High-throughput discovery of moir\'e homobilayers guided by topology and energetics

Abstract

Van der Waals heterostructures promise on-demand designer quantum phases through control of monolayer composition, stacking, twist angle, and external fields. Yet, experimental efforts have been narrowly focused, leaving much of this vast moir\'e landscape unexplored and potential promises unrealized. Here, we present a scalable workflow for high-throughput characterization of twisted homobilayers and apply it to $K$-valley semiconductors. Combining small-scale density functional theory with perturbation theory, we efficiently extract moir\'e band gaps, valley Chern numbers, magic angles, and the threshold for lattice relaxation. Beyond this rapid high-throughput characterization, we parameterize a continuum model for each material, which provides a starting point for more detailed study. Our survey delivers an actionable map for systematic exploration of correlated and topological phases in moir\'e homobilayers, and identifies promising new platforms: chromium-based transition metal dichalcogenides for high-temperature quantum anomalous Hall effects, transition metal nitride halides for intertwined superconducting and moir\'e physics, and atomically thin $\rm{III-V}$ semiconductors for room-temperature-scale moir\'e effects.