Quantization of spin Hall conductivity in two-dimensional topological insulators versus symmetry and spin-orbit interaction

Abstract

The third-rank tensor of the static spin Hall conductivity is investigated for two-dimensional (2D) topological insulators by electronic structure calculations. Its seeming quantization is numerically demonstrated for highly symmetric systems independent of the gap size. 2D crystals with hexagonal and square Bravais lattice show similar effects, while true rectangular translational symmetry yields conductivity values much below the quantum $e^2/h$. Field-induced lifting the inversion symmetry does not influence the quantum spin Hall state up to band inversion but the conductivity quantization. Weak symmetry-conserving biaxial but also uniaxial strain has a minor influence as long as inverted gaps dictate the topological character. The results are discussed in terms of the atomic geometry and the Rashba contribution to the spin-orbit interaction (SOI). Translational and point-group symmetry as well as SOI rule the deviation from the quantization of the spin Hall conductance.

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• Switchable large-gap quantum spin Hall state in two-dimensional MSi${}_2$Z${}_4$ materials class
• Topological nature of the proper spin current and the spin-Hall torque
• Multimechanism quantum anomalous Hall and Chern number tunable states in germanene (silicene, stanene)/$M$Bi${}_2$Te${}_4$ heterostructures
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• Quantum spin Hall effect protected by spin U(1) quasisymmetry
• Time-reversal invariant finite-size topology
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• Spin splitting and spin Hall conductivity in buckled monolayers of the group 14: First-principles calculations
• High-throughput calculations of spin Hall conductivity in non-magnetic 2D materials
• Half-integer anomalous currents in 2D materials from a QFT viewpoint
• Enhancement of temperature of quantum anomalous Hall effect in two-dimensional germanene/magnetic semiconductor heterostructures
• Functionalized Tellurene; a candidate large-gap 2D Topological Insulator
• Spin Weyl Topological Insulators
• Transitions in Xenes between excitonic, topological and trivial insulator phases: influence of screening, band dispersion and external electric field
• Persistent spin texture preserved by local symmetry in graphene/WTe${}_2$ heterostructure