Nanoscale phase separation and superconductivity in the one-dimensional Hirsch model

We investigate numerically at various fillings the ground state of the one-dimensional Hubbard model with correlated hopping x (Hirsch model) . It is found that, for a large range of filling values n around half filling, and for repulsive Coulomb interaction u <= u(c) (x,n), phase separation at a nanoscale (NPS phase) between two conducting phases at different densities occurs when x greater than or similar to 2/3. The NPS phase is accompanied by the opening of a spin gap and the system behaves as a Luther-Emery liquid with dominant superconducting correlations. Close to half filling, an anomalous peak emerges in the charge structure factor related to the density of doubly occupied sites, which determines the size of the droplets in the NPS phase. For 1/2 less than or similar to x less than or similar to 2/3 a crossover to a homogeneous phase, still superconducting, takes place.