Thermodynamics and Strong-coupling Superconducting Energy Gaps

Superconductivity is a field where much research has been conducted into explaining all aspects of this phenomenon in many materials. BCS theory provided the principal understanding of superconductivity in conventional materials yet fails to entirely describe those which exhibit greater coupling-strengths as well as the more unconventional superconductors. Formulations have been proposed which extend BCS theory in various ways such as scaling the predicted energy gap by values representative of greater coupling strengths.

In order to further extend such formulations we applied our own theory which recalculates the energy gap based solely on thermodynamic parameters, in the hope of improving their accuracy. Comparisons of this energy gap calculated from existing critical-field measurements as well as computational predictions for a range of weak- to strong-coupling type I s-wave superconductors were made with experimental tunnelling measurements. Our thermodynamic theory provided an accurate temperature-dependence of the energy gap for all these superconductors except for the strongest coupler which produced erroneous predictions.

An extra-strong-coupling superconductor Pb₀.₇Bi₀.₃ was synthesised and it’s critical-field measured in order to rigorously test our theory in the strong-coupling regime. It exhibited type II superconductivity contrary to our belief and as such measurements were insufficient for an accurate comparison. However, computational calculations predicted an accurate temperature-dependence for the energy gap of Pb₀.₇Bi₀.₃ when compared with experimental tunnelling measurements. Thus our theory appears to apply for this extra-strong-coupling type II superconductor and not for the strong-coupling type I superconductor, which prompts further investigation. These comparisons depend upon the accuracy with which the temperature-dependence of the energy gap can be measured - not an easy task.

Extension was also made to d-wave superconductivity where our theory provided little improvement over a scaled BCS interpretation for several overdoped samples of the unconventional Bi-2212 superconductor. However, and this is a most important conclusion, this is due to the weak nature of the coupling in this material which we were able to establish.

Thus our theory appears to provide several promising first-order results and warrants further investigation and application to a range of superconductors.