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Mutual independence of critical temperature and superfluid density under pressure in optimally electron-doped superconducting LaFeAsO$_{1-x}$F$_{x}$

The superconducting properties of LaFeAsO$_{1-x}$F$_{x}$ in conditions of optimal electron-doping are investigated upon the application of external pressure up to $\sim 23$ kbar. Measurements of muon-spin spectroscopy and dc magnetometry evidence a clear mutual independence between the critical temperature $T_{c}$ and the low-temperature saturation value for the ratio $n_{s}/m^{*}$ (superfluid density over effective band mass of Cooper pairs). Remarkably, a dramatic increase of $\sim 30$ % is reported for $n_{s}/m^{*}$ at the maximum pressure value while $T_{c}$ is substantially unaffected in the whole accessed experimental window. We argue and demonstrate that the explanation for the observed results must take the effect of non-magnetic impurities on multi-band superconductivity into account. In particular, the unique possibility to modify the ratio between intra-band and inter-bands scattering rates by acting on structural parameters while keeping the amount of chemical disorder constant is a striking result of our proposed model.