Condensation energy in a superconductor for all temperatures

J. Ortega, F. Zúñiga*, M. de Llano

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


An exact analytical expression for the condensation energy Econd(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 Fs(T) - Fn(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 Econd(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 languageEnglish
JournalJournal of Low Temperature Physics
VolumeFirst Online
Publication statusPublished - 29 Aug 2020


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


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