Graphene Rings in Magnetic Fields: Aharonov-Bohm Effect and Valley Splitting

TL;DR

This paper investigates the conductance of mesoscopic graphene rings under magnetic fields, revealing the Aharonov-Bohm effect, flux-induced valley splitting, and the influence of disorder and boundary conditions on quantum transport.

Contribution

It demonstrates how magnetic flux can lift valley degeneracy in graphene rings and analyzes conductance oscillations across different regimes and disorder levels.

Findings

Aharonov-Bohm oscillations observed in graphene rings.

Valley degeneracy can be lifted by small magnetic flux.

Disorder affects the visibility of quantum oscillations.

Abstract

We study the conductance of mesoscopic graphene rings in the presence of a perpendicular magnetic field by means of numerical calculations based on a tight-binding model. First, we consider the magnetoconductance of such rings and observe the Aharonov-Bohm effect. We investigate different regimes of the magnetic flux up to the quantum Hall regime, where the Aharonov-Bohm oscillations are suppressed. Results for both clean (ballistic) and disordered (diffusive) rings are presented. Second, we study rings with smooth mass boundary that are weakly coupled to leads. We show that the valley degeneracy of the eigenstates in closed graphene rings can be lifted by a small magnetic flux, and that this lifting can be observed in the transport properties of the system.