Non-adiabatic Hall effect with non-Abelian Berry curvature in bilayer graphene

For Bloch electrons moving in an external electric field, the coupling to remote bands with energy separation large compared to the field is well captured by the adiabatic approximation, which can manifest as the Berry curvature that gives rise to the Hall effect. On the other hand, when there are nearly degenerate bands, the non-perturbative inter-band transition between them can also induce a non-adiabatic Hall effect as recently discussed in monolayer graphene with a small gap. Here we consider an AB-stacked bilayer graphene system where both scenarios are relevant. The interband transitions between the lowest conduction band and top valence band are non-perturbatively treated, whereas their coupling to the higher energy bands result in non-Abelian Berry curvature in this two-band manifold. We find contributions to the current from both the non-Abelian Berry curvature and the interband coherence within the two-band manifold.