Energy spectra of graphene quantum dots induced between Landau levels

TL;DR

This paper investigates the energy spectra of graphene quantum dots formed between Landau levels, revealing conditions for simple, controllable spectra with potential for experimental probing, especially under specific magnetic fields and potential well configurations.

Contribution

It demonstrates that under certain conditions, the energy spectrum of a graphene quantum dot in a magnetic field simplifies, enabling easier experimental access and control, and introduces an approximate method for high magnetic fields.

Findings

The spectrum can be valley-specific with no crossings.

Large energy spacings are achievable for spectroscopic detection.

An approximate Dirac equation solution matches exact results at high fields.

Abstract

When an energy gap is induced in monolayer graphene the valley degeneracy is broken and the energy spectrum of a confined system such as a quantum dot, becomes rather complex exhibiting many irregular level crossings and small energy spacings which are very sensitive to the applied magnetic field. Here we study the energy spectrum of a graphene quantum dot that is formed between Landau levels, and show that for the appropriate potential well the dot energy spectrum in the first Landau gap can have a simple pattern with energies coming from one of the two valleys only. This part of the spectrum has no crossings, has specific angular momentum numbers, and the energy spacing can be large enough, consequently, it can be probed with standard spectroscopic techniques. The magnetic field dependence of the dot levels as well as the effect of the mass-induced energy gap are examined, and some regimes leading to a controllable quantum dot are specified. At high magnetic fields and negative angular momentum a simple approximate method to the Dirac equation is developed which gives further insight into the physics. The approximate energies exhibit the correct trends and agree well with the exact energies.