Noncommutative Graphene

TL;DR

This paper explores a noncommutative framework for graphene, showing that momentum noncommutativity influences energy levels but leaves Hall conductivity unchanged, providing a potential avenue to test noncommutative physics.

Contribution

It introduces a noncommutative Dirac equation for graphene and analyzes its effects on physical observables, highlighting the unique testability of noncommutativity in two-dimensional Dirac systems.

Findings

Momentum noncommutativity affects energy levels in graphene.

Hall conductivity remains unaffected by noncommutative corrections.

Graphene's two-dimensional Dirac nature makes it suitable for testing noncommutative theories.

Abstract

We consider a noncommutative description of graphene. This description consists of a Dirac equation for massless Dirac fermions plus noncommutative corrections, which are treated in the presence of an external magnetic field. We argue that, being a two-dimensional Dirac system, graphene is particularly interesting to test noncommutativity. We find that momentum noncommutativity affects the energy levels of graphene, but that it does not entail any kind of correction to the Hall conductivity.