orthorhombic phase of copper - oxides

A microscopical theory of electronic spectrum and superconductivity is formulated within the two-dimensional anisotropic t − J model with tx = ty and Jx = Jy. Renormalization of electronic spectrum and superconductivity mediated by spin-fluctuations are investigated within the Eliashberg equation in the weak coupling approximation. The gap function has d + s symmetry with the extended s-wave component being proportional to the asymmetry ty − tx. Some experimental consequences of the obtained results are discussed. Recently the d-wave symmetry of supercon-ducting pairing in cuprates was unambiguously confirmed by observation of half-integer magnetic flux quantum [1]. In a tetragonal phase of copper oxides the s-wave component must be strongly suppressed due to on-site Coulomb correlations. For the 2D t-J model it follows from the constraint of no double occupancy on a single site given by the identity [2]: ˆ a i,σ ˆ a i,−σ = 1 N kx, kyâ k,σ ˆ a −k,−σ = 0. (1) for the projected electron operatorsâ i,σ = a i,σ (1 − n i,−σ). The anomalous correlation func-tionâ k,σ ˆ a −k,−σ is proportional to the gap function , ∆(k x , k y), multiplied by a positive function symmetric in respect to the D 4h point group which defines the symmetry of the Fermi surface (FS). Therefore to satisfy the condition (1) the gap function should have a lower symmetry , e.g. B 1g , " d-wave " symmetry (see, e.g. [3]): ∆ d (k x , k y) = −∆ d (k y , k x). In the orthorhombic phase the FS has a lower symmetry, e.g., D 2h , and the condition (1) can be fulfilled for a gap function of the same symmetry (within the E 1g irreducible representation) which can be written in a general form (" d + s "): ∆(k x , k y) = ∆ d (k x , k y) + ǫ ∆ s (k x , k y). (2) where ∆ s (k x , k y) = ∆ s (k y , k x) is " the extended s-wave " component. In the present paper we calculate supercon-ducting T c for the 2D t-t ′-J model within the theory developed by us in [4], both in tetrago-nal and orthorhombic phases. The orthorhom-bic (D 2h) distortion is taken into account by introducing the asymmetric hopping parameters t ij and the exchange interaction J ij for …