Topological phonons in anomalous Hall crystals

Anomalous Hall crystals (AHCs) are an exotic phase of matter in which electrons in the presence of sufficiently concentrated Berry curvature spontaneously crystallize, forming an insulator that exhibits the quantum anomalous Hall effect (QAHE). Owing to the recent observation of an extended integer QAHE phase in rhombohedral pentalayer graphene (R5G), AHCs have become the focus of intense theoretical and experimental study. Using the time-dependent Hartree-Fock (tdHF) approach, we study collective excitations of the Wigner crystals (WCs) and AHCs that arise in toy models for R5G. We find that both time-reversal broken WCs and AHCs can host topologically non-trivial phonon and exciton modes. We also study how the topology of these modes changes in the presence of a (moiré) periodic potential, and discuss experimental probes for detecting the neutral chiral edge modes that accompany (quasi-)bosonic bands with finite Chern numbers.