Abstract
Despite its fundamental and practical interest, the understanding of mesoscopic effects in strongly coupled superconductors is still limited. Here we address this problem by studying holographic superconductivity in a disk and a strip of typical size $\ensuremath{\ell}$. For $\ensuremath{\ell}<{\ensuremath{\ell}}_{c}$, where ${\ensuremath{\ell}}_{c}$ depends on the chemical potential and temperature, we have found that the order parameter vanishes. The superconductor-metal transition at $\ensuremath{\ell}={\ensuremath{\ell}}_{c}$ is controlled by mean-field critical exponents, which suggests that quantum and thermal fluctuations induced by finite-size effects are suppressed in holographic superconductors. Intriguingly, the effective interactions that bind the order parameter increase as $\ensuremath{\ell}$ decreases. Most of these results are consistent with experimental observations in Pb nanograins at low temperature and are qualitatively different from the ones expected in a weakly coupled superconductor.
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