Thermodynamical Cross-Relations for Superconductors at the Critical Point

TL;DR

This paper derives new thermodynamical relations at the critical point of superconductors using Landau's theory, enabling the estimation of difficult-to-measure quantities and validating these relations with a two-band microscopic model.

Contribution

It introduces twelve new thermodynamical relations at the superconducting critical point, linking various measurable quantities and their derivatives, enhancing understanding and experimental analysis.

Findings

Derived twelve thermodynamical relations at the critical point.

Validated relations using a two-band microscopic model.

Showed relations accurately predict thermodynamic quantities.

Abstract

We investigate superconducting systems with the use of the phenomenological Landau's theory of second order phase transitions, including into the considerations the critical behaviour of the chemical potential. We derive in this way a variety of new thermodynamical relations at the critical point. Twelve basic relations connect critical jumps of different thermodynamical quantites (specific heat, chemical potential derivatives with respect to temperature, pressure (volume) and number of particles, volume (pressure) derivatives with respect to temperature and pressure (volume)) with the critical temperature or its derivatives with respect to the number of particles or pressure (volume). These relations allow to find plenty of cross-relations between different quantities at the critical point. The derived formulae can practically be used in many cases to find such thermodynamical quantities at the critical point which are extremely difficult to measure under the assumption that the other ones are already known. We additionally perform a test of the two derived relations by using two-band microscopic model, describing superconducting systems. We calculate the specific heat, order parameter and chemical potential as functions of temperature to show that the tested relations are very well fulfilled.