Light-Matter Interactions of Wannier-Obstructed Correlated Quantum Materials

Two-dimensional moiré heterostructures and interacting flat bands have recently emerged as strongly correlated electron systems with geometric obstructions to the formation of well-localized Wannier functions. Much of the interesting properties of such systems can be revealed from their low-frequency optical responses; however, while these should in principle be dictated by the low-energy dynamics of correlated electrons, isolating the low-energy bands of the light-matter-coupled Hamiltonian can easily violate gauge invariance. Here, we present a quantum geometric interpretation of this violation and the subsequent failure of conventional velocity gauge calculations. We provide a new prescription that factors in geometrical effects via additional Berry phase contributions that couple photons to both electron kinetics and electronic interactions. The mechanism is demonstrated on a strongly interacting 1D chain with emergent bond density wave order, which hosts a flat symmetry-protected topological band with tunable Wannier function spread. We show that our theory faithfully captures its full non-equilibrium dynamics for low-frequency optical driving fields and presents a quantum geometric interpretation of its linear and non-linear THz optical responses. Applications of the theory to two-dimensional quantum materials will be discussed.