An Effective Field Model to High Temperature Superconductors: Fitting of The Energy Gap to the Experimental Results of the Bi₂Sr₂CaCu₂O₈

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We use an effective field model (transverse Ising model) to describe the dependence on the temperature of the energy gap of some two-dimensional (2-D) superconducting systems. The order parameter of this model is put in a direct correspondence with that of the Ising model. Then, we use the exact relations for the spontaneous magnetization of the Ising model in some 2-D lattices as a means to fit the experimental results of Bi₂Sr₂CaCu₂O₈ films obtained through reflectivity measurements by Brunel et al [Phys. Rev. Lett. 66, 1346 (1991)] and the argon-annealed Bi₂Sr₂CaCu₂O₈ samples investigated by Staufer et al [Phys. Rev. Lett. 68, 1069 (1992)] through Raman scattering. The zero temperature energy gap Eg(0) relations were evaluated in various 2-D lattices and also in the (3-D) simple cubic lattice, for comparison. In the square lattice case we obtained Eg(0)=3.52kTc, coincidentally the same number as the BCS result, and in the triangular lattice case we get Eg(0)=3.30kTc in agreement with the experimental findings of Brunel et al.