  We report the results of our theoretical and numerical study on electronic
and transport properties of fermion systems with charge frustration. We
consider an extended Falicov-Kimball model in which itinerant spinless fermions
interact repulsively by U with localized particles whose distribution satisfies
a local constraint under geometrical frustration, the so-called ice rule. We
numerically calculate the density of states, optical conductivity, and inverse
participation ratio for the models on the pyrochlore, checkerboard, and kagome
lattices, and discuss the nature of metal-insulator transitions at commensurate
fillings. As a result, we show that the ice-rule local constraint leads to
several universal features in the electronic structure; a charge gap opens at a
considerably small U compared to the bandwidth, and the energy spectrum
approaches a characteristic form in the large U limit, that is, the
noninteracting tight-binding form in one dimension or the $\delta$-functional
peak. In the large U region, the itinerant fermions are confined in the
macroscopically-degenerate ice-rule configurations, which consist of a bunch of
one-dimensional loops: We call this insulating state the charge ice. On the
other hand, transport properties are much affected by the geometry and
dimensionality of lattices; e.g., the pyrochlore lattice model exhibits a
transition from a metallic to the charge-ice insulating state by increasing U,
while the checkerboard lattice model appears to show Anderson localization
before opening a gap. Meanwhile, in the kagome lattice case, we do not obtain
clear evidence of Anderson localization. Our results elucidate the universality
and diversity of phase transitions to the charge-ice insulator in fully
frustrated lattices.
