Layer pseudospin dynamics and genuine non-Abelian Berry phase in inhomogeneously strained moir\'e pattern

TL;DR

This paper develops a framework to describe the dynamics of layer pseudospin and non-Abelian Berry phases in inhomogeneously strained moiré patterns of transition metal dichalcogenides, revealing tunable non-Abelian gauge field effects.

Contribution

It introduces a model accounting for pseudospin dynamics and non-Abelian gauge fields in strained moiré structures, highlighting genuine non-Abelian Aharonov-Bohm effects.

Findings

Identification of in-plane pseudospin precession causes

Demonstration of non-Abelian gauge field effects

Observation of tunable non-Abelian Aharonov-Bohm effect

Abstract

Periodicity of long wavelength moir\'e patterns is very often destroyed by the inhomogeneous strain introduced in fabrications of van der Waals layered structures. We present a framework to describe massive Dirac fermions in such distorted moir\'e pattern of transition metal dichalcogenides homobilayers, accounting for the dynamics of layer pseudospin. In decoupled bilayers, we show two causes of in-plane layer pseudospin precession: By the coupling of layer antisymmetric strain to valley magnetic moment; and by the Aharonov-Bohm effect in the SU(2) gauge potential for the case of R-type bilayer under antisymmetric strain and H-type under symmetric strain. With interlayer coupling in the moir\'e, its interplay with strain manifests as a non-Abelian gauge field. We show a genuine non-Abelian Aharonov-Bohm effect in such field, where the evolution operators for different loops are non-commutative. This provides an exciting platform to explore non-Abelian gauge field effects on electron, with remarkable tunability of the field by strain and interlayer bias.