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We study the finite-size effects on the BCS-BEC crossover in two dimensions, occurring in confined fermionic superfluids. We analyze several thermodynamic properties, such as the chemical potential, the energy gap, and the superfluid density, taking into account unavoidable quantum fluctuations, and, by means of the renormalization group procedure, we detect the putative Berezinskii-Kosterlitz-Thouless phase transition at finite size.
Lanaro et al. (Mon,) studied this question.