Thermodynamic properties of a BCS superconductor near zero temperature

Abstract

We theoretically study the thermodynamic properties of a BCS superconductor near zero temperature. Derivations of the temperature dependence of the order parameter and an exact formula for the free-energy difference between the superconducting and normal states are presented as functions of temperature and material parameters of the superconductor. Under the condition that the cut-off energy is much greater than the temperature, formulas for the critical field and specific heat in the superconducting state are presented. Our expressions for these thermodynamic quantities show new corrections to the BCS's results.