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 ~q_TF = [4θe²N(E_F)/εin0 ^1/2 is extremely small, namely 0.2-0.3 A^-1. The electron-phonon coupling constant I(q,w) is found to be anomalously large forq ≈ ~q_TF and smallco, accounting for the CDW observed in overdoped BSCCO with wavevector 0.24 A^-1. Using the Eliashberg theory we derive from this I(q,w) a maximumT _c of about 200 K. The small electron-phonon scattering angle △θ = ~q _{F ≈} 0.3 rad acounts for the observedd-wave pairing, as originating from a phonon-mediated mechananism.