# Superfluid density and carrier concentration across a superconducting dome: the case of SrTi$_{1-x}$Nb$_{x}$O$_{3}$

## TL;DR

This study investigates how superfluid density and carrier concentration in SrTi$_{1-x}$Nb$_{x}$O$_{3}$ evolve across the superconducting dome, revealing a density mismatch in the overdoped regime linked to the dirty limit and multiband effects.

## Contribution

It provides the first detailed analysis of superfluid density versus carrier concentration in SrTi$_{1-x}$Nb$_{x}$O$_{3}$, highlighting the density mismatch and dirty-limit effects.

## Key findings

- Superfluid density equals normal carrier density at low doping.
- Density mismatch increases with doping, especially in the overdoped regime.
- Superfluid density vanishes before carrier density in overdoped samples.

## Abstract

We present a study of the lower critical field, \hc1, of \STO as a function of carrier concentration with the aim of quantifying the superfluid density. At low carrier concentration (i.e. the underdoped side), superfluid density and the carrier concentration in the normal state are equal within experimental margin. A significant deviation between the two numbers starts at optimal doping and gradually increases with doping. The inverse of the penetration depth and the critical temperature follow parallel evolutions as in the case of cuprate superconductors. In the overdoped regime, the zero-temperature superfluid density becomes much lower than the normal-state carrier density before vanishing all together. We show that the density mismatch and the clean-to-dirty crossover are concomitant. Our results imply that the discrepancy between normal and superconducting densities is expected whenever the superconducting gap becomes small enough to put the system in the dirty limit. A quantitative test of the dirty BCS theory is not straightforward, due to he multiplicity of the bands in superconducting strontium titanate.