Theory of the Franck-Condon blockade regime

TL;DR

This paper develops a theoretical framework for the Franck-Condon blockade regime in molecular electronics, highlighting the role of cotunneling and self-similar avalanche transport in current suppression and noise characteristics.

Contribution

It introduces a comprehensive theory incorporating cotunneling effects into the Franck-Condon blockade regime, revealing new transport phenomena and noise signatures.

Findings

Cotunneling dominates current at any gate voltage due to power-law suppression.

Self-similar avalanche transport persists even with cotunneling effects.

Predicted vibrational sidebands and telegraph noise in the Coulomb-blockaded regime.

Abstract

Strong coupling of electronic and vibrational degrees of freedom entails a low-bias suppression of the current through single-molecule devices, termed Franck-Condon blockade. In the limit of slow vibrational relaxation, transport in the Franck-Condon-blockade regime proceeds via avalanches of large numbers of electrons, which are interrupted by long waiting times without electron transfer. The avalanches consist of smaller avalanches, leading to a self-similar hierarchy which terminates once the number of transferred electrons per avalanche becomes of the order of unity. Experimental signatures of self-similar avalanche transport are strongly enhanced current (shot) noise, as expressed by giant Fano factors, and a power-law noise spectrum. We develop a theory of the Franck-Condon-blockade regime with particular emphasis on effects of electron cotunneling through highly excited vibrational states. As opposed to the exponential suppression of sequential tunneling rates for low-lying vibrational states, cotunneling rates suffer only a power-law suppression. This leads to a regime where cotunneling dominates the current for any gate voltage. Including cotunneling within a rate-equation approach to transport, we find that both the Franck-Condon blockade and self-similar avalanche transport remain intact in this regime. We predict that cotunneling leads to absorption-induced vibrational sidebands in the Coulomb-blockaded regime as well as intrinsic telegraph noise near the charge degeneracy point.