Rutgers relation for the analysis of superfluid density in superconductors

TL;DR

This paper demonstrates that the Rutgers relation can be used to analyze superfluid density in superconductors, allowing for the determination of the zero-temperature London penetration depth from thermodynamic and critical field data.

Contribution

It introduces a method to use the Rutgers relation for superfluid density analysis, independent of Fermi surface or gap structure complexities, to determine $ ext{λ}(0)$ from measurable quantities.

Findings

Rutgers relation applies broadly to superfluid density analysis.

Provides a new method to determine $ ext{λ}(0)$ from thermodynamic data.

Applicable when critical fluctuations are weak.

Abstract

It is shown that the thermodynamic Rutgers relation for the second order phase transitions can be used for the analysis of the superfluid density data irrespective of complexities of the Fermi surface, structure of the superconducting gap, pairing strength, or scattering. The only limitation is that critical fluctuations should be weak, so that the mean field theory of the second order phase transitions is applicable. By using the Rutgers relation, the zero temperature value of the London penetration depth, $\lambda(0)$, is related to the specific heat jump $\Delta C$ and the slope of upper critical field $dH_{c2}/dT$ at the transition temperature $T_c$, provided the data on $\Delta\lambda=\lambda(T)-\lambda(0)$ are available in a broad temperature domain. We then provide a new way of determination of $\lambda(0)$, the quantity difficult to determine within many techniques.