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

TL;DR

This study investigates how charge frustration and ice-rule constraints induce metal-insulator transitions in fermion systems on frustrated lattices, revealing universal features and lattice-dependent transport behaviors.

Contribution

It introduces a theoretical and numerical analysis of the extended Falicov-Kimball model under ice-rule constraints, highlighting universal electronic features and diverse transition mechanisms.

Findings

Charge gap opens at small U relative to bandwidth.

Large U leads to charge ice state with one-dimensional loops.

Lattice geometry influences the transition from metal to insulator.

Abstract

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.