Fluctuating-bias controlled electron transport in molecular junctions

Abstract

We consider the problem of transport through a multiterminal molecular junction in the presence of a stochastic bias, which can also be used to describe transport through fluctuating molecular energy levels. To describe these effects, we first make a simple extension of our previous work [Phys. Rev. B 91, 125433 (2015)] to show that the problem of tunneling through noisy energy levels can be mapped onto the problem of a noisy driving bias, which appears in the Kadanoff-Baym equations for this system in an analogous manner to the driving term in the Langevin equation for a classical circuit. This formalism uses the nonequilibrium Green's function method to obtain analytically closed formulas for transport quantities within the wide-band limit approximation for an arbitrary time-dependent bias and it is automatically partition free. We obtain exact closed formulas for both the colored and white noise-averaged current at all times. In the long-time limit, these formulas possess a Landauer-B\uttiker--type structure which enables the extraction of an effective transmission coefficient for the transport. Expanding the Fermi function into a series of simple poles, we find an exact formal relation between the parameters which characterize the bias fluctuations and the poles of the Fermi function. This enables us to describe the effect of the temperature and the strength of the fluctuations on the averaged current which we interpret as a quantum analog to the classical fluctuation-dissipation theorem. We use these results to convincingly refute some recent results on the multistability of the current through a fluctuating level, simultaneously verifying that our formalism satisfies some well-known theorems on the asymptotic current. Finally, we present numerical results for the current through a molecular chain which demonstrate a transition from nonlinear to linear $I\text{\ensuremath{-}}V$ characteristics as the strength of fluctuations is increased, as well as a stochastic resonance effect in the conductance of this system.