Abstract
We consider the Hubbard-Holstein model on a 2D tilted eight-site square lattice at quarter fillings having on-site (λ 1) and inter-site (λ 2) electron-phonon (EP) interactions and inter-site Coulomb repulsion (V ). Mobility of electrons decreases, and hence, localization of electrons is favored by λ 1 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 λ 1 though V favors localization. For smaller λ 1, the competition between λ 2 and V increases the delocalization effect. As λ 2 increases further, localization occurs. In the interacting case, localization occurs at much higher values of λ 2 due to the additional delocalization effect of U. On-site (S0) and/or large bipolarons are formed with λ 1 in the presence of V, and inter-site Coulomb repulsion effectively increases λ 1. 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 λ 2 = λ 2c is observed for the formation of on-site (S0) and neighboring-site (S1) bipolarons.
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