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We report the results of our theoretical and numerical study on electronicand transport properties of fermion systems with charge frustration. Weconsider an extended Falicov-Kimball model in which itinerant spinless fermionsinteract repulsively by U with localized particles whose distribution satisfiesa local constraint under geometrical frustration, the so-called ice rule. Wenumerically calculate the density of states, optical conductivity, and inverseparticipation ratio for the models on the pyrochlore, checkerboard, and kagomelattices, and discuss the nature of metal-insulator transitions at commensuratefillings. As a result, we show that the ice-rule local constraint leads toseveral universal features in the electronic structure; a charge gap opens at aconsiderably small U compared to the bandwidth, and the energy spectrumapproaches a characteristic form in the large U limit, that is, thenoninteracting tight-binding form in one dimension or the $\delta$-functionalpeak. In the large U region, the itinerant fermions are confined in themacroscopically-degenerate ice-rule configurations, which consist of a bunch ofone-dimensional loops: We call this insulating state the charge ice. On theother hand, transport properties are much affected by the geometry anddimensionality of lattices; e.g., the pyrochlore lattice model exhibits atransition from a metallic to the charge-ice insulating state by increasing U,while the checkerboard lattice model appears to show Anderson localizationbefore opening a gap. Meanwhile, in the kagome lattice case, we do not obtainclear evidence of Anderson localization. Our results elucidate the universalityand diversity of phase transitions to the charge-ice insulator in fullyfrustrated lattices.

Metal-insulator transition caused by the coupling to localized charge-frustrated systems under ice-rule local constraint