Flat-band solutions in $D$-dimensional decorated diamond and pyrochlore lattices: Reduction to molecular problem

摘要: Flat-band models have been of particular interest from both fundamental aspects and realization in materials. Beyond the canonical examples such as Lieb lattices line graphs, a variety tight-binding are found to possess flat bands. However, analytical treatment dispersion relations is limited, especially when there multiple bands with different energies. In this paper, we present how determine flat-band energies wave functions on decorated diamond pyrochlore generic dimensions $D \geq 2$. For two three dimensions, lattice structures relevant various organic inorganic materials, thus our method will be useful analyze band these