Phase separation in a lattice model of a superconductor with pair hopping

TL;DR

This paper investigates a lattice superconductor model with pair hopping, revealing phase diagrams with homogeneous and phase-separated states, and multicritical points, using variational and mean-field approaches across different dimensions.

Contribution

It introduces a detailed analysis of a superconductor model with pair hopping, including phase separation and multicritical behavior, using a combination of variational, mean-field, and approximate methods.

Findings

Identification of homogeneous superconducting and nonordered phases.

Existence of phase-separated states with coexistence of phases.

Presence of multicritical points including tricritical points.

Abstract

We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The model can be treated as a simple effective model of a superconductor with very short coherence length in which electrons are localized and only electron pairs have possibility of transferring. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We have also obtained rigorous results for a linear chain (d=1) in the ground state. Moreover, at T=0 some results derived within the random phase approximation (and the spin-wave approximation) for d=2 and d=3 lattices and within the low density expansions for d=3 lattices are presented. Our investigation of the general case (as a function of the electron concentration and as a function of the chemical potential) shows that, depending on the values of interaction parameters, the system can exhibit not only the homogeneous phases: superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS-NO). The system considered exhibits interesting multicritical behaviour including tricritical points.