Hofstadter Butterfly in Graphene

TL;DR

This review summarizes recent advances in observing the Hofstadter butterfly fractal spectrum in graphene, focusing on experimental realizations using various superlattice structures like graphene-hBN and twisted bilayer graphene.

Contribution

It provides a comprehensive overview of how the Hofstadter butterfly spectrum has been realized and studied in graphene systems, highlighting experimental techniques and specific superlattice configurations.

Findings

Observation of fractal Hofstadter spectra in graphene-hBN superlattices

Identification of Hofstadter butterfly features in twisted bilayer graphene

Discussion of experimental methods to realize fractal spectra in graphene

Abstract

This is a short review of the recent progresses on Hofstadter butterfly in graphene, organized in the following. We first briefly introduce the Hofstadter butterfly, including the theoretic toy model of Bloch electrons in the magnetic field, the resulting Harper's equation and its solution, and realizations in non-graphene systems. Then, we discuss the ways to realize the fractal Hofstadter spectra in graphene, and introduce three types of graphene superlattice structure, including graphene-hBN, twisted graphene layers, nanofabricated graphene superlattice. In particular, details about the fractal Hofstadter spectrum in graphene will be focused and discussed in the graphene-hBN superlattice and the twisted bilayer graphene.