# Influence of the symmetry of the hybridization on the critical temperature of multi-band superconductors

## TL;DR

This study models a two-band superconductor with strong correlations, showing how hybridization, pressure, and symmetry influence the critical temperature and phase transitions.

## Contribution

It introduces a detailed two-band model incorporating hybridization and correlations, analyzing their effects on superconductivity and phase diagrams.

## Key findings

- Critical temperature increases with hybridization in many cases.
- Pressure can induce first-order phase transitions.
- Superconductivity can be suppressed at specific band-fillings.

## Abstract

In this work we study a two-band model of a superconductor in a square lattice. One band is narrow in energy and includes local Coulomb correlations between its quasi-particles. Pairing occurs in this band due to nearest neighbor attractive interactions. Extended s-wave, as well as d-wave symmetries of the superconducting order parameter are considered. The correlated electrons hybridize with those in another, wide conduction band through a k-dependent mixing, with even or odd parity depending on the nature of the orbitals. The many-body problem is treated within a slave-boson approach that has proved adequate to deal with the strong electronic correlations that are assumed here. Since applied pressure changes mostly the ratio between hybridization and bandwidths, we can use this ratio as a control parameter to obtain the phase diagrams of the model. We find that for a wide range of parameters, the critical temperature increases as a function of hybridization (pressure), with a region of first-order transitions. When frustration is introduced it gives rise to a stable superconducting phase. We find that superconductivity can be suppressed for specific values of band-filling due to the Coulomb repulsion. We show how pressure, composition and strength of correlations affect the superconductivity for different symmetries of the order parameter and the hybridization.