## Abstract

An exact analytical expression for the condensation energy E_{cond}(T) of a phonon-driven superconductor for all absolute temperatures T and for any coupling strength is introduced so as to calculate the Helmholtz free energy difference F_{s}(T) - F_{n}(T) between superconducting (s) and normal (n) states. This is achieved via a boson–fermion ternary gas theory—called the generalized Bose–Einstein condensation (GBEC) theory—which includes two-hole Cooper pairs, two-electron ones as well as single, free/unbound electrons. The GBEC formalism turns out to be quite useful in dealing with nonzero T values of E_{cond}(T) and reproduces several well-known experimental results. An expression for the condensation energy per atom is also calculated and applied to aluminum and niobium, and both results are compared with experimental data.

Original language | English |
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Journal | Journal of Low Temperature Physics |

Volume | First Online |

DOIs | |

Publication status | Published - 29 Aug 2020 |

## Keywords

- BCS theory
- Condensation energy
- Generalized Bose–Einstein condensation (GBEC) theory
- Two-electron and two-hole Cooper pairs