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

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.

7 pages, 5 figures

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Cited by in corpus (9)

• Chaos in Dirac electron optics: Emergence of a relativistic quantum chimera
• Density of states as a probe of electrostatic confinement in graphene
• Zero-energy vortices in Dirac materials
• Electrons trapped in graphene magnetic quantum dots with mass term
• Gate-tunable regular and chaotic electron dynamics in ballistic bilayer graphene cavities
• Decay of semiclassical massless Dirac fermions from integrable and chaotic cavities
• Density of States Analysis of Electrostatic Confinement in Gapped Graphene
• The weak side of strong topological insulators
• Band strutures of hybrid graphene quantum dots with magnetic flux