Anomalous Electron-Phonon Coupling in Cuprates and its Doping Dependence

It is well known that conventional superconductivity is mediated by phonons. Phonon renormalization at specific wavevectors (Kohn anomalies) appears in phonon dispersions in many of these compounds with high T$_{c}$s in agreement with LDA calculations. In the case of the cuprates, LDA calculations predict neither any significant Kohn anomalies nor electron-phonon coupling strong enough to account for high T$_{c}$ superconductivity. However, inelastic neutron and x-ray scattering experiments found huge softening and broadening of the bond-stretching phonons indicating that electron-phonon coupling in the cuprates is much stronger than expected from LDA. In the LaSrCuO family phonon renormalization has been observed in the vicinity of the reduced in-plane wavevector q$_{in}$=(0.25, 0) (in units of (2$\pi $/a,2$\pi $/a where a is the near-neighbor Cu-Cu distance). The effect is strongest at low temperatures and in compositions that exhibit the so-called stripe order where it occurs at the wavevector that corresponds to the charge order. Detailed \textbf{q}-dependent studies revealed that the underlying electronic instability is 2D in nature in the 214 compounds, i.e. for q$_{in}$=(0.25, K), it is peaked at K=0 with the full width at half maximum of about 0.15 r.l.u. The strength of this phonon renormalization tracks T$_{c}$ disappearing at the nonsuperconducting extremes of doping. In YBCO the similar phonon anomaly is quasi-1D with bond-stretching phonon renormalization occurring around q$_{in}$=(H, 0.25) for all investigated H (in units of (2$\pi $/a,2$\pi $/b where a/b is the near-neighbor Cu-Cu distance in the direction paralle/perpendicular to the Cu-O chains). Relationship between these effects and band structure will be explored. Experimental results will also be compared with expectations of LDA-based calculations as well as with predictions of models based on dynamic stripes.