Genuine non-Abelian Berry phase in inhomogeneously strained moir\'e pattern

Periodicity of long wavelength moir\'e patterns is often destroyed by 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 patterns of transition metal dichalcogenides homobilayers, accounting for the dynamics of layer pseudospin [1]. 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 (AB) 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 AB effect in such field, where the evolution operators for different loops are noncommutative. 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.

[1] Dawei Zhai and Wang Yao, submitted.