Material-specific gap function in the high-temperature superconductors

Abstract

We present theoretical arguments and experimental support for the idea that high-Tc superconductivity can occur with s-wave, d-wave, or mixed-wave pairing in the context of a magnetic mechanism. The size and shape of the gap is different for different materials. The theoretical arguments are based on the t-J model as derived from the Hubbard model so that it necessarily includes three-site terms. We argue that this should be the basic minimal model for high-Tc systems. We analyze this model starting with the dilute limit which can be solved exactly, passing then to the Cooper problem which is numerically tractable, then ending with a mean field approach. It is found that the relative stability of s-wave and d-wave depends on the size and the shape of the Fermi surface. We identify three striking trends. First, materials with large next-nearest-neighbor hopping (such as YBa(2)Cu(3)O(7-x)) are nearly pure d-wave, whereas nearest-neighbor materials (such as La(2-x)Sr(x)CuO(4)) tend to be more s-wave-like. Second, low hole doping materials tend to be pure d-wave, but high hole doping leads to s-wave. Finally, the optimum hole doping level increases as the next-nearest-neighbor hopping increases. We examine the experimental evidence and find support for this idea that gap function in the high-temperature superconductors is material-specific.

20 pages; requires revtex.sty v3.0, epsf.sty; includes 6 EPS figures; Postscript version also available at http://lifshitz.physics.wisc.edu/www/koltenbah/papers/gapfunc2.ps . This version contains an extensive amount of new work including theoretical background, an additional mean field treatment with new figures, and a more thorough experimental survey

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• Two phase transitions in $(d_{x^2-y^2}+is)$-wave superconductors
• Superconductivity of overdoped cuprates: the modern face of the ancestral two-electron exchange
• d-wave pairing symmetry in cuprate superconductors
• Nonlinear Magnetization in Superconductors with s+d Ordering
• Two-dimensional topological superconducting phases emerged from d-wave superconductors in proximity to antiferromagnets
• Chiral d+is superconducting state in the two dimensional t-t' Hubbard model
• On the derivation of the t-J model: electron spectrum and exchange interactions in narrow energy bands
• Hole-pair symmetry and excitations in the strong-coupling extended t-Jz model: competition between d-wave and p-wave
• Plaquette-centered rotation symmetry and octet-nodal superconductivity in ${\text{KFe}}_2{\text{As}}_2$