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

TL;DR

This paper presents an analytical model for the energy spectrum of a circular graphene quantum dot under a perpendicular magnetic field, aligning with experimental observations but limited by geometric and disorder factors.

Contribution

The authors develop an analytical approach to calculate the energy spectrum of a graphene quantum dot with magnetic field effects, including boundary conditions and known limits.

Findings

Model captures essential experimental features

Quantitative discrepancies due to geometry and disorder

Provides a basis for understanding magnetic effects in graphene dots

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.