Anomalously strong small-q electron-phonon coupling in cuprates due to dielectricity

We consider the role of the enormous ionic dielectric constant ε₀ ≈ 30-50 in the cuprates. The ionically-screened Thomas-Fermi screening parameter q̃_TF = [4πe²N(E_F)/ε₀]^1/2 is extremely small, namely 0.2-0.3 Å^-1. The electron-phonon coupling constant I(q, ω) is found to be anomalously large for q ≈ q̃_TF and small ω, accounting for the CDW observed in overdoped BSCCO with wavevector 0.24 Å^-1. Using the Eliashberg theory we derive from this I(q, ω) a maximum T_c of about 200 K. The small electron-phonon scattering angle Δθ = q̃_TFk_F≈0.3 rad acounts for the observed d-wave pairing, as originating from a phonon-mediated mechananism.