Excitonic Order and Superconductivity in the Two-Orbital Hubbard Model: Variational Cluster Approach

TL;DR

This study uses the variational cluster approach to explore excitonic order and superconductivity in a two-orbital Hubbard model, revealing various insulating and superconducting phases depending on interaction strengths.

Contribution

It demonstrates the emergence of multiple ordered states, including excitonic and superconducting phases, within the two-orbital Hubbard model using a variational cluster method.

Findings

Identification of excitonic, antiferromagnetic Mott insulator, and band insulator states.

Discovery of $s^{}$-wave and $d_{x^2 - y^2}$-wave superconducting states.

Comparison of band gap formation due to different orders.

Abstract

Using the variational cluster approach based on the self-energy functional theory, we study the possible occurrence of excitonic order and superconductivity in the two-orbital Hubbard model with intra- and inter-orbital Coulomb interactions. It is known that an antiferromagnetic Mott insulator state appears in the regime of strong intra-orbital interaction, a band insulator state appears in the regime of strong inter-orbital interaction, and an excitonic insulator state appears between them. In addition to these states, we find that the $s^{\pm}$-wave superconducting state appears in the small-correlation regime, and the $d_{x^2 - y^2}$-wave superconducting state appears on the boundary of the antiferromagnetic Mott insulator state. We calculate the single-particle spectral function of the model and compare the band gap formation due to the superconducting and excitonic orders.