Origin of Vibrational Instabilities in Molecular Wires with Separated Electronic States

Unraveling current-induced dissociation mechanisms in single-molecule junctions

Understanding current-induced bond rupture in single-molecule junctions is both of fundamental interest and a prerequisite for the design of molecular junctions, which are stable at higher-bias voltages. In this work, we use a fully quantum mechanical method based on the hierarchical quantum master equation approach to analyze the dissociation mechanisms in molecular junctions. Considering a wide range of transport regimes, from off-resonant to resonant, non-adiabatic to adiabatic transport, and weak to strong vibronic coupling, our systematic study identifies three dissociation mechanisms. In the weak and intermediate vibronic coupling regime, the dominant dissociation mechanism is stepwise vibrational ladder climbing. For strong vibronic coupling, dissociation is induced via multi-quantum vibrational excitations triggered either by a single electronic transition at high bias voltages or by multiple electronic transitions at low biases. Furthermore, the influence of vibrational relaxation on the dissociation dynamics is analyzed and strategies for improving the stability of molecular junctions are discussed.

Nonthermal vibrations in biased molecular junctions

We study vibrational statistics in current-carrying model molecular junctions using a master equation approach. In particular, we concentrate on the validity of using an effective temperature T_{eff} to characterize the nonequilibrium steady state of a vibrational mode. We identify cases in which a single T_{eff} cannot fully describe one vibrational state. In such cases, the probability distribution among different vibrational states does not follow the Boltzmann type. Consequently, the actual entropy (free energy) of the vibrational mode is lower (higher) than the corresponding thermal value given by T_{eff}, indicating extra work can be extracted from these states. Our results will be useful for the study of a nonthermal vibrational state in the thermodynamics of nanoscale systems, and its usage in nanoscale heat engines.

Waiting time between charging and discharging processes in molecular junctions

When electric current flows through a molecular junction, the molecule constantly charges and discharges by tunneling electrons. These charging and discharging events occur at specific but random times and are separated by stochastic time intervals. These time intervals can be associated with the dwelling time for a charge (electron or hole) to reside on the molecule. In this paper, the statistical properties of these time intervals are studied and a general formula for their distribution is derived. The theory is based on the Markovian master equation which takes into account transitions between the vibrational states of charged and neutral molecules in the junction. Two quantum jump operators are identified from the Liouvillian of the master equation-one corresponds to charging of the molecule and the other discharges the molecule back to the neutral state. The quantum jump operators define the conditional probability that given that the molecule was charged by a tunneling electron at time t, the molecule becomes neutral at a later time t + τ discharging the electron to the drain electrode. Statistical properties of these time intervals τ are studied with the use of this distribution.

Kinetic Schemes in Open Interacting Systems

We discuss utilization of kinetic schemes for description of open interacting systems, focusing on vibrational energy relaxation for an oscillator coupled to a nonequilibirum electronic bath. Standard kinetic equations with constant rate coefficients are obtained under the assumption of time scale separation between the system and bath, with the bath dynamics much faster than that of the system of interest. This assumption may break down in certain limits, and we show that ignoring this may lead to qualitatively wrong predictions. Connection with more general, nonequilibrium Green's function (NEGF) analysis is demonstrated. Our considerations are illustrated within generic molecular junction models with electron-vibration coupling.