Electron-phonon coupling and d-wave superconductivity in the cuprates.

Abstract

We derive an effective single-band Hubbard-type Hamiltonian for ${\mathrm{CuO}}_{2}$ planes in the cuprate high-${\mathit{T}}_{\mathit{c}}$ superconductors. The Hamiltonian includes both electron-electron repulsion and electron-phonon coupling to oxygen vibrational modes. The effective Hamiltonian is derived by mapping from the multiband constrained-density-functional-theory Hamiltonian to a one-band model. A Hartree-Fock mapping leads to t=0.66 eV, t'=-0.14 eV, and U=4.0 eV. Very similar parameters are obtained by exact diagonalization of finite clusters. The electron-phonon coupling to oxygen breathing modes gives \ensuremath{\lambda}=0.57 for s-wave and \ensuremath{\lambda}=0.35 for ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ pairing. d-wave superconductivity is predicted to occur at 30 K for doped ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$, while the strong Coulomb repulsion suppresses the s-wave ${\mathit{T}}_{\mathit{c}}$ to 10 K.