Spin accumulation without spin current

TL;DR

This paper demonstrates that spin accumulation can occur without a corresponding spin Hall current in systems with spin-orbit coupling, challenging traditional understanding of spin transport phenomena.

Contribution

It introduces a new approach to calculate spin response to electric-field gradients and shows spin accumulation can exist independently of spin Hall conductivity.

Findings

Spin accumulation occurs even when spin Hall conductivity is zero.

Derived a generic formula for spin response using Bloch wave functions.

Analyzed the Rashba model with disorder, confirming nonzero spin accumulation.

Abstract

The spin Hall (SH) effect is a phenomenon in which the spin current flows perpendicular to an applied electric field and causes the spin accumulation at the boundaries. However, in the presence of spin-orbit couplings, the spin current is not well defined. Here, we calculate the spin response to an electric-field gradient, which naturally appears at the boundaries. We derive a generic formula using the Bloch wave functions and the phenomenological relaxation time. We also calculate the response for the uniform Rashba model with $\delta$-function nonmagnetic disorder within the first-order Born approximation and corresponding vertex corrections. We find the nonzero spin accumulation, although the SH conductivity exactly vanishes.