Aharonov-Bohm-Coulomb Problem in Graphene Ring

TL;DR

This paper explores how Coulomb-like potentials affect the energy spectrum and persistent currents of Dirac electrons in a graphene ring under Aharonov-Bohm conditions, revealing symmetry-breaking effects and valley polarization.

Contribution

It introduces a detailed analysis of scalar and vector Coulomb couplings in graphene rings, highlighting their distinct impacts on symmetry and electronic properties.

Findings

Scalar coupling breaks time-reversal symmetry and causes valley polarization.

Vector coupling preserves symmetries and shifts energy spectra uniformly.

Persistent currents are asymmetric in scalar coupling and symmetric in vector coupling.

Abstract

We study the Aharonov-Bohm-Coulomb problem in a graphene ring. We investigate, in particular, the effects of a Coulomb type potential of the form $\xi/r$ on the energy spectrum of Dirac electrons in the graphene ring in two different ways: one for the scalar coupling and the other for the vector coupling. It is found that, since the potential in the scalar coupling breaks the time-reversal symmetry between the two valleys as well as the effective time-reversal symmetry in a single valley, the energy spectrum of one valley is separated from that of the other valley, demonstrating a valley polarization. In the vector coupling, however, the potential does not break either of the two symmetries and its effect appears only as an additive constant to the spectrum of Aharonov-Bohm potential. The corresponding persistent currents, the observable quantities of the symmetry-breaking energy spectra, are shown to be asymmetric about zero magnetic flux in the scalar coupling, while symmetric in the vector coupling.