A correlation between energy gap, critical current density and relaxation of a superconductor

Abstract: Superconductors like other solids cannot relax instantaneously from excited states to thermodynamic equilibrium. In this paper, relaxation from thermal excitations is investigated, like after absorption of radiation or, under conductor movement, release and transformation of mechanical tension to thermal energy. Relaxation proceeds within finite periods of time the length of which increases the more strongly the closer the superconductor temperature has already approached its critical value. Properties of many-particle systems (as explained, by an analogy to nuclear physics), basic thermodynamic considerations (temperature uniquely defined under solely equilibrium condition) and standard, multi-component heat transfer principles (solid conduction plus radiation in thin films) are applied as tools to prove this expectation. Energy gap, superconductor critical current density and critical temperature, as a result, are tightly related to relaxation rates and relaxation times of the superconductor electron system. By numerical simulations, an attempt is made to find a quantitative correlation of these properties in a thin film superconductor.