Adiabatic nature of hole-doped states in strongly coupled electron-phonon systems

We investigate the effects of hole doping in the charge-density wave (CDW) state that has the strong electron-phonon $(\equiv e-p)$ interactions by using the two-dimensional molecular crystal model. In calculations, we use the mean-field theory for the interelectronic interactions and the adiabatic approximation for phonons. In order to clarify how the structural changes are induced by hole doping, we calculate the e-p states for various values of the doping concentration of holes (≡ρ). The doped holes have a strong tendency to collectively construct the longer periodic CDW than the half filled one, and it coexists with domainlike localized structures of other holes. As a consequence of this, the doped systems come to have a multistability of the e-p states intrinsically. This is nothing but the increase of the structural fluctuation just before the phase changes from the insulating CDW state to the metal. Including the effects of this multistability in our theory, we also calculate the correlation function for the pairing tendency between holes, and find that it is enhanced just before the phase transition. These results convince us that the multistable nature of the doped states plays an important role on the phase transition from the CDW to the metallic or the superconducting state of the strongly coupled e-p systems.