Impact of electron-electron interactions on the superfluid density of dirty superconductors

Landau's theory of the Fermi liquid is adapted to analyze the impact of electron-electron (interactions on the deficit of the superfluid density ${\ensuremath{\rho}}_s0={\ensuremath{\rho}}_s(T=0)$ in dirty superconducting electron systems in which the damping $\ensuremath{\gamma}$ of single-particle excitations exceeds the zero-temperature BCS gap ${\mathrm{\ensuremath{\Delta}}}₀$. In the dirty strong-coupling limit $\ensuremath{\gamma}/{\mathrm{\ensuremath{\Delta}}}₀\ensuremath{\gg}1,{m}^*/{m}_e\ensuremath{\gg}1$, the formula derived for ${\ensuremath{\rho}}_s0$ is shown to coincide with the well-known empirical Uemura relation provided pair-breaking contributions are nonexistent. The roles of the crystal lattice and magnetic pair-breaking effects in the observed decline of the zero-temperature superfluid density ${\ensuremath{\rho}}_s0$ in overdoped ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Sr}}_x{\mathrm{CuO}}₄$ compounds are also discussed, and our procedure is applied to elucidation of results from the pioneering experimental studies performed recently by Bozovic and collaborators in these compounds.