Umklapp electron-electron scattering resistivity of half-filled copper-oxygen chains and planes

The resistivity due to Umklapp electron-electron scattering is calculated for half-filled one-dimensional and two-dimensional tight-binding bands corresponding to the copper-oxygen chains and planes found in the high-temperature superconductor YBa2Cu3O/sub 7-//sub x/. In the simple models studied, this resistivity is shown to be proportional to the temperature. The Umklapp electron-electron scattering rate for the model is very sensitive to doping, and thus does not explain the observed resistivity of YBa2Cu3O/sub 7-//sub x/, in which the planes are believed to be doped away from half filling. Nonetheless, the calculated magnitude of the resistivity is similar to that observed experimentally in the superconducting cuprates