×
Wang, Guo-Dong; Wang, An-Min

RKKY interaction in three-dimensional tilted Dirac and Weyl semimetals. (English) Zbl 1479.82081

Phys. Lett., A 384, No. 16, Article ID 126327, 9 p. (2020).
Summary: We theoretically investigate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities of the tilted Dirac and Weyl semimetals in three dimensions. In accordance with the untilted scenario, the RKKY interaction contains three terms, namely the Heisenberg term, the Ising term, and the Dzyaloshinsky-Moriya term. The main influence of tilt on the RKKY Hamiltonian is a modulation to the oscillation frequencies of range functions. Our results enrich the knowledge of the magnetic properties of materials with tilted Dirac cones and may see an important application in spintronics.

MSC:

82D35 Statistical mechanics of metals
82D40 Statistical mechanics of magnetic materials

Keywords:

tilted Dirac cones; RKKY interaction; Dirac and Weyl semimetals; magnetic impurities
Cite Review PDF
Full Text: DOI

References:

[1] Young, S. M.; Zaheer, S.; Teo, J. C.Y.; Kane, C. L.; Mele, E. J.; Rappe, A. M., Phys. Rev. Lett., 108, Article 140405 pp. (2012)
[2] Armitage, N. P.; Mele, E. J.; Vishwanath, A., Rev. Mod. Phys., 90, Article 015001 pp. (2018)
[3] Bansil, A.; Lin, H.; Das, T., Rev. Mod. Phys., 88, Article 021004 pp. (2016)
[4] Katayama, S.; Kobayashi, A.; Suzumura, Y., J. Phys. Soc. Jpn., 75, Article 054705 pp. (2006)
[5] Goerbig, M. O.; Fuchs, J.-N.; Montambaux, G.; Piéchon, F., Phys. Rev. B, 78, Article 045415 pp. (2008)
[6] Kobayashi, A.; Suzumura, Y.; Fukuyama, H., J. Phys. Soc. Jpn., 77, Article 064718 pp. (2008)
[7] Soluyanov, A. A.; Gresch, D.; Wang, Z.-J.; Wu, Q.-S.; Troyer, M.; Dai, X.; Bernevig, B. A., Nature, 527, 495-498 (2015)
[8] O’Brien, T. E.; Diez, M.; Beenakker, C. W.J., Phys. Rev. Lett., 116, Article 236401 pp. (2016)
[9] Proskurin, I.; Ogata, M.; Suzumura, Y., Phys. Rev. B, 91, Article 195413 pp. (2015)
[10] Yu, Z. M.; Yao, Y.; Yang, S. A., Phys. Rev. Lett., 117, Article 077202 pp. (2016)
[11] Tchoumakov, S.; Civelli, M.; Goerbig, M. O., Phys. Rev. Lett., 117, Article 086402 pp. (2016)
[12] Udagawa, M.; Bergholtz, E. J., Phys. Rev. Lett., 117, Article 086401 pp. (2016)
[13] Zyuzin, A. A.; Tiwari, R. P., JETP Lett., 103, 717 (2016)
[14] Steiner, J. F.; Andreev, A. V.; Pesin, D. A., Phys. Rev. Lett., 119, Article 036601 pp. (2016)
[15] Zyuzin, A. A.; Wu, Si; Burkov, A. A., Phys. Rev. B, 85, Article 165110 pp. (2012)
[16] Borisenko, S.; Evtushinsky, D.; Gibson, Q.; Yaresko, A.; Koepernik, K.; Kim, T.; Ali, M.; Brink, J.; Hoesch, M.; Fedorov, A., Nat. Commun., 10, 3424 (2019)
[17] Lv, B. Q.; Weng, H. M.; Fu, B. B.; Wang, X. P.; Miao, H.; Ma, J.; Richard, P.; Huang, X. C.; Zhao, L. X.; Chen, G. F.; Fang, Z.; Dai, X.; Qian, T.; Ding, H., Phys. Rev. X, 5, Article 031013 pp. (2015)
[18] Weng, H.; Fang, C.; Fang, Z.; Bernevig, B. A.; Dai, X., Phys. Rev. X, 5, Article 011029 pp. (2015)
[19] Xu, S.-Y.; Belopolski, I.; Alidoust, N.; Neupane, M.; Zhang, C.; Sankar, R.; Huang, S.-M.; Lee, C.-C.; Chang, G.; Wang, B.-K.; Bian, G.; Zheng, H.; Sanchez, D. S.; Chou, F.; Lin, H.; Jia, S.; Hasan, M. Z., Science, 349, 613 (2015)
[20] Xu, S.-Y.; Alidoust, N.; Belopolski, I.; Zhang, C.; Bian, G.; Chang, T.-R.; Zheng, H.; Strokov, V.; Sanchez, D. S.; Chang, G.; Yuan, Z.; Mou, D.; Wu, Y.; Huang, L.; Lee, C.-C.; Huang, S.-M.; Wang, B.; Bansil, A.; Jeng, H.-T.; Neupert, T., Nat. Phys., 11, 748 (2015)
[21] Shekhar, C.; Nayak, A. K.; Sun, Y.; Schmidt, M.; Nicklas, M.; Leermakers, I.; Zeitler, U.; Skourski, Y.; Wosnitza, J.; Liu, Z.; Chen, Y.; Schnelle, W.; Borrmann, H.; Grin, Y.; Felser, C.; Yan, B., Nat. Phys., 11, 645 (2015)
[22] Xu, N.; Weng, H. M.; Lv, B. Q.; Matt, C.; Park, J.; Bisti, F.; Strocov, V. N.; Gawryluk, D.; Pomjakushina, E.; Conder, K.; Plumb, N. C.; Radovic, M.; Autès, G.; Yazyev, O. V.; Fang, Z.; Dai, X.; Aeppli, G.; Qian, T.; Mesot, J.; Ding, H., Nat. Commun., 7, Article 11006 pp. (2016)
[23] Ruderman, M. A.; Kittel, C., Phys. Rev., 96, 99 (1954)
[24] Kasuya, T., Prog. Theor. Phys., 16, 45-57 (1956) · Zbl 0072.23701
[25] Yosida, K., Phys. Rev., 106, 893-898 (1957)
[26] Saremi, S., Phys. Rev. B, 76, Article 184430 pp. (2007)
[27] Brey, L.; Fertig, H. A.; Das Sarma, S., Phys. Rev. Lett., 99, Article 116802 pp. (2007)
[28] Black-Schaffer, A. M., Phys. Rev. B, 81, Article 205416 pp. (2010)
[29] Kogan, E., Phys. Rev. B, 84, Article 115119 pp. (2011)
[30] Sherafati, M.; Satpathy, S., Phys. Rev. B, 83, Article 165425 pp. (2011)
[31] Sherafati, M.; Satpathy, S., Phys. Rev. B, 84, Article 125416 pp. (2011)
[32] Uchoa, B.; Rappoport, T. G.; Castro Neto, A. H., Phys. Rev. Lett., 106, Article 016801 pp. (2011)
[33] Chang, H.-R.; Zhou, J.; Wang, S.-X.; Shan, W.-Y.; Xiao, D., Phys. Rev. B, 92, Article 241103 pp. (2015)
[34] Hosseini, M. V.; Askari, M., Phys. Rev. B, 92, Article 224435 pp. (2015)
[35] Sun, Y.; Wang, A.-M., J. Phys. Condens. Matter, 29, Article 435306 pp. (2017)
[36] Liu, Q.; Liu, C.-X.; Xu, C.; Qi, X.-L.; Zhang, S.-C., Phys. Rev. Lett., 102, Article 156603 pp. (2009)
[37] Biswas, R. R.; Balatsky, A. V., Phys. Rev. B, 81, Article 233405 pp. (2010)
[38] Zhu, J.-J.; Yao, D.-X.; Zhang, S.-C.; Chang, K., Phys. Rev. Lett., 106, Article 097201 pp. (2011)
[39] Zyuzin, A. A.; Loss, D., Phys. Rev. B, 90, Article 125443 pp. (2014)
[40] Paul, G. C.; Islam, S. F.; Saha, A., Phys. Rev. B, 99, Article 155418 pp. (2019)
[41] Zhang, S.-H.; Shao, D.-F.; Yang, W., J. Magn. Magn. Mater., 491, Article 165631 pp. (2019)
[42] Mahan, G. D., Many-Particle Physics (2007), Springer: Springer New York
[43] Kang, J.; Zang, J., Phys. Rev. B, 91, Article 134401 pp. (2015)
[44] Wang, S.-X.; Chang, H.-R.; Zhou, J.-H., Phys. Rev. B, 96, Article 115204 pp. (2017)
[45] Dzyaloshinsky, I., J. Phys. Chem. Solids, 4, 241 (1958)
[46] Moriya, T., Phys. Rev., 120, 91 (1960)
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.