Theory of the Franck-Condon blockade 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-Condonblockade 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 absorptioninduced vibrational sidebands in the Coulomb-blockaded regime as well as intrinsic telegraph noise near the charge degeneracy point.

Self-consistent theory of molecular switching

“…In the case ⌫Ͻ 0 and strong electron-ion coupling the role of cotunneling was recently studied in Ref. 31, where it was found that while it does not destroy the Franck-Condon blockade, it can dramatically affect the lowvoltage current and current noise, as well as the vibrational dynamics.…”

Lifting the Franck-Condon blockade in driven quantum dots

“…Specifically, the undriven [ f (t) = 0] variant of the system has been examined with regard to its transport properties. 18,[25][26][27][28] The most striking finding in this context is that of Franck-Condon blockade: strong electron-vibron interaction leads to formation of a composite state, called a polaron, which can be thought of as being made up of an electron and a "cloud" of vibrational excitations surrounding it. If the electron is to tunnel out of the quantum dot, this state has to be broken up, at an energy cost which strongly increases with the coupling, leading to an exponential suppression of tunneling.…”

“…More quantitatively, we note that the factor e −λ 2 /Ω 2 matches the Franck-Condon blockade strength obtained from a classical rate equation. 18 …”

“…For the purposes of the following discussion, it suffices to take into account a single lead, and instead of a steady-state current, study the tunneling rates into this lead, which in the limit of sequential tunneling is proportional to the conductance. 18 The comparability of the latter two quantities is a feature of the sequential-tunneling regime, where the current is made up of consecutive, non-overlapping single-electron tunneling transitions. The system being weakly coupled to a metallic lead with intractably many degrees of freedom allows us to perform a partial trace over the lead degrees of freedom of the model.…”

“…12,[15][16][17] A general feature of interacting systems composed of electrons and quantized mechanical vibrations ("vibrons") is the suppression of conductance, in certain parameter regimes, for strong coupling between the two degrees of freedom. This effect, commonly referred to as Franck-Condon blockade, 18 results from the atomic constituents of the system accommodating for the presence of a number of electrons by means of displacement, thus forming composite electron-vibron particles termed polarons. Electronic transport through the system requires the electron number to change and hence the polarons to be broken up, which is energetically disfavored if the electron-vibron coupling that holds them together is strong.…”