Simplified model for the energy levels of quantum rings in single layer and bilayer graphene

Details Simplified model for the energy levels of quantum rings in single layer and bilayer graphene Simplified model for the energy levels of quantum rings in single layer and bilayer graphene

2010-02-08

arxiv.org/abs/1002.1688v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

To appear in Phys. Rev. B

Scientific paper

Within a minimal model, we present analytical expressions for the eigenstates and eigenvalues of carriers confined in quantum rings in monolayer and bilayer graphene. The calculations were performed in the context of the continuum model, by solving the Dirac equation for a zero width ring geometry, i.e. by freezing out the carrier radial motion. We include the effect of an external magnetic field and show the appearance of Aharonov-Bohm oscillations and of a non-zero gap in the spectrum. Our minimal model gives insight in the energy spectrum of graphene-based quantum rings and models different aspects of finite width rings.

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