Some Effects of Energy Dependence in the Electronic Density of State on Superconductivity

Abstract

<p>Based on the assumption of unusual fine structure in the electronic density of states close to the Fermi energy, new approximate analytic expressions for the critical temperature, and.the gap parameter at absolute zero are obtained. We have represented approximately the rapid variation in N(E) by a Lorentzian form of width a and strength g superimposed on a constant background N(O). Further, we have assumed that the Fermi energy falls off the center of the peak. The solutions we have obtained for T_c and Δ (0) are significantly c modified from the BCS solutions although for a & b » k_BT_C and w_D » Δ (0) the ratio 2Δ (0)/k_BT_C remains unchanged and equal to 3.54. Mathematical studies have been done for the evaluation of the condensation energy. The shift in the chemical potential as the temperature increases above the absolute zero was calculated and it was found that the correction term due to raising the temperature is negligible and can be ignored without the introduction of any significant error. A modified finite-temperature BCS gap equation has been solved mathematically in which we have obtained a significantly new modified approximate analytic expression for Δ (T) valid in the limit when T-->T_c. The use of the equation for Δ (T) helps to evaluate the discontinuity in the electronic specific heat at the critical temperature. Finally it has been shown that in the low-temperature limit the specific heat is proportional e^-Δ(0)/k_BT as in BCS theory.</p>