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

TL;DR

This paper proposes using layer Hall counterflow as a sensitive probe to distinguish and analyze different continuum models of magic-angle twisted bilayer graphene, aiding in understanding its correlated electronic properties.

Contribution

It demonstrates that layer Hall counterflow varies significantly across models, providing a new method to refine model parameters and study strong correlations in MATBG.

Findings

Layer Hall counterflow differs in magnitude and sign between models.

Self-consistent Hartree calculations show renormalized Hall conductivity.

Layer-projected Hall conductivity is sensitive to model details.

Abstract

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 a convenient tunability. These correlations in flat bands result in the 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 wavefunction--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.