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Abstract Kagome materials have become solid grounds to study the interplay among geometry, topology, correlation, and magnetism. Recently, niobium halide semiconductors Nb 3 X 8 ( X  = Cl, Br, I) have been predicted to be two-dimensional magnets and these materials are also interesting for their breathing kagome geometry. However, experimental electronic structure studies of these promising materials are still lacking. Here, we report the spectroscopic evidence of flat and weakly dispersing bands in breathing-kagome semiconductor Nb 3 I 8 around 500 meV binding energy, which is well supported by our first-principles calculations. These bands originate from the breathing kagome lattice of niobium atoms and have niobium d -orbital character. They are found to be sensitive to the polarization of the incident photon beam. Our study provides insight into the electronic structure and flat band topology in an exfoliable kagome semiconductor, thereby providing an important platform to understand the interaction of geometry and electron correlations in two-dimensional materials.

Euclidean geometry is the fundamental mathematical framework of classical crystallography. Traditionally, layered materials are grown on flat substrates; growing Euclidean crystals on non-Euclidean surfaces has rarely been studied. We present a general model describing the growth of layered materials with screw-dislocation spirals on non-Euclidean surfaces and show that it leads to continuously twisted multilayer superstructures. This model is experimentally demonstrated by growing supertwisted spirals of tungsten disulfide (WS₂) and tungsten diselenide (WSe₂) draped over nanoparticles near the centers of spirals. Microscopic structural analysis shows that the crystal lattice twist is consistent with the geometric twist of the layers, leading to moiré superlattices between the atomic layers.