Abstract
In the weak coupling limit, the 2D Hubbard model extended by on-site (local) and inter-site (long range) electron-phonon (EP) interaction has been investigated within Lanczos method of exact diagonalization (ED). On-site (S0) bipolaron formation has been favored by on-site EP interaction induced effective attraction between electrons. But, inter-site phonon mediated interaction between electrons helps to form both S0 and neighboring site (S1) bipolaron. It is further observed that both types of bipolaron formation are suppressed by on-site Hubbard repulsion.
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