Specific heat of a 2D superconductor in the BEC limit

We analyze the evolution of the temperature dependence of the specific heat between BCS and BEC regimes in a 2D superconductor. In 2D, two fermions in a vacuum form a bound pair at energy E₀ at arbitrary weak attraction, and this allows one to study BCS-BEC crossover at weak coupling, as the function of the ratio of E₀ and the Fermi energy E_F. A conventional BCS-type behavior holds when E_F>>E₀. In the BEC limit at E_F<<E₀, bound fermionic pairs are formed at T^*∼E₀ (modulo logarithmic corrections), while 2D superconductivity develops at T_c∼E_F due to strong phase fluctuations. In the mean-field description of this regime, the specific heat jumps at T^* and shows superconducting-like behavior at smaller T, with no signatures at the actual T_c. A generic reasoning is that beyond mean-field, the jump at T^* should be replaced by a maximum, with a new jump appearing at T_c, where the true condensate is formed. We go beyond mean-field and verify this assertion in explicit calculations, which include thermal fluctuations.