  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.
