Network model and four-terminal transport in minimally twisted bilayer graphene

TL;DR

This paper models electronic transport in minimally twisted bilayer graphene, revealing how valley Hall states form a network with tunable modes, leading to observable Aharonov-Bohm resonances and Hall responses under various fields.

Contribution

It introduces a two-channel scattering model based on symmetry for the valley Hall network, analyzing transport phenomena and resonances in twisted bilayer graphene.

Findings

A phenomenological parameter tunes between zigzag modes and pseudo-Landau levels.

Robust Aharonov-Bohm resonances are observed in longitudinal conductance.

Finite Hall response occurs when zigzag branches are weakly coupled, revealing Hofstadter physics.

Abstract

We construct a two-channel scattering model for the triangular network of valley Hall states in interlayer-biased minimally twisted bilayer graphene from symmetry arguments and investigate electronic transport in a four-terminal setup. In the absence of forward scattering, a single phenomenological parameter tunes the network between a triplet of chiral zigzag modes and pseudo-Landau levels. Moreover, the chiral zigzag modes give rise to robust Aharonov-Bohm resonances in the longitudinal conductance in the presence of a perpendicular magnetic field or an in-plane electric field. Interestingly, we find that when both a magnetic field and an in-plane electric field are applied, the resonances of different zigzag branches split depending on their propagation direction relative to the in-plane electric field. We further demonstrate that while the Hall response vanishes in the chiral zigzag regime, a finite Hall response is obtained without destroying the Aharonov-Bohm resonances in the longitudinal response, by weakly coupling different zigzag branches, which also gives rise to Hofstadter physics at accessible magnetic fields.