Auto-resolving the atomic structure at van der Waals interfaces using a generative model.

The high-resolution visualization of atomic structures is significant for understanding the relationship between the microscopic configurations and macroscopic properties of materials. However, a rapid, accurate, and robust approach to automatically resolve complex patterns in atomic-resolution microscopy remains difficult to implement. Here, we present a Trident strategy-enhanced disentangled representation learning method (a generative model), which utilizes a few unlabelled experimental images with abundant low-cost simulated images to generate a large corpus of annotated simulation data that closely resembles experimental results, producing a high-quality large-volume training dataset. A structural inference model is then trained via a residual neural network which can directly deduce the interlayer slip and rotation of diversified and complicated stacking patterns at van der Waals (vdW) interfaces with picometer-scale accuracy across various materials (e.g. MoS, WS, ReS, ReSe, and 1 T'-MoTe) with different layer numbers (bilayer and trilayers), demonstrating robustness to defects, imaging quality, and surface contaminations. The framework can also identify pattern transition interfaces, quantify subtle motif variations, and discriminate moiré patterns that are difficult to distinguish in frequency domains. Finally, the high-throughput processing ability of our method provides insights into a vdW epitaxy mode where various thermodynamically favorable slip stackings can coexist.