EFFECTIVE SINGLE-BAND HAMILTONIAN FOR ELECTRON-PHONON COUPLING IN CUPRATE SUPERCONDUCTORS

We derive an effective single-band Hubbard type Hamiltonian for CuO2 p lanes. The Hamiltonian includes both electron-electron repulsion and e lectron-phonon coupling to oxygen vibrational modes. We start with fir st-principles density functional theory parameters and then map onto a single-band model. Unlike previous mappings to a single-band Hamilton ian, ours explicitly preserves the Fermi surface shape and matrix elem ents of the many-band Hamiltonian. We consider both in-plane oxygen br eathing modes as well as out-of-plane tilting modes. The latter modes have a quadratic electron-phonon coupling, and are also highly anharmo nic in La2CUO4 based superconductors. The coupling to breathing modes is too small to account for high T-c, while the coupling to quadratic modes is much stronger even though they would be neglected in a standa rd Migdal-Eliashberg approach to superconductivity.