$\eta$-superconductivity in the one-dimensionnal pair hopping model

TL;DR

This paper demonstrates that the one-dimensional pair hopping model exhibits an $ ext{eta}$-superconducting phase transition at negative interaction values, with the transition occurring at any band filling and varying critical points.

Contribution

The study provides exact numerical evidence of $ ext{eta}$-superconductivity in a 1D pair hopping model for negative W, detailing the phase transition across different fillings.

Findings

Phase transition into $ ext{eta}$-superconducting state at negative W

Transition occurs at any band filling

Critical W varies with particle number

Abstract

Using exact Lanczos diagonalizations we have shown that the pair-hopping model for {\it negative} $W$ exhibits a phase transition into $\eta$-{\it superconducting state}. The transition occurs at {\it any band filling} and the critical value $W_{c}$ varies between $W_{c} \simeq -1.75t$ at half-filling to $W_{c} \simeq -2t$ for two particles on the lattice.