Aharonov-Bohm effect in relativistic and nonrelativistic two-dimensional electron gases: A comparative study

作者：Slobodeniuk A O^*; Sharapov S G; Loktev V M

来源：Physical Review B, 2010, 82(7): 075316.

DOI：10.1103/PhysRevB.82.075316

We carry out a comparative study of electronic properties of two-dimensional 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 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 density of states (LDOS) and total density of states 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.

• 出版日期2010-8-16