Unconventional electron-phonon interactions in high-temperature superconductors

The infrared absorption of the 155-${\mathrm{cm}}^{\mathrm{-}1}$ c-axis mode of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ is calculated on the basis of an anharmonic-electron-phonon-interaction model and a large enhancement of its intensity is obtained. A double-well potential in the electron-phonon interaction gives the right order of magnitude for shifts in the bridging O(4) position in agreement with recent x-ray-absorption fine-structure data. Electron-density–two-phonon–interaction terms are derived which represent a violation of the Migdal theorem and a BCS-type superconducting state with nonlinearly enhanced electron-phonon coupling is expected together with an anisotropy of the superconducting energy gap.