Abstract
We investigate the topological phase transitions on the square-octagon lattice with an intrinsic spin-orbit coupling and an additional real next-nearest-neighbor hopping. We study the evolution of the band structure under the next-nearest-neighbor hopping parameters. Based on the spin Chern numbers, we present the phase diagrams of our model and find that a quantum spin Hall phase can be realized at different filling factors. Upon the inclusion of the staggered potential, we also discuss the effect of the time-reversal symmetry breaking term on the stability of the quantum spin Hall state. The variation of the spin-dependent staggered potential is shown to induce the time-reversal symmetry-broken quantum spin Hall phases, and the spin-imbalanced and spin-filtered quantum anomalous Hall phases. The phase transitions are always accompanied by closing of the bulk band gap. We finally demonstrate the edge-state properties of different topological phases.
Graphical abstract
Similar content being viewed by others
References
C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005)
M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010)
X.L. Qi, S.C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)
B.A. Bernevig, S.C. Zhang, Phys. Rev. Lett. 96, 106802 (2006)
C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 146802 (2005)
D.N. Sheng, Z.Y. Weng, L. Sheng, F.D.M. Haldane, Phys. Rev. Lett. 97, 036808 (2006)
E. Prodan, Phys. Rev. B 80, 125327 (2009)
Y. Yang, Z. Xu, L. Sheng, B.G. Wang, D.Y. Xing, D.N. Sheng, Phys. Rev. Lett. 107, 066602 (2011)
A. Zhao, S.-Q. Shen, Phys. Rev. B 85, 085209 (2012)
J. Cao, S.-J. Xiong, Phys. Rev. B 88, 085409 (2013)
N. Goldman, W. Beugeling, C. Morais Smith, Europhys. Lett. 97, 23003 (2012)
W. Beugeling, N. Goldman, C. Morais Smith, Phys. Rev. B 86, 075118 (2012)
Z. Qiao, S.A. Yang, W.-X. Feng, W.-K. Tse, J. Ding, Y.-G. Yao, J. Wang, Q. Niu, Phys. Rev. B 82, 161414(R) (2010)
W.-K. Tse, Z.-H. Qiao, Y.-G. Yao, A.H. MacDonald, Q. Niu, Phys. Rev. B 83, 155447 (2011)
R. Chen, B. Zhou, Phys. Lett. A 381, 944 (2017)
W. Beugeling, J.C. Everts, C. Morais Smith, Phys. Rev. B 86, 195129 (2012)
R. Liu, W.C. Chen, Y.F. Wang, C.D. Gong, J. Phys.: Condens. Matter 24, 305602 (2012)
W.C. Chen, R. Liu, Y.F. Wang, C.D. Gong, Phys. Rev. B 86, 085311 (2012)
M. Di Liberto, O. Tieleman, V. Branchina, C. Morais Smith, Phys. Rev. A 84, 013607 (2011)
J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, P. Windpassinger, Phys. Rev. Lett. 108, 225304 (2012)
M. Kargarian, G.A. Fiete, Phys. Rev. B 82, 085106 (2010)
Y. Yang, J. Yang, X.B. Li, Y. Zhao, Phys. Lett. A 382, 723 (2018)
A. Bao, H.-S. Tao, H.-D. Liu, X.Z. Zhang, W.-M. Liu, Sci. Rep. 4, 6918 (2014)
X.-P. Liu, W.-C. Chen, Y.-F. Wang, C.-D. Gong, J. Phys.: Condens. Matter 25, 305602 (2013)
B. Pal, Phys. Rev. B 98, 245116 (2018)
Y.-T. Kang, C. Lu, F. Yang, D.-X. Yao, Phys. Rev. B 99, 184506 (2019)
Y. Hatsugai, Phys. Rev. B 48, 11851 (1993)
Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993)
M. Ezawa, Phys. Rev. Lett. 110, 026603 (2013)
L. Xu, Y. Zhou, J. Zhang, Solid State Commun. 212, 41 (2015)
A. Mishra, S.B. Lee, Phys. Rev. B 98, 235124 (2018)
S. Taniguchi, T. Nishikawa, Y. Yasui, Y. Kobayashi, M. Sato, T. Nishioka, M. Kontani, K. Sano, J. Phys. Soc. Jpn. 64, 2758 (1995)
M.-R. He, R. Yu, J. Zhu, Angew. Chem. 124, 7864 (2012)
X.-L. Sheng, H.-J. Cui, F. Ye, Q.-B. Yan, Q.-R. Zheng, G. Su, J. Appl. Phys. 112, 074315 (2012)
A.I. Podlivaev, L.A. Openov, Phys. Solid State 55, 2592 (2013)
G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, T. Esslinger, Nature 515, 237 (2014)
P. Soltan-Panahi, J. Struck, P. Hauke, A. Bick, W. Plenkers, G. Meineke, C. Becker, P. Windpassinger, M. Lewenstein, K. Sengstock, Nat. Phys. 7, 434 (2011)
G.B. Jo, J. Guzman, C.K. Thomas, P. Hosur, A. Vishwanath, D.M. Stamper-Kurn, Phys. Rev. Lett. 108, 045305 (2012)
V. Apaja, M. Hyrkas, M. Manninen, Phys. Rev. A 82, 041402 (2010)
N. Goldman, D.F. Urban, D. Bercioux, Phys. Rev. A 83, 063601 (2011)
L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, T. Esslinger, Nature 483, 302 (2012)
N. Goldman, I. Satija, P. Nikolic, A. Bermudez, M.A. MartinDelgado, M. Lewenstein, I.B. Spielman, Phys. Rev. Lett. 105, 255302 (2010)
Y.-J. Lin, K. Jimenez-Garcia, I.B. Spielman, Nature (London) 471, 83 (2011)
Z. Wu, L. Zhang, W. Sun, X.-T. Xu, B.-Z. Wang, S.-C. Ji, Y. Deng, S. Chen, X.-J. Liu, J.-W. Pan, Science 354, 83 (2016)
E. Alba, X. Fernandez-Gonzalvo, J. Mur-Petit, J.K. Pachos, J.J. Garcia-Ripoll, Phys. Rev. Lett. 107, 235301 (2011)
E. Zhao, N. Bray-Ali, C.J. Williams, I.B. Spielman, I.I. Satija, Phys. Rev. A 84, 063629 (2011)
N. Goldman, J. Beugnon, F. Gerbier, Phys. Rev. Lett. 108, 255303 (2012)
M. Buchhold, D. Cocks, W. Hofstetter, Phys. Rev. A 85, 063614 (2012)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yang, Y., Li, X. Topological phase transitions on the square-octagon lattice with next-nearest-neighbor hopping. Eur. Phys. J. B 92, 277 (2019). https://doi.org/10.1140/epjb/e2019-100488-5
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2019-100488-5