Rutgers relation for the analysis of superfluid density in superconductors

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.