Slave-boson approach to the metallic stripe phases with large unit cells

Using a rotationally invariant version of the slave-boson approach in spin space we analyze the stability of stripe phases with large unit cells in the two-dimensional Hubbard model. This approach allows one to treat strong electron correlations in the stripe phases relevant in the low doping regime, and gives results representative of the thermodynamic limit. Thereby we resolve the longstanding controversy concerning the role played by the kinetic energy in stripe phases. While the transverse hopping across the domain walls yields the largest kinetic energy gain in the case of the insulating stripes with one hole per site, the holes propagating along the domain walls stabilize the metallic vertical stripes with one hole per two sites, as observed in the cuprates. We also show that a finite next-nearest neighbor hopping $t$ can tip the energy balance between the filled diagonal and half-filled vertical stripes, which might explain a change in the spatial orientation of stripes observed in the high $T_c$ cuprates at the doping $xsimeq 1/16$.