Streda-like formula in spin Hall effect

Abstract

A generalized Streda formula is derived for the spin transport in spin-orbit coupled systems. As compared with the original Streda formula for charge transport, there is an extra contribution of the spin Hall conductance whenever the spin is not conserved. For recently studied systems with quantum spin Hall effect in which the z-component spin is conserved, this extra contribution vanishes and the quantized value of spin Hall conductivity can be reproduced in the present approach. However, as spin is not conserved in general, this extra contribution can not be neglected, and the quantization is not exact.

4 pages, no figure

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• Unified role of Green's function poles and zeros in topological insulators
• Kubo-Bastin approach for the spin Hall conductivity of decorated graphene
• Viscoelastic-electromagnetism and Hall viscosity
• Bulk and surface spin conductivity in topological insulators with hexagonal warping
• Halperin States of Particles and Holes in Ideal Time Reversal Invariant Pairs of Chern Bands and The Fractional Quantum Spin Hall Effect in Moiré MoTe${}_2$
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• Spin-Hall effect due to the bulk states of topological insulators: Extrinsic contribution to the conserved spin current
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• Quantum Hall effect induced by chiral Landau levels in topological semimetal films
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• Thin film of a topological insulator as a spin Hall insulator
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• Electrical Conductivity in Quantum Materials