Dominance of the electron-phonon interaction with forward scattering peak in high-Tcsuperconductors: Theoretical explanation of the ARPES kink

Abstract

The angle-resolved photoelectron spectroscopy (ARPES) spectra in high-${T}_{c}$ superconductors show four distinctive features in the quasiparticle self-energy $\ensuremath{\Sigma}(\mathbf{k},\ensuremath{\omega})$. 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 $70\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ in the superconducting state, contrary to the observed shift of the antinodal singularity at $40\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. The theory predicts a kneelike structure of $\ensuremath{\mid}\mathrm{Im}\phantom{\rule{0.2em}{0ex}}\ensuremath{\Sigma}(\ensuremath{\omega})\ensuremath{\mid}=\ensuremath{\mid}\mathrm{Im}\phantom{\rule{0.2em}{0ex}}{\ensuremath{\Sigma}}_{\mathit{ph}}(\ensuremath{\omega})+\mathrm{Im}\phantom{\rule{0.2em}{0ex}}{\ensuremath{\Sigma}}^{C}(\ensuremath{\omega})\ensuremath{\mid}$, which is phonon dominated, $\ensuremath{\mid}\mathrm{Im}\phantom{\rule{0.2em}{0ex}}\ensuremath{\Sigma}({\ensuremath{\omega}}_{\mathit{ph}})\ensuremath{\mid}\ensuremath{\approx}\ensuremath{\mid}\mathrm{Im}\phantom{\rule{0.2em}{0ex}}{\ensuremath{\Sigma}}_{\mathit{ph}}({\ensuremath{\omega}}_{\mathit{ph}})\ensuremath{\mid}\ensuremath{\sim}\ensuremath{\pi}{\ensuremath{\lambda}}_{\mathit{ph}}{\ensuremath{\omega}}_{\mathit{ph}}∕2$, for $\ensuremath{\omega}\ensuremath{\approx}{\ensuremath{\omega}}_{\mathit{ph}}^{(70)}$, and for $\ensuremath{\omega}>{\ensuremath{\omega}}_{\mathit{ph}}^{(70)}$ shows linear behavior $\ensuremath{\mid}\mathrm{Im}\phantom{\rule{0.2em}{0ex}}\ensuremath{\Sigma}(\ensuremath{\omega})\ensuremath{\mid}\ensuremath{\approx}\ensuremath{\mid}\mathrm{Im}\phantom{\rule{0.2em}{0ex}}{\ensuremath{\Sigma}}_{\mathit{ph}}({\ensuremath{\omega}}_{\mathit{ph}})\ensuremath{\mid}+\ensuremath{\pi}{\ensuremath{\lambda}}_{C,\ensuremath{\varphi}}\ensuremath{\omega}∕2$, due to the Coulomb scattering. ARPES spectra give ${\ensuremath{\lambda}}_{\mathit{ph}}>1$---which is obtained from $\mathrm{Re}\phantom{\rule{0.2em}{0ex}}\ensuremath{\Sigma}$, and ${\ensuremath{\lambda}}_{C}<0.4$---obtained from $\mathrm{Im}\phantom{\rule{0.2em}{0ex}}\ensuremath{\Sigma}$, i.e., ${\ensuremath{\lambda}}_{\mathit{ph}}⪢{\ensuremath{\lambda}}_{C}$. The dip-hump structure in the spectral function $A({\mathbf{k}}_{F},\ensuremath{\omega})$ comes out naturally from the proposed theory.