# Mixed temperature-dependent order parameters in the extended Hubbard model

## TL;DR

This paper investigates how the symmetry of superconducting order parameters in the extended Hubbard model varies with temperature, revealing symmetry transitions below the critical temperature that impact the understanding of unconventional superconductors.

## Contribution

It provides a detailed analysis of the temperature dependence of order parameter symmetries and introduces conditions on the temperature profile of the gap function in the extended Hubbard model.

## Key findings

- Symmetry of the order parameter depends on temperature.
- Existence of symmetry transitions below T_c.
- Formulation of conditions on the temperature profile of the gap.

## Abstract

The extended Hubbard model can host s-wave, d-wave and p-wave superconducting phases depending on the values of the on-site and nearest-neighbour interactions. Upon detailed examination of the free energy functional of the gap in this model, we show that these symmetries are often dependent on temperature. The critical points of this functional are constrained by symmetry and allow us to formulate stringent conditions on the temperature profile of the gap function, applicable to other models as well. We discuss the finite temperature phase diagram of the extended Hubbard model, and point out the existence of symmetry transitions below $T_c$. Understanding the nature of these transitions is crucial to assessing the symmetry of unconventional superconductors.