Topological spin current

TL;DR

This paper derives an exact expression for non-commuting coordinates in spin-orbit systems, revealing a quantized spin-Hall conductance and proposing an experiment to test these topological effects.

Contribution

It provides an exact derivation of non-commuting coordinates in 2D spin-orbit systems and predicts a quantized spin-Hall conductance, advancing understanding of topological spin transport.

Findings

Quantized spin-Hall conductance in units of egμ_B/h

Exact non-dissipative Hall current derived

Charge-Hall conductivity proportional to magnetic field with Zeeman interaction

Abstract

We present an exact derivation for non-commuting coordinates induced by the SU(2) transformation used to diagonalize the spin-orbit hamiltonian in two dimension.As a result an exact non-dissipative Hall current less sensitive to disorder and complementary to the dissipative conductivity is found. We compute the non-dissipative charge and spin-Hall conductance for the spin-orbit problem.We find that the spin-Hall conductance is quantized in units of $\frac{eg\mu_{B}}{h}$ .In the presence of a Zeeman interaction the charge-Hall conductivity is proportional to the magnetic field. We propose an experiment to test our theory.