Analytic Model for the Energy Spectrum of a Graphene Quantum Dot in a Perpendicular Magnetic Field

Abstract

We analytically calculate the energy spectrum of a circular graphene quantum dot with radius R subjected to a perpendicular magnetic field B by applying the infinite-mass boundary condition. We can retrieve well-known limits for the cases R, B going to infinity and B going to zero. Our model is capable of capturing the essential details of recent experiments. Quantitative agreement between theory and experiment is limited due to the fact that a circular dot is not close enough to the experimental geometry, that disorder plays a significant role, and that interaction effects may be relevant.

arXiv comment4 pages, 3 figures

References in corpus (7)

• Electric Field Effect in Atomically Thin Carbon Films
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Chaotic Dirac billiard in graphene quantum dots
• Boundary conditions for Dirac fermions on a terminated honeycomb lattice
• Tuning of energy levels and optical properties of graphene quantum dots
• The Fock-Darwin States of Dirac Electrons in Graphene-based Artificial Atoms

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