Transport and Quantum Coherence in Graphene Rings: Aharonov–Bohm Oscillations, Klein Tunneling, and Particle Localization

Abstract

Simulating quantum transport through mesoscopic, ring-shaped graphene structures, we address various quantum coherence and interference phenomena. First, a perpendicular magnetic field, penetrating the graphene ring, gives rise to Aharonov-Bohm oscillations in the conductance as a function of the magnetic flux, on top of the universal conductance fluctuations. At very high fluxes the interference gets suppressed and quantum Hall edge channels develop. Second, applying an electrostatic potential to one of the ring arms, nn n-or npn-junctions can be realized with particle transmission due to normal tunneling or Klein tunneling. In the latter case the Aharonov-Bohm oscillations weaken for smooth barriers. Third, if potential disorder comes in to play, both Aharonov-Bohm and Klein tunneling effects rate down, up to the point where particle localization sets in.Keywords mesocopic transport · quantum interferece · graphene-based nanostructures · Aharonov-Bohm effect · disorder effects PACS 73.23.-b · 72.80.Vp · 73.43.Jn · 73.20.Fz

Electronic properties of α − 𝒯3 quantum dots in magnetic fields

“…As a matter of course, imperfections will strongly influence the transport through contacted Dirac-cone systems [57,64,65]. This holds true even up to the point of complete suppression, e.g., by Anderson localisation [66].…”

“…Investigating the electronic properties of α − T 3 quantum dots in magnetic fields, we also start from such a description, and therefore must implement a boundary condition when the dot is cut out from the plane [39,54,55]. Of course, this approach has to be approved by comparison with lattice model results obtained numerically [55][56][57]. Addressing the transport behaviour of contacted dots and the influence of disorder on that we have to work with the full lattice model in any case.…”

Electronic Properties of $α-\mathcal{T}_3$ Quantum Dots in Magnetic Fields

“…As a matter of course, imperfections will strongly influence the transport through contacted Dirac-cone systems [64,65,57]. This holds true even up to the point of complete suppression, e.g., by Anderson localisation [66].…”

“…Investigating the electronic properties of α − T 3 quantum dots in magnetic fields, we also start from such a description, and therefore must implement a boundary condition when the dot is cut out from the plane [54,39,55]. Of course, this approach has to be approved by comparison with lattice model results obtained numerically [56,55,57]. Addressing the transport behaviour of contacted dots and the influence of disorder on that we have to work with the full lattice model in any case.…”