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Multiple solutions for the equilibrium populations in BCS superconductors

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  • Anghel, Dragoş-Victor

Abstract

It was recently shown that the BCS formalism leads to several solutions for the energy gap and the equilibrium quasiparticle distribution, with a phase transition temperature which depends on the position of the chemical potential within the attraction band (the attraction band AB is defined as the single-particle energy interval in which the pairing interaction is manifested). Moreover, in some cases, the phase transition may be of the first, not of the second order. Here I will find two sets of solutions for any temperature below the phase transition temperature. I will also show that, when the AB is symmetric with respect to the chemical potential (the textbook BCS problem) there are still two solutions, with different energy gaps: one solution is the typical (textbook) BCS solution, whereas the other one has a smaller energy gap and non-zero quasiparticle populations down to zero temperature. At zero temperature, the energy gap corresponding to the second solution is one third of the typical BCS solution.

Suggested Citation

  • Anghel, Dragoş-Victor, 2021. "Multiple solutions for the equilibrium populations in BCS superconductors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    • Handle: RePEc:eee:phsmap:v:572:y:2021:i:c:s0378437121001515
    DOI: 10.1016/j.physa.2021.125879
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