Theory for electron- and hole-doped cuprate superconductors: d-wave symmetry order parameter

Using as a model the Hubbard Hamiltonian, we determine various basic properties of electron- and hole-doped cuprate superconductors for a spin-fluctuation-induced pairing mechanism. We find for both hole- and electron-doped cuprates d_{x² − y²} symmetry for the superconducting order parameter. We find a narrow doping range of superconductivity for electron-doped superconductors like Nd_{2 − x}Ce_xCuO₄ and Pr_{2 − x}Ce_xCuO₄. The superconducting transition temperatures T_c(x) for various electron doping concentrations x are calculated to be much smaller than for hole-doped cuprates due to the different energy dispersion and a flat band well below the Fermi level for electron-doped superconductors. Lattice disorder may sensitively distort the symmetry d_{x² − y²} via electron-phonon interaction. We present a general discussion of the symmetry of the order parameter which should apply also to other spin-fluctuation-induced superconductors. Furthermore, we show how our theory may also explain the neutron scattering data.