Layer Hall counterflow as a model probe of magic-angle twisted bilayer graphene

The recent constructions of flat moir\'e minibands in specifically twisted multilayer graphene and twisted transition metal dichalcogenides (TMDs) have facilitated the observation of strong correlations with convenient tunability. These correlations in flat bands result in band dispersion heavily influenced by carrier densities, leading to filling-dependent quasiparticle band renormalizations. Particularly, in magic-angle twisted bilayer graphene (MATBG), the band structure---including the quasiparticle energy and wave function---is crucial in understanding the correlated properties. Previous theoretical studies have demonstrated the presence of a time-reversal-even charge Hall counterflow in response to a direct current (DC) electric field in twisted bilayers as chiral structures. In this study, we show that such layer Hall counterflow can serve as a sensitive probe for MATBG model parameters, which are currently ambiguous as a result of unavoidable structural relaxation and twist-angle disorder. We present the layer Hall counterflow and the associated in-plane magnetization for three different MATBG continuum models, based on which many-body interacting models have been widely applied to study strong correlations in MATBG. At the single-particle level, our findings indicate notable differences in layer-projected Hall conductivity, both in magnitude and sign, between different MATBG continuum models. Furthermore, our self-consistent Hartree calculations, performed on each of these single-particle continuum models, reveal renormalized layer-projected Hall conductivity by the self-consistent Hartree field.