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

TL;DR

This paper compares the electronic properties of relativistic and nonrelativistic 2D electron gases in an Aharonov-Bohm setup, revealing distinct local density of states behaviors near a vortex, with implications for scanning tunneling spectroscopy.

Contribution

It provides analytical solutions for the density of states in both relativistic and nonrelativistic 2DEG under Aharonov-Bohm conditions, clarifying their contrasting local electronic responses.

Findings

Graphene shows an LDOS excess near the vortex.

2DEG exhibits LDOS depletion near the vortex.

Results are relevant for interpreting scanning tunneling spectroscopy data.

Abstract

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.