Superconductivity in the Hubbard model with pair hopping

TL;DR

This paper explores the phase diagrams and superconducting properties of the extended Hubbard model with pair hopping, revealing diverse phases and the evolution of pairing regimes across different lattice dimensions.

Contribution

It provides a detailed analysis of the extended Hubbard model with pair hopping across various dimensions, highlighting the diversity of phases and the differences from the attractive Hubbard model.

Findings

Nine phases at half-filling in 1D including superconducting, magnetic, and charge-density states.

Reduced stability of bond orderings with increasing lattice dimension.

Distinct electron pair dynamics leading to different electrodynamic properties.

Abstract

The phase diagrams and superconducting properties of the extended Hubbard model with pair hopping interaction, i.e. the Penson-Kolb-Hubbard model are studied. The analysis of the model is performed for d-dimensional hypercubic lattices, including d=1 and d=$\infty$, by means of the (broken symmetry) Hartree-Fock approximations and, for d=$\infty$, by the slave-boson mean-field method. For d=1, at half-filling the phase diagram is shown to consist of nine different phases including two superconducting states with center-of-mass momentum q=0 and q=Q ($\eta$-pairing), site and bond-located antiferromagnetic and charge-density wave states as well as three mixed phases with coexisting site and bond orderings. The stability range of the bond-type orderings is shrank with increasing lattice dimensionality d and for d=$\infty$ the corresponding diagram consists of four phases only, involving exclusively site-located orderings. Comparing the pair hopping model with the attractive Hubbard model we found in the both cases gradual evolution from the BCS-like limit to the tightly bound pairs regime and a monotonic increase of the gap in the excitation spectrum with increasing coupling. However, the dynamics of electron pairs in both models is qualitatively different, which results in different dependences of condensation energies and critical temperatures on interaction parameters as well as in different electrodynamic properties, especially in a strong coupling regime.