BCS Superconductivity with Fixed Number Parity

TL;DR

This paper explores how fixed number parity affects BCS superconductivity, revealing small corrections to the gap equation and deviations in physical properties, aligning with experimental observations.

Contribution

It introduces a theoretical framework for superconductivity with fixed number parity, highlighting deviations from traditional BCS theory and matching experimental behaviors.

Findings

Small corrections to BCS gap and energy spectrum at low temperatures

Linear decrease of even-odd free energy difference with temperature

Deviations from BCS predictions in specific heat and electromagnetic responses

Abstract

We investigate superconductivity in a grand canonical ensemble with {\it fixed number parity} (even or odd). In the low temperature limit we find small corrections to the BCS gap equation and energy spectrum $E(k)$. The even-odd free energy difference in the same limit decreases linearly with temperature, in accordance with the behavior observed experimentally and previously arrived at from a quasiparticle model. The theory yields deviations from the BCS predictions for the specific heat, ultrasound attenuation, NSR relaxation rate, and electromagnetic absorption.