Aharonov-Bohm-Coulomb Problem in Graphene Ring
arXiv:1104.0369 · doi:10.1088/1751-8113/45/5/055301
Abstract
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 on the energy spectrum of Dirac electrons in the graphene ring in two different ways: one for the scalar coupling and the other for the vector coupling. It is found that, since the potential in the scalar coupling breaks the time-reversal symmetry between the two valleys as well as the effective time-reversal symmetry in a single valley, the energy spectrum of one valley is separated from that of the other valley, demonstrating a valley polarization. In the vector coupling, however, the potential does not break either of the two symmetries and its effect appears only as an additive constant to the spectrum of Aharonov-Bohm potential. The corresponding persistent currents, the observable quantities of the symmetry-breaking energy spectra, are shown to be asymmetric about zero magnetic flux in the scalar coupling, while symmetric in the vector coupling.
20 pages, 12 figures (V2) 18 pages, accepted in JPHYSA
References in corpus (21)
- The electronic properties of graphene
- Substrate-induced band gap opening in epitaxial graphene
- Valley filter and valley valve in graphene
- Andreev reflection and Klein tunneling in graphene
- Spin qubits in graphene quantum dots
- Aharonov-Bohm effect and broken valley-degeneracy in graphene rings
- Casimir interaction between a perfect conductor and graphene described by the Dirac model
- Chiral Gauge Theory for Graphene
- Bound states and magnetic field-induced valley splitting in gate-tunable graphene quantum dots
- The Schwinger mechanism and graphene
- Graphene Rings in Magnetic Fields: Aharonov-Bohm Effect and Valley Splitting
- Weyl-Gauge Symmetry of Graphene
- Interplay of the Aharonov-Bohm effect and Klein tunneling in graphene
- Aharonov-Bohm effect in undoped graphene: Magnetotransport via evanescent waves
- Planar QED at finite temperature and density: Hall conductivity, Berry's phases and minimal conductivity of graphene
- Electronic Properties and Hidden Symmetries of Graphene
- Persistence of zero modes in a gauged Dirac model for bilayer graphene
- An Index Theorem for Graphene
- Quantum Hall effect in graphene: A functional determinant approach
- Electronic zero modes of vortices in Hall states of gapped graphene
- Induced Current and Aharonov-Bohm Effect in Graphene