# Aharonov-Bohm effect and broken valley degeneracy in graphene rings

@article{Recher2007AharonovBohmEA, title={Aharonov-Bohm effect and broken valley degeneracy in graphene rings}, author={Patrik Recher and Bjorn Trauzettel and Adam Rycerz and Yaroslav M. Blanter and C. W. J. Beenakker and Alberto F. Morpurgo}, journal={Physical Review B}, year={2007}, volume={76}, pages={235404} }

We analyze theoretically the electronic properties of Aharonov-Bohm rings made of graphene. We show that the combined effect of the ring confinement and applied magnetic flux offers a controllable way to lift the orbital degeneracy originating from the two valleys, even in the absence of intervalley scattering. The phenomenon has observable consequences on the persistent current circulating around the closed graphene ring, as well as on the ring conductance. We explicitly confirm this…

## 175 Citations

### Graphene rings in magnetic fields: Aharonov–Bohm effect and valley splitting

- Physics
- 2009

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…

### The Aharonov–Bohm–Coulomb problem in a graphene ring

- Physics
- 2012

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 ξ/r on the energy spectrum of Dirac electrons in the…

### Aharonov-Bohm effect in graphene Möbius strips: an analytical treatment

- Physics
- 2017

Abstract
In this work, the influence of an Aharonov-Bohm flux on the low energy physical properties of graphene nanorings exhibiting Möbius topology is examined. Our approach lies in the continuum…

### Size effects in Aharonov–Bohm graphene rings

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2010

It is shown that the energy difference between the two valleys and the amplitude of the oscillating PCs increase with the decrease of the radius of the graphene ring, implying that the AB effect and size-dependent PCs in ring-shaped microstructures could be tested at room temperature.

### Interplay of the Aharonov-Bohm effect and Klein tunneling in graphene

- Physics
- 2010

We numerically investigate the effect of Klein tunneling on the Aharonov-Bohm oscillations in graphene rings using a tight-binding model with nearest-neighbor couplings. In order to introduce Klein…

### Patterns of the Aharonov-Bohm oscillations in graphene nanorings

- Physics
- 2012

Using extensive tight-binding calculations, we investigate (including the spin) the Aharonov-Bohm (AB) effect in monolayer and bilayer trigonal and hexagonal graphene rings with zigzag boundary…

### Electronic confinement in graphene quantum rings due to substrate-induced mass radial kink

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2016

The results suggest that any defect line that is closed in a loop, with any geometry, would produce the same qualitative results as the circular ones investigated here, as a manifestation of the topologically protected nature of the ring-like states investigated here.

### Nanophysics in graphene: neutrino physics in quantum rings and superlattices

- PhysicsPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2010

In this article, it is demonstrated that the spectrum reveals signatures of ‘effective time-reversal symmetry breaking’, in which the spectra are most naturally interpreted in terms of effective magnetic flux contained in the ring, even when no real flux is present.

### Electronic properties of graphene quantum ring with wedge disclination

- PhysicsThe European Physical Journal B
- 2021

We study the energy spectrum and persistent current of charge carriers confined in a graphene quantum ring geometry of radius R and width w subject to a magnetic flux. We consider the case where the…

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