Elastic Response and Instabilities of Anomalous Hall Crystals

Anomalous Hall crystals (AHCs) are exotic phases of matter that simultaneously break continuous translation symmetry and exhibit the quantum anomalous Hall effect. AHCs have recently been proposed to explain the observation of an integer quantum anomalous Hall phase in a multilayer graphene system. Despite intense theoretical and experimental interest, little is known about the mechanical properties of AHCs. We study the elastic properties of AHCs first by using a continuum model with quadratic dispersion and uniform Berry curvature. We find using time-dependent Hartree-Fock that the stiffness of the AHC is an order of magnitude smaller than that of the WC, which we attribute to the finite Chern number of the AHC preventing exponential localization of the charge density. By modifying the dispersion relation to include a local minimum modeled after that of rhombohedral pentalayer graphene (R5G), we find that deformations away from the triangular lattice minimize the AHC's kinetic energy, which overwhelms the small stiffness and triggers a mechanical instability. Using a microscopic model of R5G, we observe a similar mechanical instability over an experimentally relevant parameter regime. We conclude that the topologically limited stiffness of AHCs makes them susceptible to mechanical instabilities, an important consideration when interpreting experiments in terms of AHCs.