Cooper Instability in the Occupation Dependent Hopping Hamiltonians

TL;DR

This paper investigates how orbital contraction affects Cooper instability in occupation-dependent hopping Hamiltonians, revealing unique fluctuation behaviors and the emergence of a parity gap, with numerical and analytical insights into superconductivity conditions.

Contribution

It introduces a generic Hamiltonian incorporating orbital contraction effects and analyzes its impact on superconductivity and Cooper instability through both analytical and numerical methods.

Findings

Orbital contraction influences the critical temperature and relaxation rate.

A parity gap appears under certain parameters indicating Cooper instability.

Numerical Hubbard model calculations do not show superconductivity in small clusters.

Abstract

A generic Hamiltonian, which incorporates the effect of the orbital contraction on the hopping amplitude between the nearest sites, is studied both analytically at the weak coupling limit and numerically at the intermediate and strong coupling regimes for finite atomic cluster. The effect of the orbital contraction due to hole localization at atomic sites is specified with two coupling parameters V and W (multiplicative and additive contraction terms). The singularity of the vertex part of the two-particle Green's function determines the critical temperature Tc and the relaxation rate Gamma(T) of the order parameter at temperature above Tc. Unlike in conventional BCS superconductors, Gamma has a non-zero imaginary part which may influence the fluctuation conductivity of superconductor above Tc. We compute the ground state energy as a function of the particle number and magnetic flux through the cluster, and show the existence of the parity gap Delta appearing at the range of system parameters consistent with the appearance of Cooper instability. Numeric calculation of the Hubbard model (with U>0) at arbitrary occupation does not show any sign of superconductivity in small cluster.