FFLO Superconductivity Mediated by Excitonic Fluctuation in Semimetallic Ta$_2$NiSe$_5$

TL;DR

This paper explores how excitonic fluctuations in Ta$_2$NiSe$_5$ can mediate FFLO superconductivity, especially under high pressure, by analyzing a three-chain Hubbard model and identifying conditions for different excitonic orders.

Contribution

It introduces a theoretical framework linking excitonic fluctuations to FFLO superconductivity in Ta$_2$NiSe$_5$, highlighting the role of band-overlap and Fermi surface nesting.

Findings

Enhanced uniform excitonic fluctuations near excitonic insulator transition.

Dominance of non-uniform excitonic fluctuations with finite momentum in large band-overlap.

Prediction of FFLO superconductivity mediated by excitonic fluctuations under high pressure.

Abstract

We investigate the excitonic fluctuation and its mediated superconductivity in the quasi one-dimensional three-chain Hubbard model for Ta$_2$NiSe$_5$ known as a candidate material for the excitonic insulator. In the semiconducting case and the semimetallic case with a small band-overlapping where one conduction ($c$) band and one valence ($f$) band cross the Fermi level, the excitonic fluctuation with $\bm{q}=\bm{0}$ is enhanced due to the $c$-$f$ Coulomb interaction and diverges towards the uniform excitonic order corresponding to the excitonic insulator. On the other hands, in the semimetallic case with a large band-overlapping where two $c$ bands and one $f$ band cross the Fermi level, the non-uniform excitonic fluctuation with $\bm{q}\neq \bm{0}$ corresponding to the nesting vector between the $c$ and $f$ Fermi-surfaces (FSs) becomes dominant and results in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) excitonic order characterized by the condensation of excitons with finite center-of-mass momentum $\bm{q}$. Near the instability, the largely enhanced excitonic fluctuations mediate the $c$-$f$ interband Cooper pairs with finite center-of-mass momentum resulting in the FFLO superconductivity, which is expected to be realized in the semimetallic Ta$_2$NiSe$_5$ under high pressure.