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

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. Electronic states of the itinerant fermions are studied by approximating the statistical average by the arithmetic mean over different configurations of localized particles under the constraint. We numerically calculate the density of states, optical conductivity, and inverse participation ratio for models on the pyrochlore, checkerboard, and kagome lattices, and discuss the nature of metal-insulator transitions at commensurate fillings. The results are compared with exact solutions for models on Husimi cacti as well as with numerical results for completely random distributions of localized particles. As a result, we show that the ice-rule local constraint leads to several universal features in the electronic structure common to different lattice structures; 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 a d-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 the lattices; e.g., the pyrochlore lattice model exhibits a transition from a metallic to the charge-ice insulating state with 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.