The direct relation between the coefficient of the low temperature resistivity T^2 term and the superconducting transition temperature Tc

TL;DR

This paper explores the empirical relationship between the T^2 coefficient of resistivity and the superconducting transition temperature Tc, revealing a fundamental link in Fermi liquids and proposing a method to determine the coupling constant from transport properties.

Contribution

It demonstrates a universal relation between resistivity and Tc in superconductors and introduces a method to determine the coupling constant from transport measurements.

Findings

Higher resistivity correlates with higher Tc.

The relation holds under varying external parameters like pressure.

The method is validated using superfluid 3He transport data.

Abstract

In several superconductors above the superconducting transition temperature Tc, the electrical resistivity is of the form {\rho} =AT^2. We show that there exists an empirical relation between Tc and A when both vary with an external parameter, e.g. pressure. The more resistive the sample the higher the Tc. Landau theory shows that it is a general feature of Fermi Liquids, as {\rho} is governed by the scattering that bounds the pairs condensing at Tc. We develop a method that allows the determination of the coupling constant {\lambda} that is validated when used to the transport properties of superfluid 3He.