New phenomenology from an old theory--new equilibrium states in the BCS model

TL;DR

This paper explores how asymmetry in the attraction band affects equilibrium states in BCS superconductors, revealing new stable and metastable solutions and conditions under which superconductivity can or cannot form.

Contribution

It introduces a novel analysis of the BCS model considering asymmetric attraction bands, identifying multiple solutions and their stability, which extends understanding of superconducting states.

Findings

Two solutions for the energy gap, one stable and one metastable.

Asymmetry leads to quasiparticle imbalance and potential suppression of superconductivity.

Stable solutions become unphysical when particle number is conserved with asymmetric bands.

Abstract

I analyze the low temperature limit of the BCS theory of s-wave single-band superconductors, when the attraction band may be asymmetric with respect to the chemical potential. I discuss equilibrium systems, taking consistently into account the variation of the energy and of the total number of particles with the populations of the quasiparticle energy levels. I show that the equation for the energy gap has two solutions, one of which is stable and the other one is metastable. When the chemical potential is the center of the attraction band (the standard BCS assumption), the energy gap in the stable solution is $\Delta_0$, whereas in the metastable one is $\Delta_0/3$. If the chemical potential is not in the center of the attraction band, then a quasiparticle imbalance appears. If the absolute value of the difference between the chemical potential and center of the attraction band is bigger than $2\Delta_0$, then the superconducting energy gap cannot be formed. If the number of particles is conserved and the attraction band is asymmetric, then the stable solution is unphysical and only metastable solutions are realized.