Thermodynamic properties of a BCS superconductor

On the basis of the Bardeen-Cooper-Schrieffer (BCS) gap equation, we derive complete expressions for the free-energy density, and heat capacity differences between the normal and superconducting states as functions of the superconducting energy gap Delta(T), Debye cut-off energy omega(D) and temperature T near the critical temperature T-c. We have analyzed these expressions at T-c as well as at the temperature near T-c for s and d types of pairing. The critical field and specific heat versus omega(D)/T-c curves show that the BCS universal values are recovered in the omega(D)/T-c --> infinity limit. Corrections to BCS's approximate results are given as functions of experimentally measured parameters and temperature. (C) 2000 Elsevier Science B.V. All rights reserved.