Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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. 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.

13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom