EFFECTS OF AN ENERGY-DEPENDENT GAP PARAMETER ON THERMODYNAMIC PROPERTIES OF THE SUPERCONDUCTING STATE

In a previous paper [Z. Hao, Mod. Phys. Lett. B7, 1439 (1993)] we have derived an energy dependent gap parameter, with the magnitude \Delta( k)\ being appreciable within only a few k(B)T(c) around the Fermi leve l. In this paper we use this energy dependent \Delta(k)\ to calculate the critical magnetic field H-c, electronic specific heat C, and Josep hson critical current density I-c of an SIS junction, and compare the results with those obtained by using the cutoff approximation. The mai n significant difference is that the present result for I-c is much sm aller than that of the cutoff approximation, with the ratio between th e former and the latter at T = 0 being only 0.35 for symmetric junctio ns and even less for asymmetric junctions. As to the temperature depen dences of H-c, C and I-c, the differences between the present results and those of the cutoff approximation are much less significant; i.e., there exist only minor numerical modifications. A qualitative discuss ion is also given on the physical significance of the phase theta(k) o f the gap parameter (Delta(k) = \Delta(k)\e(i theta k)).