Interplay between antiferromagnetic spin fluctuation and electron-phonon coupling and the origin of the peak-dip-hump structure in the anti-nodal spectrum of high-$T_{c}$ cuprate superconductors

TL;DR

This study investigates how antiferromagnetic spin fluctuations and electron-phonon interactions influence spectral features in high-$T_c$ cuprates, revealing the suppression of phonon effects by spin fluctuations and linking spectral signatures to pseudogap phenomena.

Contribution

It demonstrates the suppression of electron-phonon coupling by spin fluctuations and clarifies the origin of the peak-dip-hump structure in cuprates' spectra, highlighting the role of spin fluctuations in pseudogap physics.

Findings

Vertex correction suppresses electron-phonon coupling at q→0.

Spin fluctuations enhance the phonon contribution to PDH.

Suppression of PDH linked to changes in spin fluctuation nature at pseudogap end.

Abstract

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 $CuO_{2}$ plane has been proposed to be responsible for the dramatic peak-dip-hump(PDH) structure in the anti-nodal spectrum. The recent observation of the exceptional flat quasiparticle dispersion in the anti-nodal 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. We show that the coupling strength to the $B_{1g}$ buckling mode is strongly suppressed by the vertex correction caused by the antiferromagnetic spin fluctuation in the $\mathbf{q}\rightarrow 0$ 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. 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 anti-nodal 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 anti-nodal 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.