  The superconductor-insulator transition (SIT) is considered an excellent
example of a quantum phase transition which is driven by quantum fluctuations
at zero temperature. The quantum critical point is characterized by a diverging
correlation length and a vanishing energy scale. Low energy fluctuations near
quantum criticality may be experimentally detected by specific heat, $c_{\rm
p}$, measurements. Here, we use a unique highly sensitive experiment to measure
$c_{\rm p}$ of two-dimensional granular Pb films through the SIT. The specific
heat shows the usual jump at the mean field superconducting transition
temperature $T_{\rm c}^{\rm {mf}}$ marking the onset of Cooper pairs formation.
As the film thickness is tuned toward the SIT, $T_{\rm c}^{\rm {mf}}$ is
relatively unchanged, while the magnitude of the jump and low temperature
specific heat increase significantly. This behaviour is taken as the
thermodynamic fingerprint of quantum criticality in the vicinity of a quantum
phase transition.
