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 ${\rho }_{s0}={\rho }_s(T=0)$ in dirty superconducting electron systems in which the damping $\gamma$ of single-particle excitations exceeds the zero-temperature BCS gap ${\mathrm{\Delta }}_0$. In the dirty strong-coupling limit $\gamma /{\mathrm{\Delta }}_0\gg 1,m^{*}/m_e\gg 1$, the formula derived for ${\rho }_{s0}$ 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 ${\rho }_{s0}$ in overdoped ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ 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.

Figure 1

(a) Ratio ${\rho }_{s0}/n$ vs $m^{*}/m_e$ evaluated from Eq. (24) at $\gamma =2{\mathrm{\Delta }}_0$ (blue line), $\gamma =5{\mathrm{\Delta }}_0$ (green line), and $\gamma =8{\mathrm{\Delta }}_0$ (red line). (b) Ratio ${\rho }_{s0}/n$ vs $\gamma /{\mathrm{\Delta }}_0$ evaluated from Eq. (24) at $m^{*}/m_e=1$ and 10 for the $S$-wave gap $\mathrm{\Delta }={\mathrm{\Delta }}_0$ (blue lines) and $D$-wave gap $\mathrm{\Delta }={\mathrm{\Delta }}_{0}cos2\phi$ (red lines).