Effect of fluctuation on two-band superconductor specific heat

It is easily shown that the Ginzburg-Landau equations of a two-band superconductors derived by Moscalenco V.A. can be obtained introducing a free-energy functional depending an a complex two-band order parameter ψ = [ψa (x), ψb (x)]. Quite generally this functional can be viewed as a reduced energy, averaged over all degrees of freedom of the system, except those associated with the two component order parameters. The partition function becomes a functional integral over the field parameters ψa and ψb. For particles whose dimensions are smaller then the coherence length, the spatial uniform mode dominates and the partition functions reduce to a quadrature. The contribution to the zero-dimensional two-bands superconductor specific heat is calculated. The estimation of the influence of the thermodynamic fluctuations on the behaviour of the specific heat shows that the discontinuity is replaced by a smooth variation through Tc. (Author)