High-throughput discovery of moiré homobilayers guided by topology and energetics

TL;DR

This work addresses the vast moiré landscape of twisted K-valley semiconductors by introducing a scalable, high-throughput workflow that combines small-scale DFT with perturbation theory to rapidly extract moiré band gaps, valley Chern numbers, and magic angles, along with a lattice-relaxation threshold. The method yields material-specific continuum-model parameters, enabling an actionable map for exploring correlated and topological phases in moiré homobilayers. Key findings include a substantial prevalence of topological moiré bands (≈42%), identification of chromium-based TMDs and transition-metal nitride halides as platforms for high-temperature QAH and moiré-induced superconductivity, and the prospect of room-temperature moiré effects in atomically thin III–V semiconductors. The results provide a practical path for targeted experimental searches and deeper theoretical studies, supported by publicly available parameter tables and relaxed structures.

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 moiré 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 moiré 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 moiré 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 moiré physics, and atomically thin $\rm{III-V}$ semiconductors for room-temperature-scale moiré effects.

Figures (7)

• Figure 1: Schematic representation of our workflow for high-throughput characterization of twisted semiconducting homobilayers. (a) Starting from the list of twistable materials identified in Ref. jiang20242d, (b) small-scale commensurate DFT calculations efficiently characterize the moiré field variations across the long-wavelength moiré pattern, which (c) allows a rapid estimation of the valley-resolved Chern number, moiré band gap, and magic angle via perturbation theory crepel2025efficient. This perturbative limit is analytically justified when the moiré period is large compared to the monolayer lattice constant but small enough that the monolayer kinetic energy exceeds the moiré potentials and in-plane lattice relaxation remains weak, which typically holds for twist angles $\theta \gtrsim 3^\circ$.
• Figure 2: High-throughput characterization of moiré properties for all $K$-valley semiconducting moiré homobilayers. Each horizontal line corresponds to a theoretically stable twistable material with either (a) an electron-like or (b) a hole-like $K$-valley pocket jiang20242d; dashed (solid) gray lines indicates the presence (absence) of spin-orbit coupling. The left panels of (a) and (b) summarize the results of our perturbation theory crepel2025efficient: the position of the markers and the adjacent value gives the moiré gap amplitude (gaps $>30$meV are clipped on the edge) and their color encodes the topology of the bilayer (red for topological, gold for trivial). The right panels show the estimated magic angles (stars) and twist angles $\theta_{\rm relax}$ where in-plane lattice relaxation becomes significant (triangles, none if elastic coefficients are not available). Our predictions are only formally justified above this relaxation threshold (thick colored line). Names of certain material families are colored for reference in the text: transition metal dichalcogenides (purple), transition metal nitride halides (blue), transition metal phosphorus trichalcogenide (green), and a selection of one-atom thick componds (brown). The two lines labeled SnPS$_3$ represent different crystal structures with the same chemical composition; see full list of parameters in Methods.
• Figure 3: Moiré band structures for the continuum model of (a) hole-doped CrTe$_2$, a magnetic topological insulator; (b) eletron-doped ZrNCl, a 2d superconductor; and (c) hole-doped GaP, a large-angle moiré material. Their twist angles are $\theta = 2.0^\circ$, $2.5^\circ$, and $7.0^\circ$, respectively. The blue integers indicate the valley Chern numbers, the red arrow shows the doping direction. The inset in the upper-left shows the moiré Brillouin zone.
• Figure 4: Electric field amplitude produced within the ferroelectric domains for the 20 $K$-valley semiconductors with the highest values. Symbols, colors, and linestyles follow those of Fig. \ref{['fig_fullclassification']}. The spin-orbit coupled listed ZrNBr in the second row has a different lattice structure but identical chemical composition than the ZrNBr listed in Fig. \ref{['fig_fullclassification']} without spin-orbit coupling; see full list of parameters in Methods.
• Figure S1: (a) 1st harmonic of the continuum model renormalized by in-plane relaxation, obtained by minimization of the bilayer lattice energy as a function of atomic displacements for ZrBr$_2$. The red solid line, red dashed line, and blue line represent $v_{\rm eff}$, $w_{\rm eff}$, and $\psi_{\rm eff}$, respectively. The left vertical axis shows the energy scale for $v_{\rm eff}$ and $w_{\rm eff}$ in meV, while the right vertical axis shows the angle (in degrees) for $\psi_{\rm eff}$. (b) Chern number obtained from perturbation theory; a transition to a topological band is observed as the twist angle is reduced below $1^\circ$.