Dirac model of an isolated graphene antidot in a magnetic field

Abstract

We consider a single graphene antidot, modeled via a circularly symmetric mass term in the Dirac Hamiltonian, in the presence of an external magnetic field. We derive analytical expressions for the eigenstate spinors, and use these to formulate an eigenvalue condition for the system. We find that electron-hole symmetry is broken in the individual valleys, while the combined spectrum of both valleys retains this symmetry. In the limit of an infinite mass term, we arrive at approximate analytical expressions for the energies. We discuss the dependence of the energy spectrum and the eigenstate spinors on the mass term and the magnetic field, as well as on the angular momentum of the eigenstate. We show that the density of states exhibits a very rich structure if the antidot radius is of the order of the magnetic length. By simulating scanning tunneling microscopy measurements, we discuss the possibility of experimentally probing states localized around the antidot.