Finite Size Corrections for the Pairing Hamiltonian

TL;DR

This paper derives finite size corrections for the pairing Hamiltonian in small metallic grains, providing explicit formulas for energy and excitation corrections based on an expansion of the Richardson model.

Contribution

It introduces a method to calculate finite size effects in superconducting grains using an expansion derived from the Richardson model's exact solution.

Findings

Finite size corrections to ground state energy are explicitly calculated.

Finite size effects on the Matveev-Larkin parameter are determined.

Excitation energies are corrected for finite size effects.

Abstract

We study the effects of superconducting pairing in small metallic grains. We show that in the limit of large Thouless conductance one can explicitly determine the low energy spectrum of the problem as an expansion in the inverse number of electrons on the grain. The expansion is based on the formal exact solution of the Richardson model. We use this expansion to calculate finite size corrections to the ground state energy, Matveev-Larkin parameter, and excitation energies.