Holstein polarons in a strong electric field: delocalized and stretched states

TL;DR

This paper investigates the behavior of Holstein polarons under strong electric fields, revealing conditions for delocalization and complex spectral structures, with implications for tunneling transport properties.

Contribution

It provides an analytical and numerical study of Holstein polarons in strong fields, identifying resonance conditions that lead to delocalized states and semi-continuous bands.

Findings

Resonance condition causes Wannier-Stark ladder to form semi-continuous bands.

Delocalized 'tunneling' and 'stretched' polarons emerge under certain regimes.

Spectral structures exhibit nearly-fractal modulation affecting transport properties.

Abstract

The coherent dynamics of a Holstein polaron in strong electric fields is considered under different regimes. Using analytical and numerical analysis, we show that even for small hopping constant and weak electron-phonon interaction, the original discrete Wannier-Stark (WS) ladder electronic states are each replaced by a semi-continuous band if a resonance condition is satisfied between the phonon frequency and the ladder spacing. In this regime, the original localized WS states can become {\em delocalized}, yielding both `tunneling' and `stretched' polarons. The transport properties of such a system would exhibit a modulation of the phonon replicas in typical tunneling experiments. The modulation will reflect the complex spectra with nearly-fractal structure of the semi-continuous band. In the off-resonance regime, the WS ladder is strongly deformed, although the states are still localized to a degree which depends on the detuning: Both the spacing between the levels in the deformed ladder and the localization length of the resulting eigenfunctions can be adjusted by the applied electric field. We also discuss the regime beyond small hopping constant and weak coupling, and find an interesting mapping to that limit via the Lang-Firsov transformation, which allows one to extend the region of validity of the analysis.