Quantum criticality at the superconductor to insulator transition revealed by specific heat measurements

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\mathrm{.}Here,weuseauniquehighlysensitiveexperimenttomeasure$c_{\rm p}$ of two-dimensional granular Pb films through the SIT. The specific heat shows the usual jump at the mean field superconducting transition temperature $T_{\mathrm{c}}^{\mathrm{m}\mathrm{f}}$ marking the onset of Cooper pairs formation. As the film thickness is tuned toward the SIT, $T_{\mathrm{c}}^{\mathrm{m}\mathrm{f}}$ 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.