Properties of the moving Holstein large polaron in one-dimensional molecularcrystals

Abstract

The features of the moving large polaron are investigated within Holstein’s molecularcrystal model. The necessity to account for the phonon dispersion is emphasized and itsimpact on polaron properties is examined in detail. It was found that the largepolaron dynamics is described by the nonlocal nonlinear Schrödinger equation. Thecharacter of its solutions is determined by the degree of nonlocality, which isspecified by the polaron velocity and group velocity of the lattice modes. An analyticsolution for the polaron wavefunction is obtained in the weakly nonlocal limit. Itwas found that the polaron velocity and phonon dispersion have a significantimpact on the parameters and dynamics of large polarons. The polaron amplitudeand effective mass increase while its spatial extent decreases with a rise in thedegree of nonlocality. The criterion for the stability of large polaron is formulatedin terms of the values of the degree of nonlocality, the magnitude of the basicenergy parameters of the system and the polaron velocity. It turns out that thelarge polaron velocity cannot exceed a relatively small limiting value. A similarlimitation on large polaron velocity has not been found in previous studies. Theconsequences of these results on polaron dynamics in realistic conditions are discussed.