Enhanced bound-state formation in two dimensions via stripelike hopping anisotropies

We investigate two-electron bound-state formation in a square two-dimensional t-J-U model with hopping anisotropies for zero-electron density; these anisotropies are introduced to mimic the hopping energies similar to those expected in the stripelike arrangements of holes and spins found in various transition metal oxides. We provide complete analytical solutions to this problem, and thus demonstrate that bound-state formation occurs at a critical exchange coupling, J_c, that decreases to zero in the limit of extreme hopping anisotropy t_y/t_x→0. This behavior is found to be qualitatively identical to that of two electrons on a two-leg ladder in the limit of t_interchain/t_intrachain→0. Using the latter result as guidance, we have determined that this bound state corresponds to one electron moving along one chain, with the second electron moving along the opposite chain, similar to two electrons confined to move along parallel neighboring metallic stripes. Further, we have found that similar behavior is found in systems doped with two holes away from half filling.