Strong Coupling Expansion for the Pairing Hamiltonian

TL;DR

This paper develops a systematic strong coupling expansion for the pairing Hamiltonian in small metallic grains, enabling explicit determination of low energy spectra and excitations in the strong coupling regime.

Contribution

It introduces a novel systematic expansion based on the Richardson model for analyzing superconducting pairing in small grains at strong coupling.

Findings

Explicit expressions for low energy spectra at strong coupling

Determination of energy and spin gaps in the many-body spectrum

Convergence of the expansion for realistic coupling values

Abstract

The paper is devoted to the effects of superconducting pairing in small metallic grains. It turns out that at strong superconducting coupling and in the limit of large Thouless conductance one can explicitly determine the low energy spectrum of the problem. We start with the strong coupling limit and develop a systematic expansion in powers of the inverse coupling constant for the many-particle spectrum of the system. The strong coupling expansion is based on the formal exact solution of the Richardson model and converges for realistic values of the coupling constant. We use this expansion to study the low energy excitations of the system, in particular energy and spin gaps in the many-body spectrum.