Dynamics and transport of a large acoustic polaron in one dimension

Abstract

We have studied the dynamics and transport relaxation of a large polaron in a one-dimensional (1-D) system with an acoustic- (Debye) type phonon spectrum and a deformation potential electron-phonon interaction. The dynamics is treated in a collective coordinate formalism which shows that such a polaron moves as a heavy quasi-particle that carries energy and (crystal) momentum. For thermal energies less than the polaron binding energy, its transport relaxation is dominated by collision processes wherein a thermal phonon is reflected off the polaron with a momentum transfer that is small compared to the thermal polaron momentum. The phonon reflectivity is estimated and found to exhibit a maximum (resonance) for phonon wavelengths that match the polaron size. Furthermore, the reflectivity is largely independent of the polaron momentum. We incorporate these results into a semi-classical (Boltzmann) kinetic theory and obtain a polaron mobility that is independent of the polaron effective mass and decreases monotonically with increasing temperature. These results are compared to and found to be substantially different from those obtained recently for the large polaron in the 1-D molecular cystal model wherein the underlying phonon spectrum has optical (Einstein) character. To study the effects of three-dimensional (3-D) coupling on the 1-D polaron, we propose a simple 3-D extension of the 1-D acoustic model which includes both electronic and elastic interchain interactions. We briefly discuss the question of polaron stability in the presence of 3-D coupling and the criteria of validity for the purely 1-D treatment.