Sum rules for spin-Hall conductivity cancelation

TL;DR

This paper demonstrates that the zero bulk spin-Hall conductivity is an intrinsic property of the free-electron Hamiltonian, with scattering revealing this cancellation, and explores its behavior under magnetic fields and resonant conditions.

Contribution

It provides a theoretical proof that the zero spin-Hall conductivity is intrinsic and unaffected by scattering, extending understanding of spin transport in Rashba systems.

Findings

Zero bulk spin conductivity is intrinsic to the free-electron Hamiltonian.

Scattering reveals the intrinsic zero conductivity but does not alter it.

Spin conductivity exhibits resonant increase at cyclotron frequency before decaying.

Abstract

It has been shown recently that the universal dc spin conductivity of two-dimensional electrons with a Rashba spin-orbit interaction is canceled by vertex corrections in a weak scattering regime. We prove that the zero bulk spin conductivity is an intrinsic property of the free-electron Hamiltonian and scattering is merely a tool to reveal this property in terms of the diagrammatic technique. When Zeeman energy is neglected, the zero dc conductivity persists in a magnetic field. Spin conductivity increases resonantly at the cyclotron frequency and then decays towards the universal value.