Low-lying spectra of massless Dirac electron in magnetic dot and ring

Abstract

Both the size and the magnetic-field dependences of low-lying spectra of two-dimensional (2D) graphene based magnetic dot and ring in perpendicular inhomogeneous magnetic fields, where the magnetic field is zero inside the dot and ring, and constant elsewhere, are studied by the massless Dirac–Weyl equation. Numerical results obtained from direct diagonalization with 2D harmonic basis show that, under nonuniform magnetic fields, the higher Landau levels (N≥1) for such massless Dirac electron interacting system in general become nondegenerate and split into discrete angular momentum states with level crossings with the lowest one (N=0) being an exception.