Landau levels for graphene layers in noncommutative plane

TL;DR

This paper develops a method to determine Landau level eigenstates and energies for single and bilayer graphene in a noncommutative plane, revealing energy spectrum shifts due to noncommutativity.

Contribution

It introduces a novel approach to construct Landau level spectra in noncommutative geometry for graphene, extending previous models to include noncommutative effects.

Findings

Energy spectra are shifted in noncommutative space compared to commutative space.

General formulas for Landau levels in noncommutative graphene are derived.

The method applies to both single and bilayer graphene.

Abstract

Starting from the zero modes of the single and bilayer graphene Hamiltonians we develop a mechanism to construct the eigenstates and eigenenergies for Landau levels in noncommutative plane. General formulas for the spectrum of energies are deduced, for both cases, single and bilayer graphene. In both cases we find that the effect to introduce noncommutative coordinates is a shift in the energy spectrum with respect to result obtained in commutative space.