Quantum dot in a graphene layer with topological defects

Abstract

In this paper we use an exactly solvable model in order to investigate a magnetization and persistent current of massless Dirac fermions confined in a quantum dot in a graphene layer with a topological defect. We study the low-energy electronic spectrum of a graphene layer structure using the continuum approach and introduce a disclination by means of the geometric theory of defects. The model of the confining potential is introduced into the system via the Dirac oscillator, which provides a harmonic confinement for quasiparticles, in order to study a behaviour of quantum dots in graphene. The exact energy spectrum and wave functions are obtained analytically for the model, in the case where a thin magnetic flux confined to the dot centre, and the arising of persistent currents is investigated. A uniform magnetic field is introduced in a quantum dot, and this model is used to study persistent currents and magnetization in the graphene dot. We have derived exact expressions both for the magnetic moment and for the current carried by quasiparticle states.