Polaron Crossover in Molecular Solids

TL;DR

This paper investigates the transition between large and small polarons in molecular solids using an analytical variational approach, revealing how dimensionality and inter-molecular forces influence polaron properties and self-trapping phenomena.

Contribution

It introduces a modified Lang-Firsov method that captures polaron self-trapping transitions and analyzes their dependence on dimensionality and electron-phonon coupling.

Findings

Polaron crossover becomes smoother with increased inter-molecular forces.

Self-trapping occurs when electron energies match phonon energies, especially in adiabatic regimes.

Polaron effective masses range from 5 to 40 times the bare mass at crossover.

Abstract

An analytical variational method is applied to the molecular Holstein Hamiltonian in which the dispersive features of the dimension dependent phonon spectrum are taken into account by a force constant approach. The crossover between a large and a small size polaron is monitored, in one, two and three dimensions and for different values of the adiabatic parameter, through the behavior of the effective mass as a function of the electron-phonon coupling. By increasing the strength of the inter-molecular forces the crossover becomes smoother and occurs at higher {\it e-ph} couplings. These effects are more evident in three dimensions. We show that our Modified Lang-Firsov method starts to capture the occurence of a polaron self-trapping transition when the electron energies become of order of the phonon energies. The self-trapping event persists in the fully adiabatic regime. At the crossover we estimate polaron effective masses of order $\sim 5 - 40$ times the bare band mass according to dimensionality and value of the adiabatic parameter. Modified Lang-Firsov polaron masses are substantially reduced in two and three dimensions. There is no self-trapping in the antiadiabatic regime.