Polaron Effective Mass, Band Distortion, and Self-Trapping in the Holstein Molecular Crystal Model

TL;DR

This paper comprehensively analyzes polaron effective masses, band structures, and self-trapping transitions in the 1-D Holstein model across various coupling regimes using variational and perturbation methods.

Contribution

It provides a detailed phase diagram of polaron regimes, precisely locating self-trapping and band narrowing transitions across different coupling and adiabatic regimes.

Findings

Self-trapping transition is broad and smooth at finite parameters.

Polaron phase diagram with three distinct regimes.

Consistency with critical phenomena in the adiabatic limit.

Abstract

We present polaron effective masses and selected polaron band structures of the Holstein molecular crystal model in 1-D 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 non-adiabatic, 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 thusly shown to be a broad and smooth phenomenon at finite parameter values, consistency with notion of self-trapping 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.