LAUSR

We consider the Hubbard-Holstein model on a 2D tilted eight-site square lattice at quarter fillings having on-site (λ1) and inter-site (λ2) electron-phonon (EP) interactions and inter-site Coulomb repulsion (V ). Mobility of electrons decreases, and hence, localization of electrons is favored by λ1 as well as inter-site Coulomb repulsion in the non-interacting limit (U/t = 0.0). In the interacting case (U/t = 8.0), an initial delocalization effect observed due to the competition between on-site Coulomb repulsion and EP interaction λ1 though V favors localization. For smaller λ1, the competition between λ2 and V increases the delocalization effect. As λ2 increases further, localization occurs. In the interacting case, localization occurs at much higher values of λ2 due to the additional delocalization effect of U. On-site (S0) and/or large bipolarons are formed with λ1 in the presence of V, and inter-site Coulomb repulsion effectively increases λ1. Thus, V favors the formation of S0 bipolarons. However, the formation of S1 bipolarons is suppressed by inter-site Coulomb repulsion. An existence of critical λ2 = λ2c is observed for the formation of on-site (S0) and neighboring-site (S1) bipolarons.