A Noncommutative Space Approach to Confined Dirac Fermions in Graphene

TL;DR

This paper introduces a noncommutative algebra framework to model confined Dirac fermions in graphene, successfully reproducing experimental Landau plots and providing a novel theoretical approach to carrier confinement.

Contribution

It develops a noncommutative coordinate approach incorporating gauge fields to model confined Dirac fermions in graphene, aligning with experimental observations.

Findings

Reproduces the Landau plot of graphene's Shubnikov-de Haas oscillations

Establishes a relation between energy levels and magnetic field maxima

Provides a new theoretical formulation for confined massless Dirac fermions

Abstract

A generalized algebra of noncommutative coordinates and momenta embracing non-Abelian gauge fields is proposed. Through a two-dimensional realization of this algebra for a gauge field including electromagnetic vector potential and two spin-orbit-like coupling terms, a Dirac-like Hamiltonian in noncommutative coordinates is introduced. We established the corresponding energy spectrum and from that we derived the relation between the energy level quantum number and the magnetic field at the maxima of Shubnikov-de Haas oscillations. By tuning the non-commutativity parameter \theta in terms of the values of magnetic field at the maxima of Shubnikov-de Haas oscillations we accomplished the experimentally observed Landau plot of the peaks for graphene. Accepting that the experimentally observed behavior is due to the confinement of carriers, we conclude that our method of introducing noncommutative coordinates provides another formulation of the confined massless Dirac fermions in graphene.