Excitation Gap of Fractal Quantum Hall States in Graphene

TL;DR

This paper develops a Hartree-Fock theoretical framework to analyze electron-electron interactions in fractal Hofstadter's butterfly states in graphene, revealing excitation gaps consistent with experimental results.

Contribution

It introduces a novel Hartree-Fock approach incorporating spin and valley degrees of freedom to study fractal quantum Hall states in graphene.

Findings

Excitation gaps match experimental observations.

Theoretical results are consistent between finite and infinite samples.

Electron crystal model captures key features of Hofstadter's butterfly states.

Abstract

In the presence of a magnetic field and an external periodic potential, the Landau level spectrum of a two-dimensional electron gas exhibits a fractal pattern in the energy spectrum which is described as the Hofstadter's butterfly. In this work, we develop a Hartree-Fock theory to deal with the electron-electron interaction in the Hofstadter's butterfly state in a finite-size graphene with periodic boundary conditions, in which we include both spin and valley degrees of freedom. We then treat the butterfly state as an electron crystal so that we could obtain the order parameters of the crystal in the momentum space and also in an infinite sample. The excitation gaps obtained in the infinite sample is comparable to those in the finite-size study, and agree with a recent experimental observation.