Spin Hall conductivity in insulators with non-conserved spin

Abstract

We study the linear response of a spin current to a small electric field in a two-dimensional crystalline insulator with non-conserved spin. We adopt the spin current operator proposed in [J. Shi et al., Phys. Rev. Lett. 96, 076604 (2006)], which satisfies a continuity equation and fits the Onsager relations. We use the time-independent perturbation theory to present a formula for the spin Hall conductivity, which consists of a "Chern-like" term, reminiscent of the Kubo formula obtained for the quantum Hall systems, and a correction term that accounts for the non-conservation of spin. We illustrate our findings on the Bernevig-Hughes-Zhang model and the Kane-Mele model for time-reversal symmetric topological insulators and show that the correction term scales quadratically with the amplitude of the spin-conservation-breaking terms. In both models, the spin Hall conductivity deviates from the quantized value when spin is not conserved.

9 pages, 2 figures

References in corpus (8)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling
• On A Proper Definition of Spin Current
• Robustness of the Spin-Chern number
• Spin Hall Effect
• Quantization of spin Hall conductivity in two-dimensional topological insulators versus symmetry and spin-orbit interaction
• Streda-like formula in spin Hall effect

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• Spin-Hall effect due to the bulk states of topological insulators: Extrinsic contribution to the conserved spin current
• Spin-Hall effect in topological materials: Evaluating the proper spin current in systems with arbitrary degeneracies
• Elasto-Dynamical Induced Spin and Charge Pumping in Bulk Heavy Metals
• From charge to spin: analogies and differences in quantum transport coefficients
• From orbital magnetism to bulk-edge correspondence
• Coherence Control of Directional Nonlinear Photocurrent in Spatially Symmetric Systems
• Purely linear response of the quantum Hall current to space-adiabatic perturbations
• Spin transport and lack of quantisation for time-reversal symmetric insulators on the honeycomb structure