Systematic study of electron-phonon coupling to oxygen modes across the cuprates

The large variations in T-c across the cuprate families is one of the major unsolved puzzles in condensed matter physics and is poorly understood. Although there appears to be a great deal of universality in the cuprates, several orders of magnitude changes in T-c can be achieved through changes in the chemical composition and structure of the unit cell. In this paper we formulate a systematic examination of the variations in electron-phonon coupling to oxygen phonons in the cuprates, incorporating a number of effects arising from several aspects of chemical composition and doping across cuprate families. It is argued that the electron-phonon coupling is a very sensitive probe of the material-dependent variations in chemical structure, affecting the orbital character of the band crossing the Fermi level, the strength of local electric fields arising from structural-induced symmetry breaking, doping-dependent changes in the underlying band structure, and ionicity of the crystal governing the ability of the material to screen c-axis perturbations. Using electrostatic Ewald calculations and known experimental structural data, we establish a connection between the material's maximal T-c at optimal doping and the strength of coupling to c-axis modes. We demonstrate that materials with the largest coupling to the out-of-phase bond-buckling (B-1g) oxygen phonon branch also have the largest T-c's. In light of this observation we present model T-c calculations using a two-well model where phonons work in conjunction with a dominant pairing interaction, presumably due to spin fluctuations, indicating how phonons can generate sizeable enhancements to T-c despite the relatively small coupling strengths. Combined, these results can provide a natural framework for understanding the doping and material dependence of T-c across the cuprates.