Robustness of Quantum Spin Hall Effect in an External Magnetic Field

Abstract

The edge states in the quantum spin Hall effect are expected to be protected by time reversal symmetry. The experimental observation of the quantized conductance was reported in the InAs/GaSb quantum well {[}Du et al, arXiv:1306.1925{]}, up to a large magnetic field, which raises a question on the robustness of the edge states in the quantum spin Hall effect under time reversal symmetry breaking. Here we present a theoretical calculation on topological invariants for the Benevig-Hughes-Zhang model in an external magnetic field, and find that the quantum spin Hall effect retains robust up to a large magnetic field. The critical value of the magnetic field breaking the quantum spin Hall effect is dominantly determined by the band gap at the $\Gamma$ point instead of the indirect band gap between the conduction and valence bands. This illustrates that the quantum spin Hall effect could persist even under time reversal symmetry breaking.

arXiv comment9 pages, 5 figures, to appear in Phys. Rev. B

References in corpus (22)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Evidence for Helical Edge Modes in Inverted InAs/GaSb Quantum Wells
• The Quantum Spin Hall Effect: Theory and Experiment
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Topological Anderson Insulator
• Massive Dirac fermions and spin physics in an ultrathin film of topological insulator
• Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z_2 topology
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Theory of the topological Anderson insulator
• Time-reversal-symmetry-broken quantum spin Hall effect
• Resonant Spin Hall Conductance in Two-Dimensional Electron Systems with Rashba Interaction in a Perpendicular Magnetic Field
• Localization in a quantum spin Hall system
• Quantum Transport in Magnetic Topological Insulator Thin Films
• Resonant spin Hall conductance in quantum Hall systems lacking bulk and structural inversion symmetry

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