Efficient prediction of superlattice and anomalous miniband topology from quantum geometry

Two dimensional materials subject to long-wavelength modulations have emerged as novel platforms to study topological and correlated quantum phases. In this article, we develop a versatile and computationally inexpensive method to predict the topological properties of materials subjected to a superlattice potential by combining degenerate perturbation theory with the method of symmetry indicators. In the absence of electronic interactions, our analysis provides a systematic rule to find the Chern number of the superlattice-induced miniband starting from the harmonics of the applied potential and a few material-specific coefficients. Our method also applies to anomalous (interaction-generated) bands, for which we derive an efficient algorithm to determine all Chern numbers compatible with a self-consistent solution to the Hartree-Fock equations. Our approach gives a microscopic understanding of the quantum anomalous Hall insulators recently observed in rhombohedral graphene multilayers.