The success of topological band theory and symmetry-based topological classification significantly advances our understanding of the Berry phase. Based on the critical concept of topological obstruction, efficient theoretical frameworks, including topological quantum chemistry and symmetry indicator theory, were developed, making a massive characterization of real materials possible. However, the classification of magnetic materials often involves the complexity of their unknown magnetic structures, which are often hard to know from experiments, thus, hindering the topological classification. In this paper, we design a high-throughput workflow to classify magnetic topological materials by automating the search for collinear magnetic structures and the characterization of their topological natures. We computed 1049 chosen transition metal compounds (TMCs) without oxygen and identified 64 topological insulators and 53 semimetals, which become 73 and 26 when U correction is further considered. Due to the lack of magnetic structure information from experiments, our high-throughput predictions provide insightful reference results and make the first step towards a complete diagnosis of magnetic topological materials.

Flat bands are rare in pristine solid systems and are unstable against electronic correlations or other types of order. Compared to the atomic scale Hubbard systems and the Moiré materials, where the electronic correlations are confined to the lattice sites in the former and operate in a long-range fashion in the latter, flat band systems with short-range interactions that are free of spontaneous symmetry breaking are severely lacking. Such systems would nicely interpolate the atomic Mott insulator and the Moiré correlated insulators, providing a platform for understanding the connection of the two phases. With elegant analytical analysis and further verified by advanced numerical calculations, we convincingly reveal that monolayer Nb3Cl8 is a novel pristine flat band system with short-range nonlocal interactions. We provide strong evidence for it being a cluster Mott insulator and argue that it may constitute a rare candidate for molecular quantum spin liquid with flat bands. Furthermore, based on the cluster Mott insulator picture, we nicely solved the discrepancy recently observed in angle-resolved photoemission spectroscopy and density-functional theory calculations.