Large calculated electron-phonon interactions in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathit{M}}_{\mathit{x}}$${\mathrm{CuO}}_4$

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.