Influences of the coordinate dependent noncommutative space on charged and spin currents

TL;DR

This paper investigates how coordinate-dependent noncommutative space influences charged and spin currents, revealing modifications to charge transport while spin currents remain unaffected at leading order.

Contribution

It introduces a noncommutative relativistic framework and derives the effects on currents using the extended Drude model, highlighting specific impacts on charge but not spin currents.

Findings

Charged current is modified by noncommutativity.

Spin current remains unaffected at leading order.

Hall conductivity off-diagonal elements are altered.

Abstract

We study the charged and spin currents on a coordinate dependent noncommutative space. Starting from the noncommutative extended relativistic equation of motion, the non-relativistic approximation is obtained by using the Foldy-Wouthuysen transformation, and then the charged and spin currents are derived by using the extended Drude model. We find that the charged current is twisted by modifying the off-diagonal elements of the Hall conductivity, however, the spin current is not affected up to leading order of the noncommutative parameter.