Strong electron-phonon interaction in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$

The electron-phonon interaction in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ is investigated, beginning with a self-consistent linear-combination-of-atomic-orbitals band calculation, and using a tight-binding parametrization to obtain derivatives of the Hamiltonian matrix with respect to atomic displacements. The phonon spectrum is calculated on the basis of the shell model. We solve the anisotropic Eliashberg equations and obtain a high ${\mathit{T}}_{\mathit{c}}$ in accord with experiment, but also a large oxygen-isotope effect. The gap function is calculated on the different sheets of the Fermi surface. It is strongly anisotropic but nodeless.