Three-dimensional Flat-Band Models

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Typical three-dimensional flat-band models of tight-binding electronic systems on cubic and diamond lattices are presented to demonstrate the wide applicability of the method proposed by Nishino et al. [J. Phys. Soc. Jpn. 72 (2003) 2015]. Both forms of the model are realistic examples of three-dimensional flat-band models and are different from those discussed by Mielke and Tasaki [Commun. Math. Phys. 158 (1993) 341]. They can be applied even to the ultimate case in which all of the dispersion curves are flat even though many parameters do not vanish. According to the main idea of finding a localized eigenfunction in the periodic system, we derive some conditions between transfer integrals under which flat bands can exist. We expect these two examples to demonstrate the realistic flat-band models in three dimensions, as the Kagome lattice does in two dimensions.

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