Energy Levels of Graphene Magnetic Circular Quantum Dot

TL;DR

This paper analytically investigates the energy spectrum of a graphene magnetic quantum dot, revealing how energy levels depend on system parameters and exhibit interface states and energy gaps.

Contribution

It provides analytical solutions for energy levels in a graphene magnetic quantum dot system considering electrostatic potential and boundary conditions.

Findings

Energy levels depend on quantum dot radius, magnetic field, and electrostatic potential.

Energy spectrum shows interface state characteristics.

Presence of an energy gap in the spectrum.

Abstract

We study the energy levels of graphene magnetic circular quantum dot surrounded by an infinite graphene sheet in the presence of an electrostatic potential. We solve Dirac equation to derive the solutions of energy spectrum associated with different regions composing our system. Using the continuum model and applying boundary conditions at the interface, we obtain analytical results for the energy levels. The dependence of the energy levels on the quantum dot radius, magnetic field and electrostatic potential is analyzed for the two valleys $K$ and $K'$. We show that the energy levels exhibit characteristics of interface states and have an energy gap.