TBG as Topological Heavy Fermion II: Analytical approximations of the model parameters and enlarged continuous symmetries*

The recently-introduced Topological Heavy-Fermion (THF) model [1] of twisted bilayer graphene (TBG) aims to reconcile the quantum-dot-like electronic structure of the latter observed by scanning tunneling microscopy, with its electron delocalization seen in transport measurements. The THF model achieves this by coupling localized fermions with anomalous conduction electrons. Originally, the parameters of the THF model were obtained numerically from the Bistritzer-Macdonald (BM) model of TBG [1]. In this work, we derive analytical expressions for the THF model parameters using tractable BM model approximations [2]. By numerically computing the THF model parameters across a vast experimentally-relevant parameter space, we show that the resulting approximations are remarkably good, i.e. within the 20% relative error for almost the entire parameter space.  Finally, we derive enlarged continuous symmetries of the interaction Hamiltonian that arise in various limits of the model.

References:

[1]    Z. Song et al. Phys. Rev. Lett. 129, 047601 (2022)

[2]    B. A. Bernevig et al. Phys. Rev. B 103, 205411 (2021)

Funding:

We acknowledge the following support: Schmidt Fund for Innovative Research, Simons Investigator Grant No. 404513, DOE Grant No. DE-SC0016239, ERC No. 101020833, DOE grant DE-FG02-99ER45790.