Coherent motion of a hole in the copper-oxygen planes of high-temperature superconductors

Abstract

The dispersion relation for the coherent propagation of a hole moving in a two-dimensional (CuO2)N system is discussed. The (CuO2)N planes constitute the most important structural element in the high-Tc superconducting materials. The system is described by the Kondo-Heisenberg Hamiltonian, which is a simplified version of the extended Hubbard or Emery model. The calculations are based on the introduction of a trial wave function in the unitary space of the Cu spins and the O degrees of freedom. They generalize an approach recently proposed for the coherent motion of a hole in thet-J model. The propagation is mainly determined by the spin-fluctuation part of the superexchange between the copper spins. Minor contributions to the coherent hole motion are due to an effective tunneling of the hole to second and third nearest neighbors along spiral paths in the (CuO2)N plane. This mechanism can be considered as the analogue of a mechanism for coherent hole motion in thet-J model first discussed by Trugman. For the dispersion relation a cosine-band-like form is found similar to that for thet-J model. The band width, however, is somewhat increased. Except for this difference, our results seem to support the point of view of Zhang and Rice, who have claimed that there exists a one-to-one mapping between the low-lying states of the two-band model and the effectivet-J model.