Fractal Butterflies of Dirac Fermions in Monolayer and Bilayer graphene

TL;DR

This paper reviews the theoretical and experimental progress in understanding Hofstadter butterflies in monolayer and bilayer graphene, highlighting the role of Moiré patterns and electron interactions in revealing fractal energy spectra.

Contribution

It provides a comprehensive overview of the theoretical background, experimental detection, and future prospects of fractal energy spectra in graphene systems, emphasizing the influence of Moiré patterns and interactions.

Findings

Experimental detection of fractal energy spectra in graphene.

Role of Moiré patterns in butterfly structure formation.

Impact of electron-electron interactions on the Hofstadter spectrum.

Abstract

We present an overview of the theoretical understanding of Hofstadter butterflies in monolayer and bilayer graphene. After a brief introduction on the past work in conventional semiconductor systems, we discuss the novel electronic properties of monolayer and bilayer graphene that helped to detect experimentally the fractal nature of the energy spectrum. We have discussed the theoretical background on the Moir\'e pattern in graphene. This pattern was crucial in determining the butterfly structure. We have also touched upon the role of electron-electron interaction in the butterfly pattern in graphene. We conclude by discussing the future prospects of butterfly search, especially for interacting Dirac fermions.