Electron-phonon coupling is believed to be responsible for many spectral anomalies in the cuprate superconductors. In particular, the $B_{1g}$ buckling mode of the oxygen ion in the ${\text{CuO}}_2$ plane has been proposed to be responsible for the dramatic peak-dip-hump (PDH) structure in the antinodal spectrum. The recent observation of the exceptional flat quasiparticle dispersion in the antinodal region and the sudden suppression of the PDH structure around the pseudogap end point cast doubts on such a scenario. Instead, a scenario involving the coupling to the antiferromagnetic spin fluctuation seems to resolve both puzzles naturally. Here, we present a systematic study on the interplay between antiferromagnetic spin fluctuation and electron-phonon coupling in the cuprate superconductors and their respective roles in the origin of the PDH structure. We show that the coupling strength to the $B_{1g}$ buckling mode is strongly renormalized by the vertex correction caused by the antiferromagnetic spin fluctuation. In particular, the coupling strength to the $B_{1g}$ buckling mode is strongly suppressed in the $\mathbf{q}\to 0$ limit as a result of the destructive interference between electron-phonon coupling at electron momentum differ by the antiferromagnetic wave vector. Counterintuitively, we find that the same vertex correction enhances the phonon contribution to the PDH structure as a result of its highly anisotropic momentum dependence around $\mathbf{q}=0$. We also find that while the coupling to either the antiferromagnetic spin fluctuation or the $B_{1g}$ buckling mode can generate a PDH structure in the antinodal spectrum with similar phenomenologies, the sudden suppression of such a structure around the pseudogap end point should be mainly attributed to the dramatic change in the nature of the spin fluctuation at such a critical doping. We suggest to take the PDH structure in the antinodal spectrum as a spectral signature for the emergence of fluctuating local moment in the pseudogap phase and the entrance of a doped Mott insulating state.

Close

PrevNext

View figure in article

• Pseudogap
• Superconductivity
• d-wave
• High-temperature superconductors
• BCS theory
• Diagrammatic methods
• Green's function methods