Symmetry-enforced Moiré Topology

Topological flat bands in two-dimensional (2D) moiré materials have emerged as promising platforms for exploring the interplay between topology and correlation effects. However, realistic calculations of moiré band topology using density functional theory (DFT) are computationally inefficient due to the large number of atoms in a single moiré unit cell. In this work, we propose a systematic scheme to predict the topology of moiré bands from atomic symmetry data and moiré symmetry group, both of which can be efficiently extracted from DFT. Specifically, for Γ-valley electron gases, we find that certain combinations of atomic symmetry data and moiré symmetry groups can enforce nontrivial band topology in the low-energy moiré bands, as long as the moiré band gap is smaller than the atomic band splitting at the moiré Brillouin zone boundary. This symmetry-enforced nontrivial moiré topology, including both topological insulators and topological semimetals, is robust against various material-specific details such as the precise form and strength of the moiré potential or the exact twist angle. By exhaustively scanning all 2D atomic symmetry data and moiré symmetry groups, we identify 197 combinations that can yield symmetry-enforced nontrivial moiré topology, and we verify one such combination using a moiré model with cubic Rashba spin-orbit coupling. Our approach is generalizable to other valleys and provides a useful guideline for experimental efforts to discover and design new topologically nontrivial moiré materials.