Intrinsic Spin Hall Effect: Topological Transitions in Two-Dimensional Systems

TL;DR

This paper explores the spin-Hall conductivity in two-dimensional electron systems, revealing topological transitions characterized by Berry phase and winding number, with implications for experimental detection in quantum wells.

Contribution

It introduces a topological framework for understanding the spin-Hall effect, highlighting the universal and non-universal parts of conductivity linked to Berry phase and system properties.

Findings

Spin-Hall conductivity has a universal component linked to Berry phase.

Topological transitions occur as the winding number M changes.

Behavior is relevant for electron and hole states in quantum wells.

Abstract

The spin-Hall conductivity in spatially-homogeneous two-dimensional electron systems described by the spin-orbit Hamiltonian \hbar \Omega_p \sigma is presented as a sum of the universal part Me/8 \pi \hbar determined by the Berry phase \Phi=M \pi (M is an odd integer, the winding number of the vector \Omega_p) and a non-universal part which vanishes under certain conditions determined by the analytical properties of \Omega_p. The analysis reveals a rich and complicated behavior of the spin-Hall conductivity which is relevant to both electron and hole states in quantum wells and can be detected in experiments.