Temperature and filling dependence of the superconducting $\pi$-phase in the Penson-Kolb-Hubbard model

TL;DR

This study explores the temperature and filling dependence of the superconducting $$-phase in the Penson-Kolb-Hubbard model, revealing how pair-hopping influences phase stability and critical temperature.

Contribution

It provides a detailed analysis of the $$-phase's behavior in different dimensions and with additional hopping terms, including explicit solutions for the chemical potential.

Findings

The $$-phase persists for repulsive interactions due to pair-hopping.

Including next-nearest neighbor hopping increases critical temperature.

Phase diagrams vary with dimension and filling, shifting away from half-filling.

Abstract

We investigate in the Hartree Fock approximation the temperature and filling dependence of the superconducting $\pi$-phase for the Penson-Kolb-Hubbard model. Due to the presence of the pair-hopping term, the phase survives for repulsive values of the on-site Coulomb interaction, exhibiting an interesting filling and temperature dependence. The structure of the self-consistent equations peculiar to the $\pi$-phase of the model allows to explicitly solve them for the chemical potential. The phase diagrams are shown and discussed in dimension 2 and 3. We also show that, when a next-nearest neighbours hopping term is included, the critical temperature of the superconducting region increases, and the corresponding range of filling values is shifted away from half-filling. Comparison with known exact results is also discussed.