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Recent scanning tunnelling microscopy experiments in NbN thin disorderedsuperconducting films found an emergent inhomogeneity at the scale of tens ofnanometers. This inhomogeneity is mirrored by an apparent dimensional crossoverin the paraconductivity measured in transport above the superconductingcritical temperature $T_c$. This behavior was interpreted in terms of ananomalous diffusion of fluctuating Cooper pairs, that display a {\emquasi-confinement} (i.e., a slowing down of their diffusive dynamics) on lengthscales shorter than the inhomogeneity identified by tunnelling experiments.Here we assume this anomalous diffusive behavior of fluctuating Cooper pairsand calculate the effect of these fluctuations on the electron density ofstates above $T_c$. We find that the density of states is substantiallysuppressed up to temperatures well above $T_c$. This behavior, which is closelyreminiscent of a pseudogap, only arises from the anomalous diffusion offluctuating Cooper pairs in the absence of stable preformed pairs, setting thestage for an intermediate behavior between the two common paradigms in thesuperconducting-insulator transition, namely the localisation of Cooper pairs(the so-called bosonic scenario) and the breaking of Cooper pairs into unpairedelectrons due to strong disorder (the so-called fermionic scenario).

Effect of the Anomalous Diffusion of Fluctuating Cooper Pairs in the Density of States of Superconducting NbN Thin Films