Emergent Kagome lattice and non-Abelian lattice gauge field of biexcitons in t-MoTe$_2$

Abstract: Non-Abelian gauge fields, characterized by their non-commutative symmetry groups, shape physical laws from the Standard Model to emergent topological matter for quantum computation. Here we find that moir\'e exciton dimers (biexcitons) in twisted bilayer MoTe$_2$ are governed by a genuine non-Abelian lattice gauge field. These dipolar-bound exciton dimers, formed on bonds of the honeycomb moir\'e superlattice, exhibit three quadrupole configurations organized into a Kagome lattice geometry, on which the valley-flip biexciton hoppings through electron-hole Coulomb exchange act as link variables of the non-Abelian lattice gauge theory. The emergence of gauge structure here is a new possibility for composite particles, where the moir\'e electronic structure and interactions between the electron and hole constituents jointly enforce the underlying geometric constraint. The quadrupole nature of biexciton further makes possible local gate controls to isolate designated pathways from the extended lattice for exploiting consequences of non-commutative gauge structure including the genuine non-Abelian Aharonov-Bohm effect. This also provides a new approach for quantum manipulation of excitonic valley qubit. We show path interference on a simplest loop can deterministically transform the computational basis states into Bell states.