A Catalogue of Topological Moir\'{e} Bands in Twisted Semiconductors

Abstract

Twisted two-dimensional semiconductors provide a route to flat and topological moir\'e minibands, but systematic principles for organizing their material dependence have remained unclear. Here, we establish a high-throughput framework that integrates structural relaxation, first-principles electronic structure calculations, and moir\'e band topology. We apply this framework to 43 experimentally realized monolayers and 91 symmetry-inequivalent bilayer prototypes, yielding over 1,000 angle-resolved moir\'e electronic band structures. This database reveals that the low-energy moir\'e electronic structure is organized primarily by the valley character of the parent band edge together with stacking symmetry. In $\Gamma$-valley systems, the miniband width usually follows a nearly quadratic twist-angle scaling, consistent with a folding-dominated kinetic-energy scale. In $K$-valley systems, stacking-controlled interlayer hybridization governs whether parent Berry curvature is redistributed into isolated valley Chern minibands. By contrast, $M$-valley systems form a more material-specific class associated with anisotropic and symmetry-constrained band folding. The same valley-and-stacking hierarchy rationalizes the emergence or suppression of $\mathbb{Z}_2$ minibands, and surface termination in Janus bilayers provides a microscopic knob for changing the relevant valley character. These results establish a materials-level organizing principle for designing flat and topological moir\'e bands in twisted semiconductors.