The Effect of Sr Substitution on the Crystal Symmetry and Superconductivity of the High-temperature Superconductor La 2-x Sr x CuO4

About four decades elapsed since the discovery of La_2-xSr_xCuO₄ (LSCO) and still no consensus on a theoretical model to describe the phase diagram of the high-Tc cuprates, including the HTSC mechanism itself. What is new in the current treatment of research is that it may introduce a new vision for superconductive behavior in La_2-xSr_x CuO₄. This vision is based on considering aspects which were not given the needed attention. These are (1) crystal symmetry affects Sr²⁺dopants distribution on lattice sites and (2) Sr²⁺ dopants affect lattice symmetry and superconductivity, whereas all solutions are given concentrate on charge carriers but till now no conscience on it. So, using the basic aspects of the new vision, this research may succeed to a good extent to uncover and determine the role of symmetric distribution of dopants in the appearance of many anomalies like charge strips and its turnover, and of complex behavior of phases in the face diagram. So, I build models to explain experimental facts depending on symmetry aspects. The study reveals also the role of doping in superconductivity, and I think, it was successful to some extent. By analytical treatment of the distances between dopants on the lattice site in the charged strips near the point of start of superconductivity, it was found that the distances between dopants are within the coherence length (C.L _dopant. = 35.35 Å) knowing that (C.L _real = 33 Å) is the distant within which superconductivity changes. It means that the symmetric distribution of dopants affects superconductivity. Doping with Sr²⁺ leads to a change in the lattice symmetry from tetragonal to orthorhombic, analytical model was used in this research to prove the experimental facts about these changes, it was found that this symmetry change leads to the collapse of the lattice in the space around Sr²⁺ as in Fig. 3, and this collapsed can be considered equivalent to a negative charge at the center of this space. Based on the symmetric effects on dopant distribution, a model for the phase diagram can be applied easily to give explanations of the unclear changes in the phase diagram on a single scenario depending on the distribution of (1 or 2 or 3) Sr ions for all the lattice sites; this doping steps of the Sr²⁺ which are proportional to the increase in concentration can clearly explain the strange formation of the different phases in the LSCO phase diagram. Consistent with the new vision in this research on superconductivity in LSCO, a model is suggested for hole pairing, in which the O²⁻ atom in the CuO plane that is nearer to Sr²⁺ is the site around which hole pairing happens as in Fig. 5. The Coulombic repulsion between holes is zero due to the opposite directions of attraction forces with the O²⁻ ion and provides a place for superexchange mechanism for hole pairing to form Cooper pair (this O site can be considered one of Hubbard’s sits) the hole pairs can move within the a charge strip along the a or b crystal axis.