Graphene on noncommutative plane and the Seiberg-Witten map

TL;DR

This paper investigates the quantum dynamics and energy spectrum of graphene on a noncommutative plane under a magnetic field, incorporating the Seiberg-Witten map to ensure gauge invariance and exploring NC modifications to helicity.

Contribution

It introduces a gauge-invariant NC Dirac theory for graphene using the Seiberg-Witten map and computes the NC-corrected Landau energy spectrum and helicity modifications.

Findings

NC parameter $ heta$ modifies the energy spectrum.

Helicity is affected by noncommutativity.

Gauge-invariant formulation via Seiberg-Witten map achieved.

Abstract

Graphene on two dimensional (2D) noncommutative (NC) plane in the presence of a constant background magnetic field has been studied. To handel the gauge-invariance issue we start our analysis by a effective massles NC Dirac field theory where we incorporate the Seiberg-Witten (SW) map along with the Moyal star ($\star$) product. The gauge-invariant Hamiltonian of a massless Dirac particle is then computed which is used to study the relativistic Landau problem of graphene on NC plane. Specifically we study the quantum dynamics of a massless relativistic electron moves on monolayer graphene, in the presence of a constant background magnetic field, on NC plane. We also compute the energy spectrum of the NC Landau system in graphene. The results obtained are corrected by the spatial NC parameter $\theta$. Finally we visit the Weyl equation for electron in graphene on NC plane. Interestingly, in this case helicity is found to be $\theta$ modified.