Spin Hall effect on a noncommutative space

TL;DR

This paper investigates how noncommutative geometry influences the spin Hall effect, revealing new correction terms and directional dependence in spin currents, and introduces a measurable parameter related to noncommutativity.

Contribution

It derives the spin Hall effect on a noncommutative space using the Foldy-Wouthuysen transformation, highlighting new correction terms and defining a measurable noncommutative parameter.

Findings

Spin Hall conductivity receives corrections due to noncommutativity.

Spin current and conductivity are direction-dependent.

A new measurable parameter = ho heta is introduced.

Abstract

We study the spin-orbital interaction and the spin Hall effect(SHE) of an electron moving on a noncommutative space under the influence of a vector potential A. On a noncommutative space we find that the commutator between the vector potential A and the electric potential V_1(r) of lattice induces a new term which can be treated as an effective electric field, and the spin-Hall conductivity obtains some correction. In addition, the spin current as well as spin-Hall conductivity have distinct values in different direction. On a noncommutative space we derive the spin-depended electric current whose expectation value gives the spin Hall effect and spin Hall conductivity. We have defined a new parameter \varsigma=\rho\theta (\rho is electron concentration, \theta is noncommutative parameter) which can be measured experimentally. Our approach is based on the Foldy-Wouthuysen transformation which give a general Hamiltonian of a non-relativistic electron moving on a noncommutative space.