Polaron effective mass, band distortion, and self-trapping in the Holstein molecular-crystal model

摘要

We present polaron effective masses and selected polaron band structures of the Holstein molecular-crystal model in one dimension as computed by the Global-Local variational method over a wide range of parameters. These results are augmented and supported by leading orders of both weak- and strong-coupling perturbation theory. The description of the polaron effective mass and polaron band distortion that emerges from this work is comprehensive, spanning weak, intermediate, and strong electron-phonon coupling, and nonadiabatic, weakly adiabatic, and strongly adiabatic regimes, Using the effective mass as the primary criterion, the self-trapping transition is precisely defined and located. Using related band-shape criteria at the Brillouin-zone edge, the onset of band narrowing is also precisely defined and located. These two lines divide the polaron parameter space into three regimes of distinct polaron structure, essentially constituting a polaron phase diagram. Though the self-trapping transition is thus shown to be a broad and smooth phenomenon at finite parameter values, consistency with the notion of self-crapping as a critical phenomenon in the adiabatic Limit is demonstrated. Generalizations to higher dimensions are considered, and resolutions of apparent conflicts with well-known expectations of adiabatic theory are suggested.[S0163-1829(99)01221-7]. [References: 57]