Quantum Dynamics of Polaron Formation

TL;DR

This paper investigates the real-time quantum dynamics of polaron formation in the Holstein model, revealing how electron-phonon interactions and phonon properties influence the formation process and timescales.

Contribution

It provides a detailed quantum dynamical analysis of polaron formation, including the effects of coupling strength, phonon frequency, and dimensionality, which advances understanding beyond static models.

Findings

Polaron formation time relates to phonon dephasing time.

Increased el-ph coupling leads to qualitative changes in polaron states.

A potential barrier exists in the adiabatic regime affecting formation dynamics.

Abstract

The formation of a polaron quasiparticle from a bare electron is studied in the framework of the Holstein model of electron-phonon coupling. Using Schr\"{o}dinger's formalism, we calculate the time evolution of the distribution of the electron and phonon density, lattice deformation, and the electron-phonon (el-ph) correlation functions in real space. The quantum dynamical nature of the phonons is preserved. The polaron formation time is related to the dephasing time of the continuum of unbound phonon excited states in the spectral function, which depends on the phonon frequency and the el-ph coupling strength. As the el-ph coupling increases, qualitative changes in polaron formation occur when the one-phonon polaron bound state forms. In the adiabatic regime, we find that a potential barrier between the quasi-free and heavy polaron states exists in both 2D and 3D, which is crucial for polaron formation dynamics. We compare to recent experiments.