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Effect of d Z2 ‐Cu and p‐O Orbital Mixing in the High‐ T c Superconducting Materials. A Three‐Dimensional Anisotropic Interaction
Author(s) -
RodríguezNúñez J. J.
Publication year - 1993
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221790117
Subject(s) - superexchange , superconductivity , condensed matter physics , anisotropy , atomic orbital , hamiltonian (control theory) , physics , hubbard model , quantum mechanics , antiferromagnetism , electron , mathematics , mathematical optimization
A three‐dimensional (3D) anisotropic interaction is obtained for the oxide high‐ T c superconductors when we take into account the mixing of d Z2 ‐Cu with the p‐O orbitals. Two hopping matrix elements, t l , on the plane, and t 2 , along the z ‐axis, are used to study anisotropy in the original Hubbard Hamiltonian. The derived interaction contains a local Hubbard term, U, and two non‐local superexchange contributions, J 1 , and J 2 . Both J 1 and J 2 strongly depend on the anisotropy ratio (α ≡ t 2 / t l ). However, for α = 0, J 2 , → 0, and J 1 , the superexchange on the plane, coincides with results previously published in 2D. Furthermore, when α = 1, J 1 ⟺ J 2 . The latter result is also known in the literature. The effective Hamiltonian presented here is more physical for studying high‐ T c superconducting materials, since the third dimension is playing an increasing role as it has been pointed out by several authors. It is also found that the hole occupation on the p,‐orbital (〈 n pz 〉), for α ≪ 1, is related to the hole occupation on the p x ‐ and p y ‐orbitals, by means of the relationship 〈 n pz 〉 ≈ α 2 〈 n px 〉, which is in qualitative agreement with experimental and theoretical findings that 〈 n pz 〉 is very small. The calculated T c versus n shows agreement with recent experiments in La 2− x Sr x CuO 4 .