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 $\lambda \left(0\right)$ is related to the specific heat jump $\Delta C$ and the slope of upper critical field $d{H}_{c2}/dT$ at the transition temperature $T_c$, provided the data on $\Delta \lambda =\lambda \left(T\right)-\lambda \left(0\right)$ are available in a broad temperature domain. We then provide a way to determine $\lambda \left(0\right)$, the quantity difficult to determine within many techniques.

• Received 29 May 2013

DOI:https://doi.org/10.1103/PhysRevB.87.214518