A Simple Heavy Fermion Model for Twisted Bilayer Graphene in Flux

The flat bands and large Coulomb scale of twisted bilayer graphene allow the low energy degrees of freedom to be written in terms of heavy fermions hybridizing with conduction electrons [1]. This work puts forward a simplified generalization of this model in flux, allowing for an analytical description of twisted bilayer graphene in magnetic field. We compare our results with a strong coupling Hofstadter calculation at rational flux. Using the recently developed gauge invariant formalism [2], we are able to reach numerically extremely small fluxes, allowing us to compare the two methods and confirm their agreement. Due to the simple nature of the heavy fermion model, we are able to give an intuitive interpretation of the spectrum of TBG in flux and provide wavefunctions for the dominant, strongly correlated Landau levels.

[1] Z.-D. Song and B. A. Bernevig, Phys. Rev. Lett. 129, 047601 (2022)

[2] J. Herzog-Arbeitman, A. Chew, and B. A. Bernevig, Phys. Rev. B 106, 085140 (2022)