Topological heavy fermions in magnetic field

TL;DR

This paper extends the topological heavy fermion model to include magnetic fields, deriving a method that accurately captures the Landau quantization and topological properties of twisted bilayer graphene's electronic spectrum.

Contribution

It provides a systematic derivation of the topological heavy fermion model in magnetic fields, enabling correct calculation of Hofstadter spectra and topological invariants.

Findings

Correctly reproduces the total Chern number of magnetic subbands.

Provides analytical understanding of strongly interacting Hofstadter bands.

Addresses limitations of naive minimal substitution in topological models.

Abstract

The recently introduced topological heavy fermion model (THFM) provides a means for interpreting the low-energy electronic degrees of freedom of the magic angle twisted bilayer graphene as hybridization amidst highly dispersing topological conduction and weakly dispersing localized heavy fermions. In order to understand the Landau quantization of the ensuing electronic spectrum, a generalization of THFM to include the magnetic field B is desired, but currently missing. Here we provide a systematic derivation of the THFM in B and solve the resulting model to obtain the interacting Hofstadter spectra for single particle charged excitations. While naive minimal substitution within THFM fails to correctly account for the total number of magnetic subbands within the narrow band i.e. its total Chern number, our method -- based on projecting the light and heavy fermions onto the irreducible representations of the magnetic translation group -- reproduces the correct total Chern number. Analytical results presented here offer an intuitive understanding of the nature of the (strongly interacting) Hofstadter bands.