Slobodeniuk A. Graphene and non-relativistic two-dimensional electron gas in non-homogeneous magnetic field

The analytic expression for the density of electronic states of two-dimensional fermions in an Aharonov-Bohm potential and in a superposition of this potential and a potential of the constant magnetic field is obtained. Appearence of an additional series of "vortex" peaks in local density of states is observed. Analytical dependence of the local density of states of two-dimensional fermions as a function of the energy is represented as the product of two functions - the first one fixes the position of Landau peaks and "vortex" peaks, the second one determines their height. The increase of the local density of states in the vicinity of a magnetic vortex in graphene compared to non-relativistic electronic gase has been demonstrated.