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Finally, we examine the various line-graph lattices detected and highlight those with gapped flat bands and those most frequently represented among this set of materials. We also identify materials which may exhibit flat topological bands. In particular, we find materials with line-graph-lattice structures beyond the two most commonly known examples, the kagomé and pyrochlore lattices. Based on that work, we conduct a high-throughput screening for line-graph lattices among the crystalline structures of the Materials Flatband Database and report on new candidates for line-graph materials and lattice models. In quantum simulation, such bands have been realized through line-graph lattices, a class of lattices known to exhibit flat bands.
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