The angle-resolved photoelectron spectroscopy (ARPES) spectra in high-$T_c$ superconductors show four distinctive features in the quasiparticle self-energy $\Sigma (\mathbf{k},\omega )$. They can be explained consistently by the phenomenological microscopic theory in which the electron-phonon interaction with the forward-scattering peak dominates over the Coulomb scattering. This theory explains why there is no shift of the nodal kink at $70\mathrm{meV}$ in the superconducting state, contrary to the observed shift of the antinodal singularity at $40\mathrm{meV}$. The theory predicts a kneelike structure of $\mid \mathrm{Im}\Sigma \left(\omega \right)\mid =\mid \mathrm{Im}{\Sigma }_{\mathit{ph}}\left(\omega \right)+\mathrm{Im}{\Sigma }^C\left(\omega \right)\mid$, which is phonon dominated, $\mid \mathrm{Im}\Sigma \left({\omega }_{\mathit{ph}}\right)\mid \approx \mid \mathrm{Im}{\Sigma }_{\mathit{ph}}\left({\omega }_{\mathit{ph}}\right)\mid \sim \pi {\lambda }_{\mathit{ph}}{\omega }_{\mathit{ph}}∕2$, for $\omega \approx {\omega }_{\mathit{ph}}^{\left(70\right)}$, and for $\omega >{\omega }_{\mathit{ph}}^{\left(70\right)}$ shows linear behavior $\mid \mathrm{Im}\Sigma \left(\omega \right)\mid \approx \mid \mathrm{Im}{\Sigma }_{\mathit{ph}}\left({\omega }_{\mathit{ph}}\right)\mid +\pi {\lambda }_{C,\phi }\omega ∕2$, due to the Coulomb scattering. ARPES spectra give ${\lambda }_{\mathit{ph}}>1$—which is obtained from $\mathrm{Re}\Sigma$, and ${\lambda }_C<0.4$—obtained from $\mathrm{Im}\Sigma$, i.e., ${\lambda }_{\mathit{ph}}⪢{\lambda }_C$. The dip-hump structure in the spectral function $A({\mathbf{k}}_F,\omega )$ comes out naturally from the proposed theory.

• Received 1 June 2004

DOI:https://doi.org/10.1103/PhysRevB.71.092505