Optical Properties of Dirac Electrons in a Parabolic Well

Abstract

A single electron transitor may be fabricated using qunatum dots. A good model for the confinement potential of a quantum dot is a parabolic well. Here we consider such a parabolic dot made of graphene. Recently, we found counter intuitively that resonant quasi-boundstates of both positive and negative energies exist in the energy spectrum. The presence of resonant quasi-boundstates of negative energies is a unique property of massless Dirac fernnions. As magnetic field B gets smaller the energy width of these states become broader and for sufficiently weak value of B resonant quasi-bound states disappear into a quasi-continuum. In the limit of small B resonant and non-resonant states transform into discrete anomalous states with a narrow probability density peak inside the well and another broad peak under the potential barrier. In this paper we compute the optical strength between resonant quasi-bound states as a function of B, and investigate how the signature of resonant quasi-bound states of Dirac electrons may appear in optical measurements.