Interacting narrow bands of twisted bilayer graphene in magnetic field
The recently introduced topological heavy fermion model [1] 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. It successfully recovers, and naturally explains, the spectrum of single particle excitations of interacting ground states at integer fillings of the narrow bands. In order to understand the Landau quantization of the ensuing electronic spectrum and compare it with existing experimental data, a generalization of topological heavy fermion model to include the magnetic field B is desired. I will discuss a systematic derivation of the topological heavy fermion mode in B and its solution, obtaining the interacting Hofstadter spectra for single particle charged excitations [2], comparing it to previous numerical results [3]. While naïve minimal substitution fails to correctly account for the total number of magnetic subbands within the narrow band i.e. its total Chern number, our novel 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 offer an intuitive understanding of the nature of the strongly interacting Hofstadter bands.
[1] Zhi-Da Song and B. Andrei Bernevig, PRL 129, 047601 (2022)
[2] K. Singh et al, arXiv:2305.08171
[3] X. Wang and O. Vafek, PRB 106, L121111 (2022)