Twisted bilayer graphene as topological heavy fermion: II. Analytical approximations of the model parameters

The recently-introduced Topological Heavy Fermion (THF) model [Phys. Rev. Lett. 129, 047601] of twisted bilayer graphene (TBG) aims to reconcile the quantum-dot-like electronic structure latter observed by scanning tunneling microscopy, with its electron delocalization seen in transport measurements. THF achieves this coupling localized (heavy) fermions anomalous conduction electrons. Originally, parameters were obtained numerically from Bistritzer-Macdonald (BM) TBG 047601]. In work, we derive analytical expressions for as a function twist angle, ratio between amplitudes at $AA$ and $AB$ regions ($w_0 / w_1$), screening length interaction potential. By computing across an extensive experimentally-relevant parameter space, show that resulting approximations are remarkably good, i.e. within 30% relative error almost entire space. At single-particle level, accurately captures energy spectrum BM over large phase space angles amplitude ratios. When interactions included, also description is good around magic angle realistic values ratios ($0.6 \leq w_0/w_1 1.0$), which hybridization $\gamma$ smaller than onsite repulsion heavy $U_1$ (i.e. $|\gamma| < U_1$).