Aharonov-Bohm effect in relativistic and nonrelativistic 2D electron gas: a comparative study

摘要

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