Energy spectrum and density of states for a graphene quantum dot in a magneticfield

Abstract

In this paper, we determine the spectrum and density of states of a graphene quantum dotin a normal quantizing magnetic field. To accomplish this, we employ the retarded Greenfunction for a magnetized, infinite-sheet graphene layer to describe the dynamics of atightly confined graphene quantum dot subject to Landau quantization. Considering aδ(2)(r) potential well that supports just one subband state in the well in the absence of a magneticfield, the effect of Landau quantization is to ‘splinter’ this single energy level into aproliferation of many Landau-quantized states within the well. Treating the graphene sheetand dot as a closed system subject to a fully Hermitian Hamiltonian (including boundaryconditions), there is no indication of decay of the Landau-quantized graphene dot statesinto the quantized states of the host graphene sheet for ‘tight’ confinement by theδ(2)(r) potential well, notwithstanding extension of the dot Green function (and eigenfunctions) outside theδ(2)(r) potential well.