Dirac Fermion Confinement in Graphene

TL;DR

This paper investigates how Dirac fermions in graphene behave under confinement and magnetic fields, revealing a crossover in electronic spectrum and oscillations that match experimental observations.

Contribution

It provides an analytical and numerical study of Dirac fermion confinement effects in graphene under magnetic fields, highlighting a field-dependent crossover in electronic behavior.

Findings

Confinement causes a transition from  to linear in B spectrum.

The crossover occurs when Landau level radius matches system width.

The theory aligns well with experimental data.

Abstract

We study the problem of Dirac fermion confinement in graphene in the presence of a perpendicular magnetic field B. We show, analytically and numerically, that confinement leads to anomalies in the electronic spectrum and to a magnetic field dependent crossover from \sqrt{B}, characteristic of Dirac-Landau level behavior, to linear in B behavior, characteristic of confinement. This crossover occurs when the radius of the Landau level becomes of the order of the width of the system. As a result, we show that the Shubnikov-de Haas oscillations also change as a function of field, and lead to a singular Landau plot. We show that our theory is in excellent agreement with the experimental data.