Overactivated transport in the localized phase of the superconductor-insulator transition

Beyond a critical disorder, two-dimensional (2D) superconductors become insulating. In this Superconductor-Insulator Transition (SIT), the nature of the insulator is still controversial. Here, we present an extensive experimental study on insulating Nb_xSi_1-x close to the SIT, as well as corresponding numerical simulations of the electrical conductivity. At low temperatures, we show that electronic transport is activated and dominated by charging energies. The sample thickness variation results in a large spread of activation temperatures, fine-tuned via disorder. We show numerically and experimentally that this originates from the localization length varying exponentially with thickness. At the lowest temperatures, there is an increase in activation energy related to the temperature at which this overactivated regime is observed. This relation, observed in many 2D systems shows that conduction is dominated by single charges that have to overcome the gap when entering superconducting grains.