Metal-to-Insulator Transition, Spin Gap Generation, and Charge Ordering in Geometrically Frustrated Electron Systems

TL;DR

This paper explores the metal-insulator transition in geometrically frustrated electron systems using Hubbard models, revealing the roles of electron correlation, charge ordering, and lattice distortion, with applications to ${\rm Tl_2Ru_2O_7}$.

Contribution

It demonstrates how geometrical frustration and electron interactions induce a metal-insulator transition with charge order and a spin gap, using renormalization group and mean field methods.

Findings

MIT driven by frustration and correlations.

Charge ordering relaxes frustration without breaking spin symmetry.

Application to ${\rm Tl_2Ru_2O_7}$ explains experimental observations.

Abstract

We investigate a (semi-)metal to insulator transition (MIT) realized in geometrically frustrated electron systems on the basis of the Hubbard model on a three-dimensional pyrochlore lattice and a two-dimensional checkerboard lattice. Using the renormalization group method and mean field analysis, we show that in the half-filling case, MIT occurs as a result of the interplay between geometrical frustration and electron correlation. In the insulating phase, which has a spin gap, the spin rotational symmetry is not broken, while charge ordering exists. The charge ordered state is stabilized so as to relax the geometrical frustration in the spin degrees of freedom. We also discuss the distortion of the lattice structure caused by the charge ordering. The results are successfully applied to the description of the MIT observed in the pyrochlore system ${\rm Tl_2Ru_2O_7}$.