An extended Falicov-Kimball model on a triangular lattice

TL;DR

This paper investigates a Falicov-Kimball model on a triangular lattice, revealing various orbital ordered ground states, some of which induce orbitally driven ferroelectricity due to broken inversion symmetry.

Contribution

It introduces an extended Falicov-Kimball model on a triangular lattice and uncovers new orbital ordered states and ferroelectricity driven by orbital orderings.

Findings

Multiple orbital ordered ground states identified

Homogeneous mixed valence due to quantum fluctuations

Broken inversion symmetry leads to ferroelectricity

Abstract

The combined effect of frustration and correlation in electrons is a matter of considerable interest of late. In this context a Falicov-Kimball model on a triangular lattice with two localized states, relevant for certain correlated systems, is considered. Making use of the local symmetries of the model, our numerical study reveals a number of orbital ordered ground states, tuned by the small changes in parameters while quantum fluctuations between the localized and extended states produce homogeneous mixed valence. The inversion symmetry of the Hamiltonian is broken by most of these ordered states leading to orbitally driven ferroelectricity. We demonstrate that there is no spontaneous symmetry breaking when the ground state is inhomogeneous. The study could be relevant for frustrated systems like $GdI_2$, $NaTiO_2$ (in its low temperature C2/m phase) where two Mott localized states couple to a conduction band.