BCS superconductivity with fixed number parity

Abstract

We investigate superconductivity in a grand canonical ensemble with fixed number parity (even or odd). In the low-temperature limit we find small corrections to the BCS gap equation and dispersion 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, nucleon spin-relaxation rate, and electromagnetic absorption.