Disordered thin films close to the superconducting-insulating phase transition (SIT) hold the key to understanding quantum phase transition in strongly correlated materials. The SIT is governed by superconducting quantum fluctuations, which can be revealed for example by tunneling measurements. These experiments detect a spectral gap, accompanied by suppressed coherence peaks that do not fit the BCS prediction. To explain these observations, we consider the effect of finite-range superconducting fluctuations on the density of states, focusing on the insulating side of the SIT. We perform a controlled diagrammatic resummation and derive analytic expressions for the tunneling differential conductance. We find that short-range superconducting fluctuations suppress the coherence peaks, even in the presence of long-range correlations. Our approach offers a quantitative description of existing measurements on disordered thin films and accounts for tunneling spectra with suppressed coherence peaks observed, for example, in the pseudo gap regime of high-temperature superconductors.
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