Results of self-consistent linearized-augmented-plane-wave calculations within the local-density-functional approximation (LDA) are presented of the electron-phonon-induced linewidths and interaction strength of selected phonons in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathit{M}}_{\mathit{x}}$${\mathrm{CuO}}_4$ at x=0.15. Through the use of a supercell geometry, rigid-ion-type approximations are avoided and the full electron-phonon matrix elements are determined from finite differences of the LDA potentials corresponding to frozen-in phonon at Γ X, and Z. At the X point, all fully symmetric ${\mathit{A}}_{\mathit{g}}$ modes (i.e., having the symmetry of the oxygen planar-breathing mode) as well as three modes having ${\mathit{B}}_{3\mathit{g}}$ symmetry are examined. Small linewidths were found for the three ${\mathit{B}}_{3\mathit{g}}$ modes, and moderate linewidths for the ${\mathit{A}}_{\mathit{g}}$ modes, the largest corresponding to ratios ${\gamma }_{\mathit{q},\nu }$/${\mathrm{\omega }}_{\mathit{q},\nu }$=0.02 for the oxygen breathing and axial modes.

The axial ${\mathit{O}}_{\mathit{z}}$ mode at the Z point has a very large width, ${\gamma }_{\mathit{q},\nu }$/${\mathrm{\omega }}_{\mathit{q},\nu }$=0.11. Unusual long-range Madelung-like interactions are found to yield large matrix elements, especially for modes near the zone center and are responsible for couplings of the cations (La) to the charge carriers. The linewidth of a mode also directly determines ${\lambda }_{\mathit{q},\nu }$, the contribution of mode (q,ν) to the electron-phonon coupling constant, λ, and an approximate average over the Brillouin zone yields λ≃1.3, about the magnitude necessary to explain ${\mathit{T}}_{\mathit{c}}$ in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathit{M}}_{\mathit{x}}$${\mathrm{CuO}}_4$. In spite of some very strong coupling to low-frequency modes, the mean frequency ${\mathrm{\omega }}_{\log }$ that is important in determining ${\mathit{T}}_{\mathit{c}}$ is large: ${\mathrm{\omega }}_{\log }$=321 ${\mathrm{cm}}^{\mathrm{-}1}$=462 K. The calculated large electron-phonon coupling arises from a combination of weak screening and unusual nonlocal Madelung-like interactions, in concert with strong Cu-O hybridization that results in good metallic behavior within the planes. These features are common to all of the layered cuprates, indicating that the entire class should show strong electron-phonon coupling.

• Received 29 June 1992

DOI:https://doi.org/10.1103/PhysRevB.47.1002