Exact treatment of some phenomenological models of layered high-Tc superconductors

Existing treatments of phenomenological models of Bi and Tl based superconductors consisting of n layers of copper oxide are unsatisfactory because they ignore the important φ⁴ terms in the free energy. An exact treatment of these models is presented, and it is shown that the condition of minimum free energy automatically excludes (n − 1) of the n critical temperatures. The critical exponent β of the order parameter is found to be independent of n and equal to as usual in the Landau theory. The specific heat discontinuity Δc at the critical temperature is calculated as a function of n. A meaningful comparison with experimental measurements of Δc at the moment is hindered by the limited availability of experimental results. Reliable determinations of Δc of a given series of layered superconductors will enable a check of the validity of theoretical results.