Large Angular Momentum States in a Graphene Film

Abstract

At energy lower than 2 eV, the dispersion law of the electrons in a graphene sheet presents a linear dependence of the energy on the kinetic momentum, which is typical of photons and permits the description of the electrons as massless particles by means of the Dirac equation and the study of massless particles acted upon by forces. We analytically solve the Dirac equation of an electron in a graphene disk with radius of 10,000 atomic units pierced by a magnetic field and find the eigenenergies and eigenstates of the particles for spin up and down. The magnetic field ranges within three orders of magnitude and is found to confine the electron in the disk. States with a relatively large total angular momentum exist and can be considered in a vorticose condition; these states are seen to peak at different distances from the disk centre and can be used to store few bit of information.