Temperature dependence of the superconductivity energy gap

Abstract

It is noted that theTaylor's series expansion at the transition temperature expresses the temperature dependence of the energy gap of a superconductor to an accuracy of better than one-half of a percent for the upper half of the superconducting temperature range, when only the first three terms of the series are retained. Because of the smallness of the third term an equally good expression over the same temperature range is the following two term formula:

$$\left[ {\frac{{\Delta \left( t \right)}}{{\Delta \left( 0 \right)}}} \right]^2 \approx 3.016\left( {1 - t} \right) - 2.400\left( {1 - t} \right)^2 ,$$

whereΔ(t) is the energy gap andt the reduced temperautre.