Wave packet dynamics in chains with delayed electronic nonlinear response

TL;DR

This paper investigates how delayed nonlinear responses affect wave packet dynamics and self-trapping phenomena in electron chains, revealing complex phase behavior depending on response speed and nonlinearity strength.

Contribution

It introduces a model with delayed cubic nonlinearity in electron-phonon interactions and analyzes how delay times influence self-trapping in electron chains.

Findings

Weaker nonlinearity induces self-trapping at short delays.

Slower nonlinear responses require stronger nonlinearity for self-trapping.

Reentrant phase diagram observed with varying delay times.

Abstract

We study the dynamics of one electron wave packet in a chain with a non-adiabatic electron-phonon interaction. The electron-phonon coupling is taken into account in the time-dependent Schr\"odinger equation by a delayed cubic nonlinearity. In the limit of an adiabatic coupling, the self-trapping phenomenon occurs when the nonlinearity parameter exceeds a critical value of the order of the band width. We show that a weaker nonlinearity is required to produce self-trapping in the regime of short delay times. However, this trend is reversed for slow nonlinear responses, resulting in a reentrant phase-diagram. In slowly responding media, self-trapping only takes place for very strong nonlinearities.