman effect in massless QED, Phys. Rev. Lett., 102, 050402 (2009)
[497]	Kojo, T.; Hidaka, Y.; McLerran, L.; Pisarski, R. D., Quarkyonic chiral spirals, Nuclear Phys., A843, 37-58 (2010)
[498]	Clogston, A., Upper limit for the critical field in hard superconductors, Phys. Rev. Lett., 9, 266-267 (1962)
[499]	Nam, S.-i., Vector current correlation and charge separation via chiral magnetic effect, Phys. Rev., D82, 045017 (2010)
[500]	Ioffe, B., Axial anomaly: the modern status, Internat. J. Modern Phys., A21, 6249-6266 (2006) · Zbl 1117.81356
[501]	Gavai, R.; Sharma, S., Anomalies at finite density and chiral fermions, Phys. Rev., D81, 034501 (2010)
[502]	Ritus, V. I., Radiative corrections in quantum electrodynamics with intense field and their analytical properties, Ann. Physics, 69, 555-582 (1972)
[503]	Freedman, B. A.; McLerran, L. D., Fermions and gauge vector mesons at finite temperature and density. 1. Formal techniques, Phys. Rev., D16, 1130 (1977)
[504]	Stueckelberg, E., Theory of the radiation of photons of small arbitrary mass, Helv. Phys. Acta, 30, 209-215 (1957) · Zbl 0077.42603
[505]	Kharzeev, D. E., Topologically induced local P and CP violation in QCD x QED, Ann. Physics, 325, 205-218 (2010) · Zbl 1184.81129
[506]	Weinberg, S., The Quantum Theory of Fields. Vol. 1: Foundations (1995), Cambridge University Press, Cambridge: Cambridge University Press, Cambridge England · Zbl 0959.81002
[507]	Kinoshita, T., Mass singularities of Feynman amplitudes, J. Math. Phys., 3, 650-677 (1962) · Zbl 0118.44501
[508]	Lee, T.; Nauenberg, M., Degenerate systems and mass singularities, Phys. Rev., 133, B1549-B1562 (1964)
[509]	Fomin, P.; Miransky, V.; Sitenko, Y., Infrared problem and boson suppression in massless Abelian gauge theory, Phys. Lett., B64, 444-446 (1976)
[510]	Miransky, V.; Sitenko, Y.; Fomin, P., Infrared singularities and suppression of bosons in massless Abelian gauge theory, Sov. J. Nuclear Phys., 25, 689-694 (1977)
[511]	Georgi, H., Unparticle physics, Phys. Rev. Lett., 98, 221601 (2007)
[512]	Golkar, S.; Son, D. T., (non)-renormalization of the chiral vortical effect coefficient, J. High Energy Phys., 1502, 169 (2015) · Zbl 1388.83348
[513]	Hou, D.-F.; Liu, H.; Ren, H.-C., A possible higher order correction to the vortical conductivity in a gauge field plasma, Phys. Rev., D86, 121703 (2012)
[514]	Jensen, K.; Kovtun, P.; Ritz, A., Chiral conductivities and effective field theory, J. High Energy Phys., 1310, 186 (2013) · Zbl 1342.83382
[515]	Kirilin, V.; Sadofyev, A.; Zakharov, V., Anomaly and long-range forces, Phys. -Usp., 57, 272-286 (2014)
[516]	Vija, H.; Thoma, M. H., Braaten-Pisarski method at finite chemical potential, Phys. Lett., B342, 212-218 (1995)
[517]	Manuel, C., Hard dense loops in a cold non-Abelian plasma, Phys. Rev., D53, 5866-5873 (1996)
[519]	Xia, L.; Gorbar, E.; Miransky, V.; Shovkovy, I., Chiral asymmetry in cold QED plasma in a strong magnetic field, Phys. Rev., D90, 085011 (2014)
[520]	Lyne, A.; Lorimer, D., High birth velocities of radio pulsars, Nat., 369, 127 (1994)
[521]	Cordes, J.; Chernoff, D. F., Neutron star population dynamics. 2. 3-D space velocities of young pulsars, Astrophys. J., 505, 315-338 (1998)
[522]	Hansen, B. M.; Phinney, E. S., The pulsar kick velocity distribution, Mon. Not. R. Astron. Soc., 291, 569 (1997)
[523]	Fryer, C.; Burrows, A.; Benz, W., Population syntheses for neutron star systems with intrinsic kicks, Astrophys. J., 496, 333 (1998)
[524]	Arzoumanian, Z.; Chernoffs, D.; Cordes, J., The Velocity distribution of isolated radio pulsars, Astrophys. J., 568, 289-301 (2002)
[525]	Chatterjee, S.; Vlemmings, W.; Brisken, W.; Lazio, T.; Cordes, J., Getting its kicks: a vlba parallax for the hyperfast pulsar b1508+55, Astrophys. J., 630, L61-L64 (2005)
[526]	Trimble, V., Motions and structure of the filamentary envelope of the Crab nebula, Astron. J., 73, 535 (1968)
[527]	Wang, C.; Lai, D.; Han, J., Neutron star kicks in isolated and binary pulsars: observational constraints and implications for kick mechanisms, Astrophys. J., 639, 1007-1017 (2006)
[528]	Kusenko, A.; Segre, G.; Vilenkin, A., Neutrino transport: No asymmetry in equilibrium, Phys. Lett., B437, 359-361 (1998)
[530]	Sagert, I.; Schaffner-Bielich, J., Pulsar kicks by anisotropic neutrino emission from quark matter in strong magnetic fields, Astron. Astrophys., 489, 281 (2008) · Zbl 1156.85312
[531]	Sagert, I.; Schaffner-Bielich, J., Pulsar kicks by anisotropic neutrino emission from quark matter, J. Phys., G35, 014062 (2008) · Zbl 1156.85312
[532]	Page, D.; Reddy, S., Dense matter in compact stars: theoretical developments and observational constraints, Ann. Rev. Nucl. Part. Sci., 56, 327-374 (2006)
[533]	Fryer, C. L.; Kusenko, A., Effects of neutrino-driven kicks on the supernova explosion mechanism, Astrophys. J. Suppl., 163, 335 (2006)
[534]	Akamatsu, Y.; Yamamoto, N., Chiral plasma instabilities, Phys. Rev. Lett., 111, 052002 (2013)
[535]	Niemi, A.; Semenoff, G., A comment on ‘Induced Chern-Simons terms at high temperatures and finite densities’, Phys. Rev. Lett., 54, 2166 (1985)
[536]	Redlich, A.; Wijewardhana, L., Induced Chern-Simons terms at high temperatures and finite densities, Phys. Rev. Lett., 54, 970 (1985)
[537]	Rubakov, V.; Tavkhelidze, A., Stable anomalous states of superdense matter in gauge theories, Phys. Lett., B165, 109-112 (1985)
[538]	Tsokos, K., Topological mass terms and the high temperature limit of chiral gauge theories, Phys. Lett., B157, 413 (1985)
[539]	Rubakov, V., On the electroweak theory at high fermion density, Progr. Theoret. Phys., 75, 366 (1986)
[540]	Joyce, M.; Shaposhnikov, M. E., Primordial magnetic fields, right-handed electrons, and the Abelian anomaly, Phys. Rev. Lett., 79, 1193-1196 (1997)
[542]	Akamatsu, Y.; Yamamoto, N., Chiral Langevin theory for non-Abelian plasmas, Phys. Rev. D, 90, 125031 (2014)
[543]	Dvornikov, M.; Semikoz, V. B., Magnetic field instability in a neutron star driven by electroweak electron-nucleon interaction versus chiral magnetic effect, Phys. Rev. D, 91, 061301 (2015)
[544]	Bzdak, A.; Koch, V.; Liao, J., Charge-dependent correlations in relativistic heavy ion collisions and the chiral magnetic effect, Lect. Notes Phys., 871, 503-536 (2013)
[545]	Basar, G.; Dunne, G. V.; Kharzeev, D. E., Chiral magnetic spiral, Phys. Rev. Lett., 104, 232301 (2010)
[546]	Kim, K.-Y.; Sahoo, B.; Yee, H.-U., Holographic chiral magnetic spiral, J. High Energy Phys., 1010, 005 (2010) · Zbl 1291.81391
[547]	Frolov, I.; Zhukovsky, V. C.; Klimenko, K., Chiral density waves in quark matter within the Nambu-Jona-Lasinio model in an external magnetic field, Phys. Rev., D82, 076002 (2010)
[549]	Taghavi, S. F.; Wiedemann, U. A., The chiral magnetic wave in an expanding QCD fluid, Phys. Rev. C, 91, 024902 (2015)
[550]	Adamczyk, L., Measurement of charge multiplicity asymmetry correlations in high energy nucleus-nucleus collisions at 200 GeV, Phys. Rev., C89, 044908 (2014)
[551]	Wang, G., Search for chiral magnetic effects in high-energy nuclear collisions, Nuclear Phys. A904-905 248c-255c (2013)
[552]	Ke, H., Charge asymmetry dependency of \(\pi^+ / \pi^-\) elliptic flow in Au + Au collisions at \(\sqrt{s_{N N}} = 200\) GeV, J. Phys. Conf. Ser., 389, 012035 (2012)
[553]	Vilenkin, A.; Leahy, D., Parity nonconservation and the origin of cosmic magnetic fields, Astrophys. J., 254, 77-81 (1982)
[554]	Semikoz, V.; Valle, J., Lepton asymmetries and the growth of cosmological seed magnetic fields, J. High Energy Phys., 0803, 067 (2008)
[555]	Semikoz, V.; Sokoloff, D.; Valle, J., Is the baryon asymmetry of the Universe related to galactic magnetic fields?, Phys. Rev., D80, 083510 (2009)
[556]	Semikoz, V.; Sokoloff, D.; Valle, J., Lepton asymmetries and primordial hypermagnetic helicity evolution, J. Cosmol. Astropart. Phys., 1206, 008 (2012)
[557]	Boyarsky, A.; Ruchayskiy, O.; Shaposhnikov, M., Long-range magnetic fields in the ground state of the Standard Model plasma, Phys. Rev. Lett., 109, 111602 (2012)
[558]	Long, A. J.; Sabancilar, E.; Vachaspati, T., Leptogenesis and primordial magnetic fields, J. Cosmol. Astropart. Phys., 1402, 036 (2014)
[559]	Dvornikov, M.; Semikoz, V. B., Instability of magnetic fields in electroweak plasma driven by neutrino asymmetries, J. Cosmol. Astropart. Phys., 1405, 002 (2014)
[560]	Durrer, R.; Neronov, A., Cosmological magnetic fields: their generation, evolution and observation, Astron. Astrophys. Rev., 21, 62 (2013)
[561]	Kahniashvili, T.; Tevzadze, A. G.; Brandenburg, A.; Neronov, A., Evolution of primordial magnetic fields from phase transitions, Phys. Rev., D87, 083007 (2013)
[562]	Cohen, M. H.; Blount, E. I., The g-factor and de Haas-van Alphen effect of electrons in bismuth, Phil. Mag., 5, 115-126 (1960)
[563]	Wolff, P., Matrix elements and selection rules for the two-band model of bismuth, J. Phys. Chem. Solids, 25, 1057-1068 (1964) · Zbl 0123.44501
[564]	Fal’kovskii, L. A., Physical properties of bismuth, Sov. Phys. Uspekhi, 94, 1 (1968)
[565]	Édel’man, V. S., Electrons in bismuth, Adv. Phys., 25, 555-613 (1976)
[566]	Édel’man, V. S., Reviews of topical problems: properties of electrons in bismuth, Sov. Phys. Uspekhi, 20, 819-835 (1977)
[567]	Lenoir, B.; Cassart, M.; Michenaud, J.-P.; Scherrer, H.; Scherrer, S., Transport properties of Bi-RICH Bi-Sb alloys, J. Phys. Chem. Solids, 57, 89-99 (1996)
[568]	Teo, J. C.Y.; Fu, L.; Kane, C. L., Surface states and topological invariants in three-dimensional topological insulators: Application to \(Bi{}_{1 - x}Sb{}_x\), Phys. Rev., B78, 045426 (2008)
[569]	Murakami, S., Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase, New J. Phys., 9, 356 (2007)
[570]	Zhang, W.; Yu, R.; Zhang, H.-J.; Dai, X.; Fang, Z., First-principles studies of the three-dimensional strong topological insulators \(Bi{}_2 Te{}_3, Bi{}_2 Se{}_3\) and \(Sb{}_2 Te{}_3\), New J. Phys., 12, 065013 (2010)
[571]	Xu, S.-Y.; Xia, Y.; Wray, L. A.; Jia, S.; Meier, F.; Dil, J. H.; Osterwalder, J.; Slomski, B.; Bansil, A.; Lin, H.; Cava, R. J.; Hasan, M. Z., Topological phase transition and texture inversion in a tunable topological insulator, Science, 332, 560 (2011)
[572]	Sato, T.; Segawa, K.; Kosaka, K.; Souma, S.; Nakayama, K.; Eto, K.; Minami, T.; Ando, Y.; Takahashi, T., Unexpected mass acquisition of Dirac fermions at the quantum phase transition of a topological insulator, Nat. Phys., 7, 840-844 (2011)
[573]	Das, T., Weyl semimetal and superconductor designed in an orbital-selective superlattice, Phys. Rev., B88, 035444 (2013)
[574]	Young, S. M.; Zaheer, S.; Teo, J. C.Y.; Kane, C. L.; Mele, E. J.; Rappe, A. M., Dirac semimetal in three dimensions, Phys. Rev. Lett., 108, 140405 (2012)
[575]	Wang, Z.; Sun, Y.; Chen, X.; Franchini, C.; Xu, G.; Weng, H.; Dai, X.; Fang, Z., Dirac semimetal and topological phase transitions in \(A_3Bi\) (A=Na, K, Rb), Phys. Rev., B85, 195320 (2012)
[576]	Wang, Z.; Weng, H.; Wu, Q.; Dai, X.; Fang, Z., Three dimensional Dirac semimetal and quantum transport in \(Cd{}_3 As{}_2\), Phys. Rev., B88, 125427 (2013)
[577]	Liu, Z. K.; Zhou, B.; Wang, Z. J.; Weng, H. M.; Prabhakaran, D.; Mo, S. K.; Zhang, Y.; Shen, Z. X.; Fang, Z.; Dai, X.; Hussain, Z.; Chen, Y. L., Discovery of a three-dimensional topological Dirac semimetal, \(Na{}_3Bi\), Science, 343, 864-867 (2014)
[578]	Neupane, M.; Xu, S.-Y.; Sankar, R.; Alidoust, N.; Bian, G.; Liu, C.; Belopolski, I.; Chang, T.-R.; Jeng, H.-T.; Lin, H.; Bansil, A.; Chou, F.; Hasan, M. Z., Observation of a topological 3D Dirac semimetal phase in high-mobility \(Cd{}_3 As{}_2\) and related materials, Nat. Commun., 05, 3786 (2014)
[579]	Borisenko, S.; Gibson, Q.; Evtushinsky, D.; Zabolotnyy, V.; Buechner, B.; Cava, R. J., Experimental realization of a three-dimensional Dirac semimetal, Phys. Rev. Lett., 113, 027603 (2014)
[581]	Wan, X.; Turner, A. M.; Vishwanath, A.; Savrasov, S. Y., Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates, Phys. Rev., B83, 205101 (2011)
[582]	Burkov, A. A.; Balents, L., Weyl semimetal in a topological insulator multilayer, Phys. Rev. Lett., 107, 127205 (2011)
[583]	Burkov, A. A.; Hook, M. D.; Balents, L., Topological nodal semimetals, Phys. Rev. B, 84, 235126 (2011)
[584]	Gorbar, E.; Miransky, V.; Shovkovy, I., Engineering Weyl nodes in Dirac semimetals by a magnetic field, Phys. Rev., B88, 165105 (2013)
[585]	Nielsen, H. B.; Ninomiya, M., Adler-Bell-Jackiw anomaly and Weyl fermions in crystal, Phys. Lett., B130, 389 (1983)
[586]	Zyuzin, A. A.; Burkov, A. A., Topological response in Weyl semimetals and the chiral anomaly, Phys. Rev. B86, 115133 (2012)
[587]	Jackiw, R., Field theoretical investigations in current algebra, (Treiman, S. B.; Jackiw, R.; Zumino, B.; Witten, E., Current Algebra and Anomalies (1986), Princeton University Press: Princeton University Press Princeton, NJ)
[588]	Katsnelson, M. I., Graphene: Carbon in Two Dimensions (2012), Cambridge University Press: Cambridge University Press Cambridge, England
[589]	Grushin, A. G., Consequences of a condensed matter realization of Lorentz violating QED in Weyl semi-metals, Phys. Rev., D86, 045001 (2012)
[590]	Aji, V., Adler-Bell-Jackiw anomaly in Weyl semi-metals: application to pyrochlore iridates, Phys. Rev. B85, 241101 (2012)
[591]	Son, D.; Spivak, B., Chiral anomaly and classical negative magnetoresistance of Weyl metals, Phys. Rev. B88, 104412 (2013)
[592]	Kim, H.-J.; Kim, K.-S.; Wang, J. F.; Sasaki, M.; Satoh, N.; Ohnishi, A.; Kitaura, M.; Yang, M.; Li, L., Dirac vs. Weyl in topological insulators: Adler-Bell-Jackiw anomaly in transport phenomena, Phys. Rev. Lett., 111, 246603 (2013)
[593]	Liang, T.; Gibson, Q.; Ali, M. N.; Liu, M.; Cava, R. J.; Ong, N. P., Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal \(Cd{}_3 As{}_2\), Nat. Mater., 14, 280-284 (2015)
[594]	Parameswaran, S.; Grover, T.; Abanin, D. A.; Pesin, D. A.; Vishwanath, A., Probing the chiral anomaly with nonlocal transport in three dimensional topological semimetals, Phys. Rev. X4, 031035 (2014)
[595]	Abrikosov, A. A., Quantum magnetoresistance, Phys. Rev., B58, 2788-2794 (1998)
[596]	Hosur, P.; Qi, X., Recent developments in transport phenomena in weyl semimetals, C. R. Phys., 14, 857 (2013)
[597]	Aharonov, Y.; Casher, A., The ground state of a spin 1/2 charged particle in a two-dimensional magnetic field, Phys. Rev., A19, 2461-2462 (1979)
[598]	Hosur, P.; Parameswaran, S. A.; Vishwanath, A., Charge transport in Weyl semimetals, Phys. Rev. Lett., 108, 046602 (2012)
[599]	Rosenstein, B.; Lewkowicz, M., Dynamics of electric transport in interacting weyl semimetals, Phys. Rev. B88, 045108 (2013)
[600]	Ashby, P. E.C.; Carbotte, J. P., Magneto-optical conductivity of Weyl semimetals, Phys. Rev. B87, 245131 (2013)
[601]	Gorbar, E.; Miransky, V.; Shovkovy, I., Chiral anomaly, dimensional reduction, and magnetoresistivity of Weyl and Dirac semimetals, Phys. Rev., B89, 085126 (2014)
[602]	Hikami, S.; Larkin, A. I.; Nagaoka, Y., Spin-orbit interaction and magnetoresistance in the two dimensional random system, Progr. Theoret. Phys., 63, 707-710 (1980)
[603]	Altshuler, B. L.; Khmel’nitzkii, D.; Larkin, A. I.; Lee, P. A., Magnetoresistance and Hall effect in a disordered two-dimensional electron gas, Phys. Rev., B22, 5142-5153 (1980)
[604]	Garate, I.; Glazman, L., Weak localization and antilocalization in topological insulator thin films with coherent bulk-surface coupling, Phys. Rev., B86, 035422 (2012)
[606]	Grushin, A. G., Consequences of a condensed matter realization of lorentz violating qed in weyl semi-metals, Phys. Rev. D86, 045001 (2012)
[607]	Vazifeh, M. M.; Franz, M., Electromagnetic response of Weyl semimetals, Phys. Rev. Lett., 111, 027201 (2013)
[608]	Goswami, P.; Tewari, S., Axionic field theory of (3+1)-dimensional weyl semi-metals, Phys. Rev. B88, 245107 (2013)
[609]	Wan, X.; Turner, A. M.; Vishwanath, A.; Savrasov, S. Y., Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates, Phys. Rev., B83, 205101 (2011)
[611]	Okugawa, R.; Murakami, S., Dispersion of Fermi arcs in Weyl semimetals and their evolutions to Dirac cones, Phys. Rev. B89, 235315 (2014)
[612]	Potter, A. C.; Kimchi, I.; Vishwanath, A., Quantum oscillations from surface Fermi-arcs in Weyl and Dirac semi-metals, Nat. Comm., 5, 5161 (2014)
[613]	Gorbar, E.; Miransky, V.; Shovkovy, I.; Sukhachov, P., Quantum oscillations as a probe of interaction effects in Weyl semimetals in a magnetic field, Phys. Rev., B90, 115131 (2014)
[614]	Douglas, M. R.; Nekrasov, N. A., Noncommutative field theory, Rev. Modern Phys., 73, 977-1029 (2001) · Zbl 1205.81126
[615]	Szabo, R. J., Quantum field theory on noncommutative spaces, Phys. Rept., 378, 207-299 (2003) · Zbl 1042.81581
[616]	Gorbar, E.; Miransky, V., Relativistic field theories in a magnetic background as noncommutative field theories, Phys. Rev., D70, 105007 (2004)
[617]	Gorbar, E.; Homayouni, S.; Miransky, V., Chiral dynamics in QED and QCD in a magnetic background and nonlocal noncommutative field theories, Phys. Rev., D72, 065014 (2005)
[618]	Dunne, G. V.; Jackiw, R.; Trugenberger, C., Topological (Chern-Simons) quantum mechanics, Phys. Rev., D41, 661 (1990)
[619]	Bigatti, D.; Susskind, L., Magnetic fields, branes and noncommutative geometry, Phys. Rev., D62, 066004 (2000)
[620]	Iso, S.; Karabali, D.; Sakita, B., One-dimensional fermions as two-dimensional droplets via Chern-Simons theory, Nuclear Phys., B388, 700-714 (1992)
[621]	Cappelli, A.; Trugenberger, C. A.; Zemba, G. R., Infinite symmetry in the quantum Hall effect, Nuclear Phys., B396, 465-490 (1993)
[622]	Guralnik, Z.; Jackiw, R.; Pi, S.; Polychronakos, A., Testing noncommutative QED, constructing noncommutative MHD, Phys. Lett., B517, 450-456 (2001) · Zbl 0971.81188
[623]	Connes, A.; Douglas, M. R.; Schwarz, A. S., Noncommutative geometry and matrix theory: Compactification on tori, J. High Energy Phys., 9802, 003 (1998) · Zbl 1018.81052
[624]	Seiberg, N.; Witten, E., String theory and noncommutative geometry, J. High Energy Phys., 9909, 032 (1999) · Zbl 0957.81085
[625]	Sheikh-Jabbari, M., Open strings in a B field background as electric dipoles, Phys. Lett., B455, 129-134 (1999) · Zbl 1058.81728
[626]	Minwalla, S.; Van Raamsdonk, M.; Seiberg, N., Noncommutative perturbative dynamics, J. High Energy Phys., 0002, 020 (2000) · Zbl 0959.81108
[627]	Gavrilov, S.; Gitman, D., Vacuum instability in external fields, Phys. Rev., D53, 7162-7175 (1996)
[628]	Slavnov, A.; Faddeev, L., Massless and massive Yang-Mills field. (In Russian), Theoret. Math. Phys., 3, 312-316 (1970)
[629]	van Dam, H.; Veltman, M., Massive and massless Yang-Mills and gravitational fields, Nuclear Phys., B22, 397-411 (1970)
[630]	Vainshtein, A.; Khriplovich, I., On the zero-mass limit and renormalizability in the theory of massive Yang-Mills field, Yad. Fiz., 13, 198-211 (1971)
[631]	Girvin, S. M.; Jach, T., Formalism for the quantum Hall effect: Hilbert space of analytic functions, Phys. Rev., B29, 5617-5625 (1984)
[632]	Kivelson, S.; Kallin, C.; Arovas, D. P.; Schrieffer, J. R., Cooperative ring exchange and the fractional quantum Hall effect, Phys. Rev., B36, 1620-1646 (1987)
[633]	Dunne, G. V.; Jackiw, R., ‘Peierls substitution’ and Chern-Simons quantum mechanics, Nuclear Phys. Proc. Suppl., 33C, 114-118 (1993) · Zbl 0991.81607
[634]	Basu, P.; Chakraborty, B.; Scholtz, F. G., A Unifying perspective on the Moyal and Voros products and their physical meanings, J. Phys., A44, 285204 (2011) · Zbl 1222.81272
[635]	Gouba, L.; Kovacevic, D.; Meljanac, S., A General formulation of the Moyal and Voros products and its physical interpretation, Modern Phys. Lett., A27, 1250005 (2012) · Zbl 1274.81143
[636]	Sinova, J.; Meden, V.; Girvin, S. M., Liouvillian approach to the integer quantum Hall effect transition, Phys. Rev., B62, 2008-2015 (2000)
[637]	Bellissard, J.; van Elst, A.; Schulz-Baldes, H., The noncommutative geometry of the quantum Hall effect, J. Math. Phys., 35, 5373-5451 (1994) · Zbl 0824.46086
[638]	Faddeev, L.; Slavnov, A., Gauge Fields: Introduction to Quantum Theory (1991), Addison-Wisley, Redwood City: Addison-Wisley, Redwood City CA · Zbl 0984.81502
[639]	Kleinert, H., Hadronization of quark theories and a bilocal form of QED, Phys. Lett., B62, 429 (1976)
[640]	Kugo, T., Dynamical instability of the vacuum in the Lagrangian formalism of the Bethe-Salpeter bound states, Phys. Lett., B76, 625 (1978)
[641]	Salim, A. J.; Sadooghi, N., Dynamics of O(N) model in a strong magnetic background field as a modified noncommutative field theory, Phys. Rev., D73, 065023 (2006)
[642]	Girotti, H.; Gomes, M.; Rivelles, V. O.; da Silva, A., A Consistent noncommutative field theory: The Wess-Zumino model, Nuclear Phys., B587, 299-310 (2000) · Zbl 1043.81725
[643]	Gorbar, E.; Hashimoto, M.; Miransky, V., Nondecoupling phenomena in QED in a magnetic field and noncommutative QED, Phys. Lett., B611, 207-214 (2005)
[644]	Cappelli, A.; Dunne, G. V.; Trugenberger, C. A.; Zemba, G. R., Conformal symmetry and universal properties of quantum Hall states, Nuclear Phys., B398, 531-567 (1993)
[645]	Polychronakos, A. P., Quantum Hall states as matrix Chern-Simons theory, J. High Energy Phys., 0104, 011 (2001)
[646]	Barrois, B. C., Superconducting quark matter, Nuclear Phys., B129, 390 (1977)
[647]	Bailin, D.; Love, A., Superfluidity in ultrarelativistic quark matter, Nuclear Phys., B190, 175 (1981)
[648]	Bailin, D.; Love, A., Superconductivity in quark matter, Nuclear Phys., B205, 119 (1982)
[649]	Iwasaki, M.; Iwado, T., Superconductivity in the quark matter, Phys. Lett., B350, 163-168 (1995)
[650]	Alford, M. G.; Rajagopal, K.; Wilczek, F., QCD at finite baryon density: Nucleon droplets and color superconductivity, Phys. Lett., B422, 247-256 (1998)
[651]	Rapp, R.; Schäfer, T.; Shuryak, E. V.; Velkovsky, M., Diquark Bose condensates in high density matter and instantons, Phys. Rev. Lett., 81, 53-56 (1998)
[652]	Shovkovy, I.; Huang, M., Gapless two flavor color superconductor, Phys. Lett., B564, 205 (2003) · Zbl 1059.81621
[653]	Rajagopal, K.; Schmitt, A., Stressed pairing in conventional color superconductors is unavoidable, Phys. Rev., D73, 045003 (2006)
[654]	Alford, M. G.; Berges, J.; Rajagopal, K., Magnetic fields within color superconducting neutron star cores, Nuclear Phys., B571, 269-284 (2000)
[655]	Gorbar, E. V., On color superconductivity in external magnetic field, Phys. Rev., D62, 014007 (2000)
[656]	Sedrakian, D.; Blaschke, D., Magnetic field of a neutron star with color superconducting quark matter core, Astrophys., 45, 166-175 (2002)
[657]	Schäfer, T., Quark hadron continuity in QCD with one flavor, Phys. Rev., D62, 094007 (2000)
[658]	Alford, M. G.; Bowers, J. A.; Cheyne, J. M.; Cowan, G. A., Single color and single flavor color superconductivity, Phys. Rev., D67, 054018 (2003)
[659]	Schmitt, A.; Wang, Q.; Rischke, D. H., Electromagnetic Meissner effect in spin one color superconductors, Phys. Rev. Lett., 91, 242301 (2003)
[660]	Schmitt, A.; Wang, Q.; Rischke, D. H., Mixing and screening of photons and gluons in a color superconductor, Phys. Rev., D69, 094017 (2004)
[661]	Feng, B.; Hou, D.; Ren, H.-c.; Wu, P.-P., The single flavor color superconductivity in a magnetic field, Phys. Rev. Lett., 105, 042001 (2010)
[662]	Wu, P.-P.; He, H.; Hou, D.; Ren, H.-c., The latent heat of single flavor color superconductivity in a magnetic field, Phys. Rev., D84, 027701 (2011)
[663]	Ferrer, E. J.; de la Incera, V.; Manuel, C., Magnetic color flavor locking phase in high density QCD, Phys. Rev. Lett., 95, 152002 (2005)
[664]	Ferrer, E. J.; de la Incera, V.; Manuel, C., Color-superconducting gap in the presence of a magnetic field, Nuclear Phys., B747, 88-112 (2006)
[665]	Manuel, C., Color superconductivity in a strong external magnetic field, Nuclear Phys., A785, 114-117 (2007)
[666]	Ferrer, E. J.; de la Incera, V., Magnetic phases in three-flavor color superconductivity, Phys. Rev. D, 76, 045011 (2007)
[667]	Noronha, J. L.; Shovkovy, I. A., Phys. Rev. D, 86, 049901 (2012), (erratum) arXiv:0708.0307
[668]	Fukushima, K.; Warringa, H. J., Color superconducting matter in a magnetic field, Phys. Rev. Lett., 100, 032007 (2008)
[669]	Feng, B.; Ferrer, E. J.; de la Incera, V., Cooper pair’s magnetic moment in mCFL color superconductivity, Nuclear Phys., B853, 213-239 (2011) · Zbl 1229.81303
[670]	Feng, B.; Ferrer, E. J.; de la Incera, V., Magnetoelectric effect in strongly magnetized color superconductivity, Phys. Lett., B706, 232-238 (2011)
[671]	Feng, B.; Ferrer, E. J.; de la Incera, V., Photon self-energy and electric susceptibility in a magnetized three-flavor color superconductor, Phys. Rev., D85, 103529 (2012)
[672]	Feng, B.; Ferrer, E. J.; de la Incera, V., Magnetic moment of cooper pairs in magnetized color superconductivity, Acta Phys. Polon. Supp., 5, 955-961 (2012)
[673]	Wen, X.-J., Color-flavor locked strange quark matter in a strong magnetic field, Phys. Rev., D88, 034031 (2013)
[674]	Ren, C.-F.; Zhang, X.-B.; Zhang, Y., Magnetic effects in color-flavor locked superconducting phase with the additional chiral condensates, Chin. Phys. Lett., 31, 062501 (2014)
[675]	Rajagopal, K.; Wilczek, F., Enforced electrical neutrality of the color flavor locked phase, Phys. Rev. Lett., 86, 3492-3495 (2001)
[676]	Ferrer, E. J.; de la Incera, V., Magnetism in dense quark matter, Lect. Notes Phys., 871, 399-432 (2013)
[677]	Fayazbakhsh, S.; Sadooghi, N., Color neutral 2SC phase of cold and dense quark matter in the presence of constant magnetic fields, Phys. Rev., D82, 045010 (2010)
[678]	Yu, L.; Shovkovy, I. A., Directional dependence of color superconducting gap in two-flavor QCD in a magnetic field, Phys. Rev., D85, 085022 (2012)
[679]	Fayazbakhsh, S.; Sadooghi, N., Two-flavor color superconductivity at finite temperature, chemical potential and in the presence of strong magnetic fields, PoS ConfinementX, 294 (2012)
[680]	Ferrer, E. J.; de la Incera, V., Magnetic fields boosted by gluon vortices in color superconductivity, Phys. Rev. Lett., 97, 122301 (2006)
[681]	Ferrer, E. J.; de la Incera, V., Chromomagnetic instability and induced magnetic field in neutral two-flavor color superconductivity, Phys. Rev., D76, 114012 (2007)
[682]	Tatsumi, T.; Maruyama, T.; Nakano, E., Ferromagnetism and superconductivity in quark matter: Color magnetic superconductivity, Progr. Theoret. Phys. Suppl., 153, 190-197 (2004)
[683]	Tatsumi, T.; Maruyama, T.; Nakano, E.; Nawa, K., Ferromagnetism in quark matter and origin of the magnetic field in compact stars, Nuclear Phys., A774, 827-830 (2006)
[684]	Iwazaki, A., Color ferromagnetism of quark matter: A Possible origin of strong magnetic field in magnetars, Phys. Rev., D72, 114003 (2005)
[685]	Chernodub, M. N., Superconductivity of QCD vacuum in strong magnetic field, Phys. Rev., D82, 085011 (2010)
[686]	Chernodub, M. N., Spontaneous electromagnetic superconductivity of vacuum in strong magnetic field: evidence from the Nambu-Jona-Lasinio model, Phys. Rev. Lett., 106, 142003 (2011)
[687]	Nielsen, N.; Olesen, P., An unstable Yang-Mills field mode, Nuclear Phys., B144, 376-396 (1978)
[688]	Ambjorn, J.; Olesen, P., Phys. Lett. B, B220, 659 (1989), (erratum)
[689]	Ambjorn, J.; Olesen, P., On electroweak magnetism, Nuclear Phys., B315, 606-614 (1989)
[690]	Braguta, V. V.; Buividovich, P. V.; Chernodub, M. N.; Polikarpov, M. I., Electromagnetic superconductivity of vacuum induced by strong magnetic field: numerical evidence in lattice gauge theory, Phys. Lett., B718, 667-671 (2012)
[691]	Braguta, V.; Buividovich, P.; Chernodub, M.; Polikarpov, M.; Kotov, A. Y., Vortex liquid in magnetic-field-induced superconducting vacuum of quenched lattice QCD, PoS ConfinementX, 083 (2012)
[692]	Braguta, V.; Buividovich, P.; Chernodub, M.; Kotov, A.; Polikarpov, M., Vortex liquid in the superconducting vacuum of the quenched QCD induced by strong magnetic field, PoS LATTICE2013, 362 (2014)
[693]	Chernodub, M. N.; van Doorsselaere, J.; Verschelde, H., Electromagnetically superconducting phase of vacuum in strong magnetic field: structure of superconductor and superfluid vortex lattices in the ground state, Phys. Rev., D85, 045002 (2012)
[694]	Chernodub, M. N.; van Doorsselaere, J.; Verschelde, H., Magnetic-field-induced superconductivity and superfluidity of W and Z bosons: in tandem transport and kaleidoscopic vortex states, Phys. Rev. D88, 065006 (2013)
[695]	Chernodub, M., Superconducting properties of vacuum in strong magnetic field, Internat. J. Modern Phys., D23, 1430009 (2014) · Zbl 1293.81002
[696]	Hidaka, Y.; Yamamoto, A., Charged vector mesons in a strong magnetic field, Phys. Rev., D87, 094502 (2013)
[697]	Chernodub, M., Vafa-Witten theorem, vector meson condensates and magnetic-field-induced electromagnetic superconductivity of vacuum, Phys. Rev., D86, 107703 (2012)
[698]	Li, C.; Wang, Q., Amending the Vafa-Witten theorem, Phys. Lett., B721, 141-145 (2013) · Zbl 1307.81066
[699]	Frasca, M., \( \rho\) condensation and physical parameters, J. High Energy Phys., 1311, 099 (2013)
[700]	Liu, H.; Yu, L.; Huang, M., Charged and neutral vector meson under magnetic field, Phys. Rev. D, 91, 014017 (2015)
[701]	Andreichikov, M. A.; Kerbikov, B. O.; Orlovsky, V. D.; Simonov, Y. A., Meson spectrum in strong magnetic fields, Phys. Rev., D87, 094029 (2013)
[702]	Erdmenger, J.; Kerner, P.; Strydom, M., Holographic superconductors at finite isospin density or in an external magnetic field, PoS FACESQCD, 004 (2010)
[703]	Callebaut, N.; Dudal, D.; Verschelde, H., Holographic rho mesons in an external magnetic field, J. High Energy Phys., 1303, 033 (2013)
[704]	Bu, Y.-Y.; Erdmenger, J.; Strydom, M.; Shock, J., Holographic superfluidity from a magnetic field, PoS ConfinementX, 268 (2012)
[705]	Bergman, O.; Erdmenger, J.; Lifschytz, G., A review of magnetic phenomena in probe-brane holographic matter, Lect. Notes Phys., 871, 591-624 (2013)
[706]	Bu, Y.-Y.; Erdmenger, J.; Shock, J. P.; Strydom, M., Magnetic field induced lattice ground states from holography, J. High Energy Phys., 1303, 165 (2013)
[707]	Callebaut, N.; Dudal, D., A magnetic instability of the non-Abelian Sakai-Sugimoto model, J. High Energy Phys., 1401, 055 (2014)
[708]	Gurarie, V.; Zee, A., Quantum Hall transition in the classical limit, Internat. J. Modern Phys., B15, 1225-1238 (2001)

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