Peierls-phase-induced topological semimetals in an optical lattice: Moving of Dirac points, anisotropy of Dirac cones, and hidden symmetry protection

doi:10.1088/1674-1056/abc0de

摘要/Abstract

Abstract: We propose a square optical lattice in which some of neighbor hoppings have a Peierls phase. The Peierls phase makes the lattice have a special band structure and induces the existence of Dirac points in the Brillouin zone, which means that topological semimetals exist in the system. The Dirac points move with the change of the Peierls phase and the Dirac cones are anisotropic for some vales of the Peierls phase. The lattice has a novel hidden symmetry, which is a composite antiunitary symmetry composed of a translation operation, a sublattice exchange, a complex conjugation, and a local U(1) gauge transformation. We prove that the Dirac points are protected by the hidden symmetry and perfectly explain the moving of Dirac points with the change of the Peierls phase based on the hidden symmetry protection.

Key words: topological semimetal, optical lattice, hidden symmetry

中图分类号: (Degenerate Fermi gases)

03.75.Ss

02.20.-a (Group theory) 03.65.Vf (Phases: geometric; dynamic or topological) 05.30.Fk (Fermion systems and electron gas)

. [J]. 中国物理B, 2020, 29(12): 120305-.

Jing-Min Hou(侯净敏). Peierls-phase-induced topological semimetals in an optical lattice: Moving of Dirac points, anisotropy of Dirac cones, and hidden symmetry protection[J]. Chin. Phys. B, 2020, 29(12): 120305-.

参考文献

[1] Hasan M Z and Kane C L Rev. Mod. Phys. 82 3045 DOI: 10.1103/RevModPhys.82.30452010
[2] Qi X L and Zhang S C Rev. Mod. Phys. 83 1057 DOI: 10.1103/RevModPhys.83.10572011
[3] Wan X, Turner A M, Vishwanath A and Savrasov S Y Phys. Rev. B 83 205101 DOI: 10.1103/PhysRevB.83.2051012011
[4] Xu G, Weng H, Wang Z, Dai X and Fang Z Phys. Rev. Lett. 107 186806 DOI: 10.1103/PhysRevLett.107.1868062011
[5] Burkov A A, Hook M D and Balents L Phys. Rev. B 84 235126 DOI: 10.1103/PhysRevB.84.2351262011
[6] Burkov A A and Balents L Phys. Rev. Lett. 107 127205 DOI: 10.1103/PhysRevLett.107.1272052011
[7] Fang C, Gilbert M J, Dai X and Bernevig B A Phys. Rev. Lett. 108 266802 DOI: 10.1103/PhysRevLett.108.2668022012
[8] Zyuzin A A, Wu S and Burkov A A Phys. Rev. 85 165110 DOI: 10.1103/PhysRevB.85.1651102012
[9] Jaksch D and Zoller P Ann. Phys. 315 52 DOI: 10.1016/j.aop.2004.09.0102005
[10] Lewenstein M, Sanpera A, Ahufinger V, Damski B, Sen A and Sen U 2007 Adv. Phys. 56 243 DOI: 10.1080/00018730701223200
[11] Bloch I, Dalibard J and Zwerger W Rev. Mod. Phys. 80 885 DOI: 10.1103/RevModPhys.80.8852008
[12] Cooper N R, Dalibard J and Spielman I B Rev. Mod. Phys. 91 015005 DOI: 10.1103/RevModPhys.91.0150052019
[13] Greiner M, Mandel O, Esslinger T, Hänsch T W and Bloch I Nature 415 39 DOI: 10.1038/415039a2002
[14] Jaksch D, Bruder C, Cirac J I, Gardiner C W and Zoller P Phys. Rev. Lett. 81 3108 DOI: 10.1103/PhysRevLett.81.31081998
[15] Hou J M and Ge M L Phys. Rev. A 67 063607 DOI: 10.1103/PhysRevA.67.0636072003
[16] Lin Y J, Compton R L, Jimènez-Garcìa K, Porto J V and Spielman I B Nature 462 628 DOI: 10.1038/nature086092009
[17] Aidelsburger M, Atala M, Nascimb\`ene S, Trotzky S, Chen Y A and Bloch I Phys. Rev. Lett. 107 255301 DOI: 10.1103/PhysRevLett.107.2553012011
[18] Miyake H, Siviloglou G A, Kennedy C J, Burton W C and Ketterle W Phys. Rev. Lett. 111 185302 DOI: 10.1103/PhysRevLett.111.1853022013
[19] Struck J, ölschläger C, Weinberg M, Hauke P, Simonet J, Eckardt A, Lewenstein M, Sengstock K and Windpassinger P Phys. Rev. Lett. 108 225304 DOI: 10.1103/PhysRevLett.108.2253042012
[20] J Struck, Weinberg M, ölschläger C, Windpassinger P, Simonet J, Sengstock K, Höppner R, Hauke P, Eckardt A, Lewenstein M and Mathey L Nat. Phys. 9 738 https://www.nature.com/articles/nphys27502013
[21] Trotzky S, Cheinet P, Fölling S, Feld M, Schnorrberger U, Rey A M, Polkovnikov A, Demler E A, Lukin M D and Bloch I Science 319 295 DOI: 10.1126/science.11508412008
[22] Eckardt A, Hauke P, Soltan-Panahi P, Becker C, Sengstock K and Lewenstein M Europhys. Lett. 89 10010 DOI: 10.1209/0295-5075/89/100102010
[23] Simon J, Bakr W S, Ma R, Tai M E, Preiss P M and Greiner M Nature 472 307 DOI: 10.1038/nature099942011
[24] Greif D, Uehlinger T, Jotzu G, Tarruell L and Esslinger T Science 340 1307 DOI: 10.1126/science.12363622013
[25] Hou J M, Yang W X and Liu X J Phys. Rev. A 79 043621 DOI: 10.1103/PhysRevA.79.0436212009
[26] Lim L K, Smith C M and Hemmerich A Phys. Rev. Lett. 100 130402 DOI: 10.1103/PhysRevLett.100.1304022008
[27] Goldman N, Kubasiak A, Bermudez A, Gaspard P, Lewenstein M and Martin-Delgado M A Phys. Rev. Lett. 103 035301 DOI: 10.1103/PhysRevLett.103.0353012009
[28] Bercioux D, Urban D F, Grabert H and Häusler W Phys. Rev. A 80 063603 DOI: 10.1103/PhysRevA.80.0636032009
[29] Sun K, Liu W V, Hemmerich A and Das Sarma S Nat. Phys. 8 67 DOI: 10.1038/nphys21342012
[30] Hou J M Phys. Rev. Lett. 111 130403 DOI: 10.1103/PhysRevLett.111.1304032013
[31] Goldman N, Anisimovas E, Gerbier F, öhberg P, Spielman I B and Juzeli\=unas G New J. Phys. 15 013025 DOI: 10.1088/1367-2630/15/1/0130252013
[32] Mai X Y, Zhang D W, Li Z and Zhu S L Phys. Rev. A 95 063616 DOI: 10.1103/PhysRevA.95.0636162017
[33] Nielsen H B and Ninomiya M 1981 Nuclear Physics B 185 20 DOI: 10.1016/0550-3213(81)90361-8
[34] Hou J M and Chen W Front. Phys. 13 130301 DOI: 10.1007/s11467-017-0712-82018
[35] Stenger J, Inouye S, Chikkatur A P, Stamper-Kurn D M, Pritchard D E and Ketterle W Phys. Rev. Lett. 82 4569 DOI: 10.1103/PhysRevLett.82.45691999
[36] Steinhauer J, Ozeri R, Katz N and Davidson N Phys. Rev. Lett. 88 120407 DOI: 10.1103/PhysRevLett.88.1204072002
[37] Stanescu T D, Galitski V and Das Sarma S Phys. Rev. A 82 013608 DOI: 10.1103/PhysRevA.82.0136082010
[38] Liu X J, Liu X, Wu C and Sinova J Phys. Rev. A 81 033622 DOI: 10.1103/PhysRevA.81.0336222010
[39] Goldman N, Beugnon J and Gerbier F Phys. Rev. Lett. 108 255303 DOI: 10.1103/PhysRevLett.108.2553032012