Thermodynamic and electromagnetic properties of the eta-pairing superconductivity in the Penson-Kolb model. (English) Zbl 07482548
Summary: In the paper, we study the thermodynamic and electromagnetic properties of the Penson-Kolb (PK) model, i.e., the tight-binding model for fermionic particles with the pair-hopping interaction \(J\). We focus on the case of repulsive \(J\) (i.e., \(J<0\)), which can stabilize the eta-pairing superconductivity with Cooper-pair center-of-mass momentum \(\vec{q} = \vec{Q}\), \(\vec{Q} = (\pi/a, \pi/a, \dots)\). Numerical calculations are performed for several \(d\)-dimensional hypercubic lattices: \(d = 2\) (the square lattice, SQ), \(d = 3\) (the simple cubic lattice) and \(d = \infty\) hypercubic lattice (for arbitrary particle concentration \(0 < n < 2\) and temperature \(T\)). The ground state \(J\) versus \(n\) phase diagrams and the crossover to the Bose-Einstein condensation regime are analyzed and the evolution of the superfluid characteristics are examined within the (broken symmetry) Hartree-Fock approximation (HFA). The critical fields, the coherence length, the London penetration depth, and the Ginzburg ratio are determined at \(T = 0\) and \(T > 0\) as a function of \(n\) and pairing strength. The analysis of the effects of the Fock term on the ground state phase boundaries and on selected PK model characteristics is performed as well as the influence of the phase fluctuations on the eta-pairing superconductivity is investigated. Within the Kosterlitz-Thouless scenario, the critical temperatures \(T_{KT}\) are estimated for \(d = 2\) SQ lattice and compared with the critical temperature \(T_c\) obtained from HFA. We also determine the temperature \(T_m\) at which minimal gap between two quasiparticle bands vanishes in the eta-phase. Our results for repulsive \(J\) are contrasted with those found earlier for the PK model with attractive \(J\) (i.e., with \(J > 0\)).
MSC:
| 82-XX | Statistical mechanics, structure of matter |
Keywords:
Penson-Kolb model; unconventional superconductivity; eta-pairing; phase diagrams; Kosterlitz-Thouless scenario; nonlocal pairing mechanismReferences:
| [1] | Penson, K. A.; Kolb, M., Real-space pairing in Fermion systems, Phys. Rev. B, 33, 1663-1666 (1986) |
| [2] | Robaszkiewicz, S.; Bułka, B. R., Superconductivity in the Hubbard model with pair hopping, Phys. Rev. B, 59, 6430-6437 (1999) |
| [3] | Affleck, I.; Marston, J. B., Field-theory analysis of a short-range pairing model, J. Phys. C: Solid State Phys., 21, 2511-2526 (1988) |
| [4] | Sikkema, A. E.; Affleck, I., Phase transitions in the one-dimensional pair-hopping model: A renormalization-group study, Phys. Rev. B, 52, 10207-10213 (1995) |
| [5] | van den Bossche, M.; Caffarel, M., One-dimensional pair hopping and attractive Hubbard models: A comparative study, Phys. Rev. B, 54, 17414-17421 (1996) |
| [6] | Bouzerar, G.; Japaridze, G. I., \( \eta \)-Superconductivity in the one-dimensional Penson-Kolb model, Z. Phys. B, 104, 215-219 (1997) |
| [7] | Japaridze, G. I.; Müller-Hartmann, E., Bond-located ordering in the one-dimensional Penson-Kolb-Hubbard model, J. Phys.: Condens. Matter, 9, 10509-10519 (1997) |
| [8] | Japaridze, G. I.; Kampf, A. P.; Sekania, M.; Kakashvili, P.; Brune, P., \( \eta \)-Pairing superconductivity in the Hubbard chain with pair hopping, Phys. Rev. B, 65, Article 014518 pp. (2001) |
| [9] | Roy, G. K.; Bhattacharyya, B., Collective excitations in the Penson-Kolb model: A generalized random-phase-approximation study, Phys. Rev. B, 55, 15506-15514 (1997) |
| [10] | Czart, W. R.; Robaszkiewicz, S., Thermodynamic and electromagnetic properties of the Penson-Kolb model, Phys. Rev. B, 64, Article 104511 pp. (2001) |
| [11] | Robaszkiewicz, S.; Czart, W. R., Properties of the \(\eta \)-pairing phase of the Penson-Kolb model, Phys. Status Solidi (B), 236, 416-419 (2003) |
| [12] | Czart, W. R.; Robaszkiewicz, S.; Tobijaszewska, B., Eta-pairing and s-wave pairing in the Penson-Kolb model with next-nearest neighbour hopping, Phys. Status Solidi (B), 244, 2327-2330 (2007) |
| [13] | Dolcini, F.; Montorsi, A., Temperature and filling dependence of the superconducting \(\pi\) phase in the Penson-Kolb-Hubbard model, Phys. Rev. B, 62, 2315-2320 (2000) |
| [14] | Hubbard, J., Electron correlations in narrow energy bands, Proc. R. Soc. A, 276, 238-257 (1963) |
| [15] | Kivelson, S.; Su, W.-P.; Schrieffer, J. R.; Heeger, A. J., Missing bond-charge repulsion in the extended Hubbard model: Effects in polyacetylene, Phys. Rev. Lett., 58, 1899-1902 (1987) |
| [16] | Ptok, A.; Kapcia, K. J., Probe-type of superconductivity by impurity in materials with short coherence length: the \(s\)-wave and \(\eta \)-wave phases study, Supercond. Sci. Technol., 28, Article 045022 pp. (2015) |
| [17] | Ptok, A.; Crivelli, D.; Kapcia, K. J., Change of the sign of superconducting intraband order parameters induced by interband pair hopping interaction in iron-based high-temperature superconductors, Supercond. Sci. Technol., 28, Article 045010 pp. (2015) |
| [18] | Kapcia, K. J.; Czart, W. R.; Ptok, A., Phase separation of superconducting phases in the Penson-Kolb-Hubbard model, J. Phys. Soc. Japan, 85, Article 044708 pp. (2016) |
| [19] | Czart, W.; Robaszkiewicz, S., Superconductivity of the two-dimensional Penson-Kolb model, Acta Phys. Pol. A, 100, 885-895 (2001) |
| [20] | Czart, W.; Robaszkiewicz, S., Superconducting properties of the eta-pairing state in the Penson-Kolb-Hubbard model, Acta Phys. Pol. A, 106, 709-714 (2004) |
| [21] | Micnas, R.; Ranninger, J.; Robaszkiewicz, S., Superconductivity in narrow-band systems with local nonretarded attractive interactions, Rev. Modern Phys., 62, 113-171 (1990) |
| [22] | Fradkin, E.; Hirsch, J. E., Phase diagram of one-dimensional electron-phonon systems. I. The Su-Schrieffer-Heeger model, Phys. Rev. B, 27, 1680-1697 (1983) |
| [23] | Miyake, K.; Matsuura, T.; Jichu, H.; Nagaoka, Y., A model for cooper pairing in heavy Fermion superconductor, Progr. Theoret. Phys., 72, 1063-1080 (1984) |
| [24] | Robaszkiewicz, S.; Micnas, R.; Ranninger, J., Superconductivity in the generalized periodic Anderson model with strong local attraction, Phys. Rev. B, 36, 180-201 (1987) |
| [25] | Bastide, C.; Lacroix, C., The Anderson lattice in the weak-hopping limit: superconductivity induced by dynamic interactions, J. Phys. C: Solid State Phys., 21, 3557-3576 (1988) |
| [26] | Robaszkiewicz, S.; Czart, W. R., Superconductivity in the two-dimensional extended Hubbard model with pair-hopping interaction, Acta Phys. Polon. B, 32, 3267-3272 (2001), https://www.actaphys.uj.edu.pl/R/32/13/3267/pdf |
| [27] | Leggett, A. J., Diatomic molecules and cooper pairs, (Pekalski, A.; Przystawa, J., Modern Trends in the Theory of Condensed Matter. Modern Trends in the Theory of Condensed Matter, Lecture Notes in Physics, vol. 115 (1980), Springer), 13-27 |
| [28] | Mierzejewski, M.; Maśśka, M. M., Critical field in a superconductivity model with local pairs, Phys. Rev. B, 69, Article 054502 pp. (2004) |
| [29] | Williams, G. V.M.; Tallon, J. L.; Haines, E. M.; Michalak, R.; Dupree, R., NMR evidence for a \(d\)-wave normal-state pseudogap, Phys. Rev. Lett., 78, 721-724 (1997) |
| [30] | Williams, G. V.M.; Tallon, J. L.; Quilty, J. W.; Trodahl, H. J.; Flower, N. E., Absence of an isotope effect in the pseudogap in \(\operatorname{Y Ba}_2 \operatorname{Cu}_4 O_8\) as determined by high-resolution \({}^{89} Y\) NMR, Phys. Rev. Lett., 80, 377-380 (1998) |
| [31] | Krasnov, V. M.; Yurgens, A.; Winkler, D.; Delsing, P.; Claeson, T., Evidence for coexistence of the superconducting gap and the pseudogap in Bi-2212 from intrinsic tunneling spectroscopy, Phys. Rev. Lett., 84, 5860-5863 (2000) |
| [32] | Krasnov, V. M.; Kovalev, A. E.; Yurgens, A.; Winkler, D., Magnetic field dependence of the superconducting gap and the pseudogap in Bi2212 and HgBr \({}_2\)-Bi2212, studied by intrinsic tunneling spectroscopy, Phys. Rev. Lett., 86, 2657-2660 (2001) |
| [33] | Marshall, D. S.; Dessau, D. S.; Loeser, A. G.; Park, C. H.; Matsuura, A. Y.; Eckstein, J. N.; Bozovic, I.; Fournier, P.; Kapitulnik, A.; Spicer, W. E.; Shen, Z.-X., Unconventional electronic structure evolution with hole doping in \(\operatorname{Bi}_2 \operatorname{Sr}_2 \operatorname{CaCu}_2 O_{8 + \delta} \): Angle-resolved photoemission results, Phys. Rev. Lett., 76, 4841-4844 (1996) |
| [34] | Ding, H.; Yokoya, T.; Campuzano, J.; Takahashi, T.; Randeria, M.; Norman, M. R.; Mochiku, T.; Kadowaki, K.; Giapintzakis, J., Spectroscopic evidence for a pseudogap in the normal state of underdoped high-\( T_c\) superconductors, Nature, 382, 51-54 (1996) |
| [35] | Norman, M. R.; Ding, H.; Randeria, M.; Campuzano, J.; Yokoya, T.; Takeuchi, T.; Takahashi, T.; Mochiku, T.; Kadowaki, K.; Guptasarma, P.; Hinks, D. G., Destruction of the Fermi surface in underdoped high-\( T_c\) superconductors, Nature, 392, 157-160 (1998) |
| [36] | Basov, D. N.; Timusk, T.; Dabrowski, B.; Jorgensen, J. D., c-axis response of \(\operatorname{Y Ba}_2 \operatorname{Cu}_4 \operatorname{O}_8\): A pseudogap and possibility of josephson coupling of \(\operatorname{CuO}_2\) planes, Phys. Rev. B, 50, 3511-3514 (1994) |
| [37] | Tallon, J. L.; Cooper, J. R.; de Silva, P. S.I. P.N.; Williams, G. V.M.; Loram, J. W., Thermoelectric power: A simple, instructive probe of high-\( T_c\) superconductors, Phys. Rev. Lett., 75, 4114-4117 (1995) |
| [38] | Balatsky, A. V.; Vekhter, I.; Zhu, J.-X., Impurity-induced states in conventional and unconventional superconductors, Rev. Modern Phys., 78, 373-433 (2006) |
| [39] | Krzyszczak, J.; Domański, T.; Wysokiński, K.; Micnas, R.; Robaszkiewicz, S., Real space inhomogeneities in high temperature superconductors: the perspective of the two-component model, J. Phys.: Condens. Matter, 22, Article 255702 pp. (2010) |
| [40] | Li, K., \( \eta \)-Pairing in correlated Fermion models with spin-orbit coupling, Phys. Rev. B, 102, Article 165150 pp. (2020) |
| [41] | Tindall, J.; Bučca, B.; Coulthard, J. R.; Jaksch, D., Heating-induced long-range \(\eta\) pairing in the Hubbard model, Phys. Rev. Lett., 123, Article 030603 pp. (2019) |
| [42] | Kaneko, T.; Shirakawa, T.; Sorella, S.; Yunoki, S., Photoinduced \(\eta\) pairing in the Hubbard model, Phys. Rev. Lett., 122, Article 077002 pp. (2019) |
| [43] | Ejima, S.; Kaneko, T.; Lange, F.; Yunoki, S.; Fehske, H., Photoinduced \(\eta \)-pairing at finite temperatures, Phys. Rev. Res., 2, Article 032008 pp. (2020) |
| [44] | Mark, D. K.; Motrunich, O. I., \( \eta \)-Pairing states as true scars in an extended Hubbard model, Phys. Rev. B, 102, Article 075132 pp. (2020) |
| [45] | Montorsi, A.; Campbell, D. K., Rigorous results on superconducting ground states for attractive extended Hubbard models, Phys. Rev. B, 53, 5153-5156 (1996) |
| [46] | Scalapino, D. J.; White, S. R.; Zhang, S., Insulator, metal, or superconductor: The criteria, Phys. Rev. B, 47, 7995-8007 (1993) |
| [47] | Czart, W. R.; Kostyrko, T.; Robaszkiewicz, S., Superfluid characteristics of the attractive Hubbard model for various lattice structures, Physica C, 272, 51-61 (1996) |
| [48] | Bułka, B. R.; Robaszkiewicz, S., Superconducting properties of the attractive Hubbard model: A slave-boson study, Phys. Rev. B, 54, 13138-13151 (1996) |
| [49] | Müller-Hartmann, E., Correlated Fermions on a lattice in high dimensions, Z. Phys. B: Condens. Matter, 74, 507-512 (1989) |
| [50] | Xu, Z. A.; Ong, N. P.; Wang, Y.; Kakeshita, T.; Uchida, S.-i., Vortex-like excitations and the onset of superconducting phase fluctuation in underdoped \(La{}_{2 - x}Sr{}_x\) CuO \({}_4\), Nature, 406, 486-488 (2000) |
| [51] | Wang, Y.; Xu, Z. A.; Kakeshita, T.; Uchida, S.; Ono, S.; Ando, Y.; Ong, N. P., Onset of the vortexlike nernst signal above \(T_c\) in \(\operatorname{La}_{2 - x} \operatorname{Sr}_x \operatorname{CuO}_4\) and \(\operatorname{Bi}_2 \operatorname{Sr}_{2 - y} \operatorname{La}_y \operatorname{CuO}_6\), Phys. Rev. B, 64, Article 224519 pp. (2001) |
| [52] | Shibauchi, T.; Krusin-Elbaum, L.; Li, M.; Maley, M. P.; Kes, P., Closing the pseudogap by Zeeman splitting in \(\operatorname{Bi}_2 \operatorname{Sr}_2 \operatorname{CaCu}_2 O_{8 + \mathit{y}}\) at high magnetic fields, Phys. Rev. Lett., 86, 5763-5766 (2001) |
| [53] | Kosterlitz, J. M.; Thouless, D. J., Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C: Solid State Phys., 6, 1181-1203 (1973) |
| [54] | Micnas, R.; Tobijaszewska, B., Superfluid properties of the extended Hubbard model with intersite electron pairing, J. Phys.: Condens. Matter, 14, 9631-9649 (2002) |
| [55] | Denteneer, P. J.H.; An, G.; van Leeuwen, J. M.J., Helicity modulus in the two-dimensional Hubbard model, Phys. Rev. B, 47, 6256-6272 (1993) |
| [56] | van Leeuwen, J. M.J.; du Croo de Jongh, M. S.L.; Denteneer, P. J.H., Spin stiffness in the Hubbard model, J. Phys. A: Math. Gen., 29, 41-57 (1996) · Zbl 0943.82512 |
| [57] | Singer, J. M.; Schneider, T.; Pedersen, M. H., On the phase diagram of the attractive Hubbard model: Crossover and quantum critical phenomena, Eur. Phys. J. B, 2, 17-30 (1998) |
| [58] | Bak, M.; Micnas, R., Superconducting properties of the attractive Hubbard model in the slave-boson approach, J. Phys.: Condens. Matter, 10, 9029-9054 (1998) |
| [59] | Chattopadhyay, B., D-wave order parameter in Bi2212 from a phenomenological model of high \(T_c\) cuprates, Phys. Lett. A, 226, 231-236 (1997) |
| [60] | Chattopadhyay, B.; Gaitonde, D. M.; Taraphder, A., Fluctuation effects and order parameter symmetry in the cuprate superconductors, Europhys. Lett., 34, 705-710 (1996) |
| [61] | Micnas, R.; Robaszkiewicz, S.; Tobijaszewska, B., Superconductivity with local, short-range attraction, J. Supercond., 12, 79-84 (1999) |
| [62] | Tobijaszewska, B.; Micnas, R., Phase fluctuations and BCS-LP crossover in 2D short coherence length superconductors, Acta Phys. Pol. A, 97, 393-398 (2000) |
| [63] | Gupta, R.; DeLapp, J.; Batrouni, G. G.; Fox, G. C.; Baillie, C. F.; Apostolakis, J., Phase transition in the \(2 \operatorname{D} \operatorname{XY}\) model, Phys. Rev. Lett., 61, 1996-1999 (1988) |
| [64] | Nozieres, P.; Schmitt-Rink, S., Bose condensation in an attractive Fermion gas: From weak to strong coupling superconductivity, J. Low Temp. Phys., 59, 195-211 (1985) |
| [65] | Kapcia, K.; Robaszkiewicz, S.; Micnas, R., Phase separation in a lattice model of a superconductor with pair hopping, J. Phys.: Condens. Matter, 24, Article 215601 pp. (2012) |
| [66] | Kapcia, K.; Robaszkiewicz, S., The magnetic field induced phase separation in a model of a superconductor with local electron pairing, J. Phys.: Condens. Matter, 25, Article 065603 pp. (2013) |
| [67] | Kapcia, K. J., Superconductivity, metastability and magnetic field induced phase separation in the atomic limit of the Penson-Kolb-Hubbard model, Acta Phys. Pol. A, 126, A53-A57 (2014) |
| [68] | Ptok, A.; Crivelli, D., The Fulde-Ferrell-Larkin-Ovchinnikov state in pnictides, J. Low. Temp. Phys., 172, 226-233 (2013) |
| [69] | Ptok, A.; Cichy, A.; Rodríguez, K.; Kapcia, K. J., Critical behavior in one dimension: Unconventional pairing, phase separation, BEC-bcs crossover, and magnetic Lifshitz transition, Phys. Rev. A, 95, Article 033613 pp. (2017) |
| [70] | Yang, C. N., \( \eta\) Pairing and off-diagonal long-range order in a Hubbard model, Phys. Rev. Lett., 63, 2144-2147 (1989) |
| [71] | Czart, W. R., Phase diagrams and electromagnetic propertiesof s-wave superconductivity of the extended Hubbard model with the attractive pair-hopping interaction, J. Supercond. Nov. Magn., 32, 1951-1966 (2019) |
| [72] | Kapcia, K. J.; Czart, W. R., Phase separations in the narrow-bandwidth limit of the Penson-Kolb-Hubbard model at zero temperature, Acta Phys. Pol. A, 133, 401-404 (2018) |
| [73] | Micnas, R.; Robaszkiewicz, S.; Kostyrko, T., Thermodynamic and electromagnetic properties of hard-core charged bosons on a lattice, Phys. Rev. B, 52, 6863-6879 (1995) |
| [74] | Jelitto, R. J., The density of states of some simple excitations in solids, J. Phys. Chem. Solids, 30, 609-626 (1969) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
