Narrow bands in magnetic field and strong-coupling Hofstadter spectra

TL;DR

This paper introduces a new method to compute Hofstadter spectra for narrow bands, including topological ones, and applies it to twisted bilayer graphene to explore Landau quantization in strong coupling regimes.

Contribution

The paper presents a novel, efficient approach to determine Hofstadter spectra for narrow bands, applicable to both topological and trivial cases, and applies it to twisted bilayer graphene.

Findings

First Hofstadter spectrum for strong-coupling excitations in twisted bilayer graphene.

Spectrum at low magnetic fields with flux ~1/25 of flux quantum.

Enables investigation of Landau levels in interaction-induced quasiparticles.

Abstract

We develop a new, efficient, and general method to determine the Hofstadter spectrum of isolated narrow bands. The method works for topological as well as for trivial narrow bands by projecting the zero $\mathbf{B}$-field hybrid Wannier states -- which are localized in one direction and Bloch extended in another direction -- onto a representation of the magnetic translation group in the Landau gauge. We then apply this method to find, for the first time, the Hofstadter spectrum for the exact single particle charged excitations in the strong coupling limit of the magic angle twisted bilayer graphene at the charge neutrality point and at $|\nu|=2$ down to low magnetic fields when the flux through the moir\'e unit cell is only $\sim 1/25$ of the electronic flux quantum i.e. $\sim 1$T at the first magic angle. The resulting spectra provide a means to investigate Landau quantization of the quasiparticles even if their dispersion is interaction induced.