Revealing the non-adiabatic and non-Abelian multiple-band effects via anisotropic valley Hall conduction in bilayer graphene

TL;DR

This paper investigates how non-adiabatic and non-Abelian multiple-band effects influence valley Hall conduction in bilayer graphene, revealing significant anisotropic responses and contributions from interband transitions beyond traditional adiabatic Berry curvature effects.

Contribution

It demonstrates the dominant role of non-adiabatic interband transitions in Hall conduction and elucidates anisotropic responses linked to non-Abelian Berry curvature in bilayer graphene.

Findings

Non-adiabatic transitions contribute an order-of-magnitude more to Hall current than adiabatic ones.

Anisotropic Hall responses are caused by trigonal warping and differ between diagonal and off-diagonal Berry curvature elements.

Distinct anisotropic features are explained through band occupations and interband coherence.

Abstract

Many quantum materials of interest, ex., bilayer graphene, possess a number of closely spaced but not fully degenerate bands near the Fermi level, where the coupling to the far detuned remote bands can induce Berry curvatures of the non-Abelian character in this active multiple-band manifold for transport effects. Under finite electric fields, non-adiabatic interband transition processes are expected to play significant roles in the associated Hall conduction. Here through an exemplified study on the valley Hall conduction in AB-stacked bilayer graphene, we show that the contribution arising from non-adiabatic transitions around the bands near the Fermi energy to the Hall current is not only quantitatively about an order-of-magnitude larger than the contribution due to adiabatic inter-manifold transition with the non-Abelian Berry curvatures. Due to the trigonal warping, the former also displays an anisotropic response to the orientation of the applied electric field that is qualitatively distinct from that of the latter. We further show that these anisotropic responses also reveal the essential differences between the diagonal and off-diagonal elements of the non-Abelian Berry curvature matrix in terms of their contributions to the Hall currents. We provide a physically intuitive understanding of the origin of distinct anisotropic features from different Hall current contributions, in terms of band occupations and interband coherence. This then points to the generalization beyond the specific example of bilayer graphenes.