Superconducting order parameter symmetry in multilayer cuprates

Abstract

In this paper we classify the allowed order parameter symmetries in multilayer cuprates and discuss their physical consequences, with emphasis on Josephson tunneling and impurity scattering. Our solutions to the gap equation are based on highly non-specific forms for the inter-and intra-plane pairing interactions in order to arrive at the most general conclusions. Within this framework, the bi-layer (N = 2) case is discussed in detail with reference to YBCO and BSCCO and the related Landau-Ginzburg free energy functional. Particular attention is paid to the role of small orthorhombic distortions as would derive from the chains in YBCO and from superlattice effects in BSCCO, which give rise to a rich and complex behavior of the multilayer order parameter. This order parameter has N components associated with each of the N bands or layers. Moreover, these components have specific phase relationships. In the orthorhombic bi-layer case the (s, −s) state is of special interest, since for a wide range of phase space, this state exhibits π phase shifts in corner Josephson junction experiments. In addition, its transition temperature is found to be insensitive to non-magnetic inter-plane disorder, as would be present at the rare earth site in YBCO, for example. Of particular interest, also, are the role of van Hove singularities which are seen to stabilize states with d x 2 −y 2 -like symmetry, (as well as nodeless s-states) and to elongate the gap functions along the four van Hove points, thereby leading to a substantial region of gaplessness. We find that d x 2 −y 2 -like states are general solutions for repulsive interactions; they possess the fewest number of nodes and therefore the highest transition temperatures. In this way, they should not be specifically associated with a spin fluctuation driven pairing mechanism.

Electronic Phase Separation and Electron–Phonon Coupling in Cuprate Superconductors

“…These values are in agreement with the corresponding parameters used in [85][86][87] to describe the experimentally observed phonon renormalization caused by the superconducting transition.…”

Electronic inhomogeneities, electron-lattice and pairing interactions in high-T c superconductors

“…U 0 and κ were estimated in [20] and are equal to U 0 ∼ 0.01 eV and κ ∼ 0.3. These values are in agreement with the values of the corresponding parameters used in [23,24] to describe the experimentally observed phonon renormalizations caused by the superconducting transition.…”

“…Although the magnetic interactions appear to be too weak to be responsible for the temperature of transition in the cuprate superconductors [24], they can significantly increase F d without changing F s and, therefore, help stabilizing the d-wave type solutions of the gap equation.…”

“…This conclusion has been verified numerically. From the analysis of phonon renormalization data given [23,24] follows that U B1g ∼ U 0 ∼ 0.01 eV.…”

Phase Separation and Pairing Fluctuations in Oxide Materials

“…U A 1g ,B 1g and κ were estimated in Ref. [89] to be U A 1g ,B 1g ∼ 100 meV and κ ∼ 0.3 and are the same parameters that allow describing the experimentally observed phonon renormalization at the superconducting transition [103][104][105].…”