Dynamical Properties of small Polarons

TL;DR

This paper investigates the spectral and dynamical properties of small polarons using exact diagonalization of a two-site model, revealing insights into localization, crossover regimes, and limitations of standard approaches.

Contribution

It provides a detailed analysis of small polaron spectral features and dynamics, highlighting the crossover between adiabatic and anti-adiabatic regimes beyond standard models.

Findings

Identification of a gap between single and bi-polaron states.

Characterization of the adiabatic to anti-adiabatic crossover.

Visualization of charge localization and dephasing dynamics.

Abstract

On the basis of the two-site polaron problem, which we solve by exact diagonalization, we analyse the spectral properties of polaronic systems in view of discerning localized from itinerant polarons and bound polaron pairs from an ensemble of single polarons. The corresponding experimental techniques for that concern photoemission and inverse photoemission spectroscopy. The evolution of the density of states as a function of concentration of charge carriers and strength of the electron-phonon interaction clearly shows the opening up of a gap between single polaronic and bi-polaronic states, in analogy to the Hubbard problem for strongly correlated electron systems. The crossover regime between adiabatic and anti-adiabatic small polarons is triggered by two characteristic time scales: the renormalized electron hopping rate and the renormalized vibrational frequency becoming equal. This crossover regime is then characterized by temporarily alternating self- localization and delocalization of the charge carriers which is accompanied by phase slips in the charge and molecular deformation oscillations and ultimately leads to a dephasing between these two dynamical components of the polaron problem. We visualize these features by a study of the temporal evolution of the charge redistribution and the change in molecular deformations. The spectral and dynamical properties of polarons discussed here are beyond the applicability of the standard Lang Firsov approach to the polaron problem.