Comment on : “ First - order phase transitions of type - I superconducting films

The theory of fluctuation induced first order phase transition from normal to uniform (Meissner) superconducting state in a zero external magnetic field was developed for thin films of type I superconductors in a series of papers [1, 2, 3, 4, 5, 6, 7]. The same problem was considered in a recent theoretical investigation [8]. The authors of the paper [8] derived an erroneous effective free energy of superconducting slabs (films) and this error led them to entirely wrong conclusions. Here we shall make clear the genesis of this mistake by using the notations in [8]. At a certain stage of derivation of the effective free energy F(φ) as a function of the modulus (φ ≡ |ψ|) of the superconducting order parameter ψ, the authors of Ref. [8] have obtained the following result