# Excitonic Phase Diagram of the Three-Chain Hubbard Model for Semiconducting and Semimetallic Ta$_2$NiSe$_5$

## TL;DR

This paper models the excitonic phase diagram of Ta$_2$NiSe$_5$ using a three-chain Hubbard model, revealing different excitonic states, including FFLO states with finite momentum pairing, depending on the Fermi surface configuration.

## Contribution

It introduces a detailed theoretical analysis of excitonic phases in Ta$_2$NiSe$_5$, highlighting the emergence of FFLO states in a multiband Hubbard model.

## Key findings

- Identification of excitonic insulator transition in semiconducting and semimetallic regimes.
- Prediction of FFLO excitonic states with finite momentum in semimetallic Ta$_2$NiSe$_5$.
- FFLO states are metallic and may be observed under high pressure.

## Abstract

Transition metal chalcogenide Ta$_2$NiSe$_5$, a promising material for the excitonic insulator, is investigated on the basis of the quasi-one-dimensional three-chain Hubbard model with two conduction ($c$) bands and one valence ($f$) band. In the semimetallic case where only one of two $c$ bands and the $f$ band cross the Fermi level, the transition from the $c$-$f$ compensated semimetal to the uniform excitonic insulator takes place at low temperature as the same as in the semiconducting case. On the other hand, when another $c$ band also crosses the Fermi level, the system shows three types of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) excitonic orders characterized by the condensation of excitons with finite center-of-mass momentum $q$ corresponding to the three types of nesting vectors between the imbalanced two $c$ and one $f$ Fermi surfaces. The obtained FFLO states are metallic in contrast to the excitonic insulator and are expected to be observed in semimetallic Ta$_2$NiSe$_5$ under high pressure.