title: Time-reversal-breaking induced quantum spin Hall effect.
abstract: We show that quantum spin Hall (QSH) effect does not occur in a square lattice model due to cancellation of the intrinsic spin-orbit coupling coming from different hopping paths. However, we show that QSH effect can be induced by the presence of staggered magnetic fluxes alternating directions square by square. When the resulting Peierls phase takes a special value , the system has a composite symmetry ΘΡ-with Θ the time-reversal operator and Ρ-transforming the Peierls phase from γ to γ - , which protects the gapless edge states. Once the phase deviates from , the edge states open a gap, as the composite symmetry is broken. We further investigate the effect of a Zeeman field on the QSH state, and find that the edge states remain gapless for . This indicates that the QSH effect is immune to the magnetic perturbation.
authors.affiliation: National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China.|School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China.
authors.forename: Wei
authors.initials: W
authors.lastname: Luo
authors.affiliation: National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China.
authors.forename: D X
authors.initials: DX
authors.lastname: Shao
authors.affiliation: National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China.
authors.forename: Ming-Xun
authors.initials: MX
authors.lastname: Deng
authors.affiliation: National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China.
authors.forename: W Y
authors.initials: WY
authors.lastname: Deng
authors.affiliation: National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China.|Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.
authors.forename: L
authors.initials: L
authors.lastname: Sheng