Effects of next-nearest-neighbor hopping on the hole motion in an antiferromagnetic background

In this paper we study the effect of next-nearest-neighbor hopping on the dynamics of a single hole in an antiferromagnetic (Neel) background. In the framework of large dimensions the Green function of a hole can be obtained exactly. The exact density of states of a hole is thus calculated in large dimensions and on a Bethe lattice with large coordination number. We suggest a physically motivated generalization to finite dimensions (e.g., 2 and 3). In d=2 we present also the momentum-dependent spectral function. With varying degree, depending on the underlying lattice involved, the discrete spectrum for holes is replaced by continuum background and a few resonances at the low-energy end. The latter are the remanents of the bound states of the t-J model. Their behavior is still largely governed by the parameters t and J. The continuum excitations are more sensitive to the energy scales t and t1