Superconductivity in two dimensions is nontrivial. One way to achieve global superconductivity is via the Berezinskii-Kosterlitz-Thouless (BKT) transition due to proliferation of vortex-antivortex pairs. This transition is expected to have a clear signature on the specific heat. The singularity at the transition temperature TBKT is predicted to be immeasurable, and a broad nonuniversal peak is expected at T>TBKT. Up to date, this has not been observed in two-dimensional superconductors; this work is then dedicated to investigate cp signatures in the limit of ultrathin 2d superconductors. We use a unique highly sensitive technique to measure the specific heat of quench condensed ultrathin Pb films. We find that thick films exhibit a specific heat jump at TC that is consistent with BCS theory. As the film thickness is reduced below the superconducting coherence length and the systems enter the 2D limit, the specific heat reveals BKT-like behavior in what can appear as to be a continuous BCS-BKT crossover as a function of film thickness. However, a number of problems arise with this interpretation. We discuss the experimental results and the possible significance of various scenarios involving BKT physics.
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