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.