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

## TL;DR

This study uses sensitive specific heat measurements on 2D granular Pb films to identify thermodynamic signatures of quantum criticality at the superconductor-insulator transition, revealing increased low-temperature specific heat near the critical point.

## Contribution

It provides experimental evidence of quantum criticality through specific heat measurements at the superconductor-insulator transition in granular Pb films.

## Key findings

- Specific heat jump at the mean field transition temperature remains unchanged near the SIT.
- Magnitude of the specific heat jump and low-temperature specific heat increase near the SIT.
- Thermodynamic behavior indicates quantum criticality at the transition.

## Abstract

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.