Thermodynamic Properties of a d-Wave Superconductor Near Zero Temperature

On the basis of Fermi liquid theory, we study the thermodynamic properties near zero temperature of a d-wave superconductor assuming the BCS pairing model. The temperature dependence of the order parameter is derived. We then obtain an analytical expression for the free energy difference between the normal and superconducting states in the vicinity of zero temperature from the coupling constant integral. New expressions for the critical field and the specific heat in the superconducting state are given as functions of temperature. We compare our expressions with previous formulas due to others.