Electronic Ferroelectricity in the Falicov-Kimball Model

TL;DR

This paper demonstrates that the Falicov-Kimball model exhibits spontaneous electric polarization, revealing a phase diagram with orbital ordering and exciton condensation, extending understanding of electronic ferroelectricity in strongly correlated systems.

Contribution

It introduces a mapping of the Falicov-Kimball model to an $xxz$ spin model to analyze ferroelectricity and phase transitions in strongly correlated electrons.

Findings

Identification of a phase transition to a ferroelectric state.

Discovery of orbital ordering and exciton Bose-Einstein condensation.

Extension of results to intermediate and weak coupling regimes.

Abstract

I show that a spontaneous electric polarization is developed in the solution of the Falicov-Kimball model (FKM) by mapping the strong coupling limit of the model into an $xxz$ spin 1/2 model with a magnetic field. In this way, I can determine the phase diagram of the strongly interacting model that shows a transition to a mixed valence regime containing two phases: orbital ordering and Bose-Einstein condensation of excitons with a built in electric polarization. The results are extended to the intermeditate and weak coupling regimes.