  We carry out a comparative study of electronic properties of 2D electron gas
(2DEG) in a magnetic field of an infinitesimally thin solenoid with
relativistic dispersion as in graphene and quadratic dispersion as in
semiconducting heterostructures. The problem of ambiguity of the zero mode
solutions of the Dirac equation is treated by considering of a finite radius
flux tube which allows to select unique solutions associated with each
$\mathbf{K}$ point of graphene's Brillouin zone. Then this radius is allowed to
go to zero. On the base of the obtained in this case analytical solutions in
the Aharonov-Bohm potential the local and total density of states (DOS) are
calculated. It is shown that in the case of graphene there is an excess of LDOS
near the vortex, while in 2DEG the LDOS is depleted. This results in excess of
the induced by the vortex DOS in graphene and in its depletion in 2DEG. We
discuss the application of the results for the local density of states for the
scanning tunneling spectroscopy done on graphene.
