Dirac Electrons in a Magnetic Quantum Ring

Abstract

The electronic structure of a magnetic quantum ring in monolayer graphene is investigated analytically. The magnetic quantum ring is formed from inhomogeneous magnetic fields perpendicular to its monolayer plane, which are zero inside the ring and constant elsewhere. The low-energy spectra and the probability density of the magnetic edge states around the magnetic quantum ring are calculated analytically by solving the single-particle Dirac equation on a single K point with continuity of the wavefunctions across the boundaries of the magnetic quantum ring and without electron-electron interactions. The results are analyzed through a comparison with a magnetic quantum ring in a two-dimensional electron gas system, showing similar angular momentum transitions in the energy dispersion. These results indicate that electronic properties are often caused by the geometric shape of the system and have little to do with the base material. The qualitative energy spectra are confirmed analytically even if the solution of the Dirac Hamiltonian is limited by not including the detailed atomic arrangement of the material.