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

TL;DR

This paper derives analytical expressions for energy levels and eigenstates of carriers in graphene quantum rings, incorporating magnetic effects, to better understand their spectral properties.

Contribution

It introduces a simplified analytical model for graphene quantum rings that captures key spectral features including magnetic field effects.

Findings

Analytical eigenvalues and eigenstates for graphene quantum rings.

Observation of Aharonov-Bohm oscillations.

Identification of a non-zero energy gap in the spectrum.

Abstract

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.