Density of states of relativistic and nonrelativistic two-dimensional electron gases in a uniform magnetic and Aharonov-Bohm fields

TL;DR

This paper analyzes the local and total density of states in two-dimensional electron gases with both nonrelativistic and relativistic dispersions under combined Aharonov-Bohm and uniform magnetic fields, revealing contrasting LDOS behaviors.

Contribution

It provides analytic solutions for the density of states in 2DEG and graphene under inhomogeneous magnetic fields, highlighting differences in LDOS modifications caused by a magnetic vortex.

Findings

LDOS is depleted in 2DEG near the vortex.

LDOS is enhanced in graphene near the vortex.

Analytic expressions for DOS in inhomogeneous magnetic fields.

Abstract

We study the electronic properties of 2D electron gas (2DEG) with quadratic dispersion and with relativistic dispersion as in graphene in the inhomogeneous magnetic field consisting of the Aharonov-Bohm flux and a constant background field. The total and local density of states (LDOS) are obtained on the base of the analytic solutions of the Schr\"{o}dinger and Dirac equations in the inhomogeneous magnetic field. It is shown that as it was in the situation with a pure Aharonov-Bohm flux, 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.