Interplay of Aharonov-Bohm and Berry phases in gate-defined graphene quantum dots

TL;DR

This paper investigates how magnetic flux and geometric shape influence electron confinement in graphene quantum dots, revealing the interplay of Aharonov-Bohm and Berry phases affects bound state formation and conductance resonances.

Contribution

It demonstrates how flux-induced phase cancellation impacts electron confinement and conductance in graphene quantum dots with different geometries.

Findings

Bound states exist in regular geometries without flux tube.

Resonance absence in non-integrable geometries with flux tube.

Conductance resonances depend on geometry and magnetic flux presence.

Abstract

We study the influence of a magnetic flux tube on the possibility to electrostatically confine electrons in a graphene quantum dot. Without magnetic flux tube, the graphene pseudospin is responsible for a quantization of the total angular momentum to half-integer values. On the other hand, with a flux tube containing half a flux quantum, the Aharonov-Bohm phase and Berry phase precisely cancel, and we find a state at zero angular momentum that cannot be confined electrostatically. In this case, true bound states only exist in regular geometries for which states without zero-angular-momentum component exist, while non-integrable geometries lack confinement. We support these arguments with a calculation of the two-terminal conductance of a gate-defined graphene quantum dot, which shows resonances for a disc-shaped geometry and for a stadium-shaped geometry without flux tube, but no resonances for a stadium-shaped quantum dot with a $\pi$-flux tube.