Optical properties of the Hofstadter butterfly in the Moir\'{e} superlattice

TL;DR

This paper explores the fractal optical properties of the Hofstadter butterfly in twisted bilayer graphene, revealing self-similar absorption spectra and selection rules governed by angular momentum conservation.

Contribution

It uncovers the recursive optical absorption patterns and nested selection rules in the Hofstadter butterfly spectrum of twisted bilayer graphene.

Findings

Optical absorption spectrum shows self-similar recursive patterns.

Optical selection rules have a nested self-similar structure.

Conservation of total angular momentum governs the selection rules.

Abstract

We investigate the optical absorption spectrum and the selection rule for the Hofstadter butterfly in twisted bilayer graphene under magnetic fields. We demonstrate that the absorption spectrum exhibits a self-similar recursive pattern reflecting the fractal nature of the energy spectrum. We find that the optical selection rule has a nested self-similar structure as well, and it is governed by the conservation of the total angular momentum summed over different hierarchies.