Multiband Superconductivity in the Exactly Solvable Hatsugai-Kohmoto Model

TL;DR

This paper investigates multiband superconductivity within an exactly solvable correlated electron model, classifying pairing symmetries and analyzing critical temperatures in a minimal multiorbital framework.

Contribution

It extends symmetry-based analysis to correlated multiband systems using the exactly solvable Hatsugai-Kohmoto model, exploring pairing states and critical temperatures.

Findings

Classified symmetry-allowed superconducting gap structures.

Computed critical temperatures for selected pairing channels.

Provided a systematic framework for multiband superconductivity analysis.

Abstract

Multiband superconductivity gives rise to a rich landscape of possible pairing states. Here we study superconductivity in the multiband extension of the Hatsugai-Kohmoto model, an exactly solvable model of correlated electrons with momentum-local interactions, which provides a minimal framework to explore the interplay of strong correlations, orbital structure and pairing symmetry. Focusing on a two-orbital system with point-group symmetry $\rm D_{4h}$, we classify the symmetry-allowed superconducting gap structures, taking into account spin, orbital and momentum degrees of freedom. We further compute the critical temperature and the superconducting order parameter for selected pairing channels as functions of interaction and pairing strength within a mean-field treatment. Our results provide a systematic framework for analyzing superconductivity in the orbital Hatsugai-Kohmoto model and extend symmetry-based approaches to correlated multiband settings.