Impact of $e-e$ interactions on the superfluid density of dirty superconductors

TL;DR

This paper investigates how electron-electron interactions affect the superfluid density in dirty superconductors, especially in the strong-coupling limit, and relates findings to experimental observations in overdoped LSCO compounds.

Contribution

It adapts Landau's Fermi liquid theory to analyze superfluid density deficits in dirty superconductors, connecting theoretical formulas with empirical relations and experimental data.

Findings

Derived a formula for superfluid density in the strong-coupling limit.

Showed the formula aligns with the Uemura relation under certain conditions.

Discussed the influence of lattice and magnetic effects on superfluid density decline.

Abstract

Landau's theory of the Fermi liquid is adapted to analyze the impact of electron-electron ($e-e$) 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 $\Delta_0$. In the dirty strong-coupling limit $\gamma/\Delta_0\gg 1,m^*/m_e\gg 1$, 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 LSCO compounds are also discussed. Our method is also applied to elucidation of results from the pioneering experimental studies performed recently by Bozovi\`c and collaborators in overdoped LSCO compounds.