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Effect of impurity scattering on percolation of bosonic islands and reentrant superconductivity in Fe implanted NbN thin films

A reentrant temperature dependence of the thermoresistivity $ρ_{\mathrm{xx}}(T)$ between an onset local superconducting ordering temperature $T_\mathrm{loc}^\mathrm{onset}$ and a global superconducting transition at $T=T_\mathrm{glo}^\mathrm{offset}$ has been reported in disordered conventional 3-dimensional (3D) superconductors. The disorder of these superconductors is a result of either an extrinsic granularity due to grain boundaries, or of an intrinsic granularity ascribable to the electronic disorder originating from impurity dopants. Here, the effects of Fe doping on the electronic properties of sputtered NbN layers with a nominal thickness of 100 nm are studied by means of low-$T$/high-$μ_{0}H$ magnetotransport measurements. The doping of NbN is achieved $via$ implantation of 35 keV Fe ions. In the as-grown NbN films, a local onset of superconductivity at $T_\mathrm{loc}^\mathrm{onset}=15.72\,\mathrm{K}$ is found, while the global superconducting ordering is achieved at $T_\mathrm{glo}^\mathrm{offset}=15.05\,\mathrm{K}$, with a normal state resistivity $ρ_{\mathrm{xx}}=22\,{μΩ}\cdot{\mathrm{cm}}$. Moreover, upon Fe doping of NbN, $ρ_{\mathrm{xx}}=40\,{μΩ}\cdot{\mathrm{cm}}$ is estimated, while $T_\mathrm{loc}^\mathrm{onset}$ and $T_\mathrm{glo}^\mathrm{offset}$ are measured to be 15.1 K and 13.5K, respectively. In Fe:NbN, the intrinsic granularity leads to the emergence of a bosonic insulator state and the normal-metal-to-superconductor transition is accompanied by six different electronic phases characterized by a $N$-shaped $T$ dependence of $ρ_{\mathrm{xx}}(T)$. The bosonic insulator state in a $s$-wave conventional superconductor doped with dilute paramagnetic impurities is predicted to represent a workbench for emergent phenomena, such as gapless superconductivity, triplet Cooper pairings and topological odd frequency superconductivity.