Oscillation of Tc depending on the number of CuO2 planes in the cuprates.pdf

1 Oscillation of Tc depending on the number of CuO2 planes in the cuprates A. Messad Laboratoire de Physique, Lycée Olympe de Gouges, 93130 Noisy-Le-Sec, France. Using the Tc formula given by BCS, together with a shear modulus varying with the numbering of planes, we can demonstrate that Tc oscillates depending on the number of the cuprate planes. The maximum in these oscillations appears for three planes irrespective of the multilayered cuprate family. Comparison with experimental data shows good agreement and suggests that the electron- phonon coupling predominate in the superconductivity of these cuprates. This model predicts that such oscillations can also occur in many others physical quantities that depend on Tc. The new Tc formula shows interesting prospects towards room temperature superconductors. PACS numbers: 74.62. -c ; 74.72. -h. Keywords: cuprates; BCS; shear modulus; Tc oscillations. 1. Introduction The critical temperature of the multilayered cuprates superconductors depends on the number of adjacent cuprate planes in the unit cell. If within a given cuprate family that is taken at the optimal doping, we vary the number n of the cuprate planes, we can observe that Tc follows a curve that looks like a dome whose maximum is at n = 3. This was experimentally well shown for the mercurocuprates family [1]. However, all experimentalists have pointed out the difficulty of elaborating and characterising compounds for which n is greater than 4 or 5 [2]. Recently, some experimentalists who used better materials have come to recognize that Tc is constant or hardly varies when n is superior to 5 or 6 [3]. Using the classic BCS expression of Tc together with a model of the shear modulus of a stacking of cuprate planes, we show that Tc oscillates depending on n and that the famous n = 3 arises naturally as being the localisation of the first maximum in these oscillations. In this paper, I expound an in-depth analysis of previous resul