Polaron and bipolaron formation in the Hubbard-Holstein model: Role of next-nearest-neighbor electron hopping

The influence of next-nearest-neighbor electron hopping ${t}^{\ensuremath{'}}$ on the polaron and bipolaron formation in a square Hubbard-Holstein model is investigated within a variational approach. The results for electron-phonon and electron-electron correlation functions show that a negative value of ${t}^{\ensuremath{'}}$ induces a strong anisotropy in the lattice distortions favoring the formation of nearest-neighbor intersite bipolaron. The role of ${t}^{\ensuremath{'}},$ electron-phonon and electron-electron interactions is briefly discussed in view of the formation of charged striped domains.