Spin Hall Effect in Noncommutative Coordinates

TL;DR

This paper explores the spin Hall effect within noncommutative coordinate systems using a semiclassical Hamiltonian approach, revealing how noncommutativity parameter theta influences spin Hall conductivities and unifies various theoretical models.

Contribution

It introduces a novel formulation of the spin Hall effect in noncommutative coordinates employing a semiclassical Hamiltonian framework, unifying different models through theta-dependent conductivities.

Findings

Noncommutative geometry affects spin Hall conductivity values.

Adjusting theta unifies different spin Hall effect formulations.

The approach is gauge independent and first-order in theta.

Abstract

A semiclassical constrained Hamiltonian system which was established to study dynamical systems of matrix valued non-Abelian gauge fields is employed to formulate spin Hall effect in noncommuting coordinates at the first order in the constant noncommutativity parameter theta . The method is first illustrated by studying the Hall effect on the noncommutative plane in a gauge independent fashion. Then, the Drude model type and the Hall effect type formulations of spin Hall effect are considered in noncommuting coordinates and \theta deformed spin Hall conductivities which they provide are acquired. It is shown that by adjusting \theta different formulations of spin Hall conductivity are accomplished. Hence, the noncommutative theory can be envisaged as an effective theory which unifies different approaches to similar physical phenomena.