Model Molecular Junctions Research Articles

Quantum bath effects on nonequilibrium heat transport in model molecular junctions.

Quantum-classical dynamics simulations enable the study of nonequilibrium heat transport in realistic models of molecules coupled to thermal baths. In these simulations, the initial conditions of the bath degrees of freedom are typically sampled from classical distributions. Herein, we investigate the effects of sampling the initial conditions of the thermal baths from quantum and classical distributions on the steady-state heat current in the nonequilibrium spin-boson model-a prototypical model of a single-molecule junction-in different parameter regimes. For a broad range of parameter regimes considered, we find that the steady-state heat currents are ∼1.3-4.5 times larger with the classical bath sampling than with the quantum bath sampling. Using both types of sampling, the steady-state heat currents exhibit turnovers as a function of the bath reorganization energy, with sharper turnovers in the classical case than in the quantum case and different temperature dependencies of the turnover maxima. As the temperature gap between the hot and cold baths increases, we observe an increasing difference in the steady-state heat currents obtained with the classical and quantum bath sampling. In general, as the bath temperatures are increased, the differences between the results of the classical and quantum bath sampling decrease but remain non-negligible at the high bath temperatures. The differences are attributed to the more pronounced temperature dependence of the classical distribution compared to the quantum one. Moreover, we find that the steady-state fluctuation theorem only holds for this model in the Markovian regime when quantum bath sampling is used. Altogether, our results highlight the importance of quantum bath sampling in quantum-classical dynamics simulations of quantum heat transport.

A model for dynamical solvent control of molecular junction electronic properties

Experimental measurements of electron transport properties of molecular junctions are often performed in solvents. Solvent-molecule coupling and physical properties of the solvent can be used as the external stimulus to control the electric current through a molecule. In this paper, we propose a model that includes dynamical effects of solvent-molecule interaction in non-equilibrium Green's function calculations of the electric current. The solvent is considered as a macroscopic dipole moment that reorients stochastically and interacts with the electrons tunneling through the molecular junction. The Keldysh-Kadanoff-Baym equations for electronic Green's functions are solved in the time domain with subsequent averaging over random realizations of rotational variables using the Furutsu-Novikov method for the exact closure of infinite hierarchy of stochastic correlation functions. The developed theory requires the use of wideband approximation as well as classical treatment of solvent degrees of freedom. The theory is applied to a model molecular junction. It is demonstrated that not only electrostatic interaction between molecular junction and solvent but also solvent viscosity can be used to control electrical properties of the junction. Alignment of the rotating dipole moment breaks the particle-hole symmetry of the transmission favoring either hole or electron transport channels depending upon the aligning potential.

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.

Current-induced atomic motion, structural instabilities, and negative temperatures on molecule-electrode interfaces in electronic junctions

Molecule-electrode interfaces in molecular electronic junctions are prone to chemical reactions, structural changes, and localized heating effects caused by electric current. These can be exploited for device functionality or may be degrading processes that limit performance and device lifetime. We develop a nonequilibrium Green's function based transport theory in which the central region atoms and, more importantly, atoms on molecule-electrode interfaces are allowed to move. The separation of time-scales of slow nuclear motion and fast electronic dynamics enables the algebraic solution of the Kadanoff-Baym equations in the Wigner space. As a result, analytical expressions for dynamical corrections to the adiabatically computed Green's functions are produced. These dynamical corrections depend not only on the instantaneous molecular geometry but also on the nuclear velocities. To make the theoretical approach fully self-consistent, the same time-separation approach is used to develop expressions for the adiabatic, dissipative, and stochastic components of current-induced forces in terms of adiabatic Green's functions. Using these current induced forces, the equation of motion for the nuclear degrees of freedom is cast in the form of a Langevin equation. The theory is applied to model molecular electronic junctions. We observe that the interplay between the value of the spring constant for the molecule-electrode chemical bond and electronic coupling strength to the corresponding electrode is critical for the appearance of structural instabilities and, consequently, telegraphic switching in the electric current. The range of model parameters is identified to observe structurally stable molecular junctions as well as various different kinds of current-induced telegraphic switching. The interfacial structural instabilities are also quantified based on current noise calculations.

Visualizing Quantum Interference in Molecular Junctions.

Electron transport across a molecular junction is characterized by an energy-dependent transmission function. The transmission function accounts for electrons tunneling through multiple molecular orbitals (MOs) with different phases, which gives rise to quantum interference (QI) effects. Because the transmission function comprises both interfering and noninterfering effects, individual interferences between MOs cannot be deduced from the transmission function directly. Herein, we demonstrate how the transmission function can be deconstructed into its constituent interfering and noninterfering contributions for any model molecular junction. These contributions are arranged in a matrix and displayed pictorially as a QI map, which allows one to easily identify individual QI effects. Importantly, we show that exponential conductance decay with increasing oligomer length is primarily due to an increase in destructive QI. With an ability to "see" QI effects using the QI map, we find that QI is vital to all molecular-scale electron transport.

Mean field theory of thermal energy transport in molecular junctions.

Mean field theory is applied to nonequilibrium thermal energy transport in a model molecular junction. An approximation to the total time-dependent heat current in the junction is constructed using an ensemble of Ehrenfest trajectories, and the average heat current in the steady state is obtained. The accuracy of this treatment is verified through benchmark comparisons with exact quantum mechanical results and various approximate quantum transport theories for the nonequilibrium spin-boson model. The performance of the multitrajectory Ehrenfest approach is found to be quite robust, displaying good accuracy in intermediate cases that remain elusive to many perturbative approximations and in the strong coupling limit where many methods break down. Thus, mean field theory and related trajectory-based approximate quantum dynamics methods emerge as a promising toolkit for the study of transport properties in nanoscale systems.

Nonequilibrium Green's function theory for nonadiabatic effects in quantum electron transport.

We develop nonequilibrium Green's function-based transport theory, which includes effects of nonadiabatic nuclear motion in the calculation of the electric current in molecular junctions. Our approach is based on the separation of slow and fast time scales in the equations of motion for Green's functions by means of the Wigner representation. Time derivatives with respect to central time serve as a small parameter in the perturbative expansion enabling the computation of nonadiabatic corrections to molecular Green's functions. Consequently, we produce a series of analytic expressions for non-adiabatic electronic Green's functions (up to the second order in the central time derivatives), which depend not solely on the instantaneous molecular geometry but likewise on nuclear velocities and accelerations. An extended formula for electric current is derived which accounts for the non-adiabatic corrections. This theory is concisely illustrated by the calculations on a model molecular junction.

Hierarchical equations of motion method applied to nonequilibrium heat transport in model molecular junctions: Transient heat current and high-order moments of the current operator

We present a theoretical approach to study nonequilibrium quantum heat transport in molecular junctions described by a spin-boson type model. Based on the Feynman-Vernon path integral influence functional formalism, expressions for the average value and high-order moments of the heat current operators are derived, which are further obtained directly from the auxiliary density operators (ADOs) in the hierarchical equations of motion (HEOM) method. Distribution of the heat current is then derived from the high-order moments. As the HEOM method is nonperturbative and capable of treating non-Markovian system-environment interactions, the method can be applied to various problems of nonequilibrium quantum heat transport beyond the weak coupling regime.

Effect of nonadiabatic electronic-vibrational interactions on the transport properties of single-molecule junctions

The interaction between electronic and vibrational degrees of freedom in single-molecule junctions may result from the dependence of the electronic energies or the electronic states of the molecular bridge on the nuclear displacement. The latter mechanism leads to a direct coupling between different electronic states and is referred to as nonadiabatic electronic-vibrational coupling. Employing a perturbative nonequilibrium Green's function approach, we study the influence of nonadiabatic electronic-vibrational coupling in model molecular junctions. Thereby, we distinguish between systems with well-separated and quasidegenerate electronic levels. The results show that the nonadiabatic electronic-vibrational interaction can have a significant influence on the transport properties. The underlying mechanisms, in particular the difference between nonadiabatic and adiabatic electronic-vibrational couplings, are analyzed in some detail.

The critical power to maintain thermally stable molecular junctions.

With the rise of atomic-scale devices such as molecular electronics and scanning probe microscopies, energy transport processes through molecular junctions have attracted notable research interest recently. In this work, heat dissipation and transport across diamond/benzene/diamond molecular junctions are explored by performing atomistic simulations. We identify the critical power Pcr to maintain thermal stability of the junction through efficient dissipation of local heat. We also find that the molecule-probe contact features a power-dependent interfacial thermal resistance RK in the order of 10(9) kW(-1). Moreover, both Pcr and RK display explicit dependence on atomic structures of the junction, force and temperature. For instance, Pcr can be elevated in multiple-molecule junctions, and streching the junction enhances RK by a factor of 2. The applications of these findings in molecular electronics and scanning probing measurements are discussed, providing practical guidelines in their rational design.

Numerically exact, time-dependent study of correlated electron transport in model molecular junctions

The multilayer multiconfiguration time-dependent Hartree theory within second quantization representation of the Fock space is applied to study correlated electron transport in models of single-molecule junctions. Extending previous work, we consider models which include both electron-electron and electronic-vibrational interaction. The results show the influence of the interactions on the transient and the stationary electrical current. The underlying physical mechanisms are analyzed in conjunction with the nonequilibrium electronic population of the molecular bridge.

A Time-Dependent Approach to Electronic Transmission in Model Molecular Junctions

We present a simple method to compute the transmission coefficient of a quantum system embedded between two conducting electrodes. Starting from the solution of the time-dependent Schrodinger equation, we demonstrate the relationship between the temporal evolution of the state vector, |ψ(t)>, initially localized on one electrode and the electronic transmission coefficient, T(E). We particularly emphasize the role of the oscillation frequency and the decay rate of |ψ(t)> in the line shape of T(E). This method is applied to the well-known problems of the single impurity, two-site systems and the benzene ring, where it agrees with well-accepted time-independent methods and gives new physical insight to the resonance and interference patterns widely observed in molecular junctions.

Meir–Wingreen formula for heat transport in a spin-boson nanojunction model

An analog of the Meir-Wingreen formula for the steady-state heat current through a model molecular junction is derived. The expression relates the heat current to correlation functions of operators acting only on the degrees of freedom of the molecular junction. As a result, the macroscopic heat reservoirs are not treated explicitly. This allows one to exploit methods based on a reduced description of the dynamics of a relatively small part of the overall system to evaluate the heat current through a molecular junction. The derived expression is applied to calculate the steady-state heat current in the weak coupling limit, where the Redfield theory is used to describe the reduced dynamics of the molecular junction. The results are compared with those of previously developed approximate and numerically exact methods.

Heat transport through model molecular junctions: A multilayer multiconfiguration time-dependent Hartree approach

A numerically exact approach is proposed to study heat transport through a molecular junction that is coupled to two phonon reservoirs at different temperatures. Within a spin-boson type model, the junction is represented by a two level subsystem and the phonon reservoirs are described by two independent harmonic baths. Quantum simulations of the thermal flux (heat current) are performed employing the multilayer multiconfiguration time-dependent Hartree theory. Results for the transient and stationary heat current are discussed for different physical regimes. Furthermore, the validity of Redfield theory, as an example of an approximate approach applicable for weak system–bath coupling, is examined using the proposed numerically exact approach.

Molecular junctions in the Coulomb blockade regime: Rectification and nesting

Quantum transport through single molecules is very sensitive to the strength of the molecule-electrode contact. Here, we investigate the behavior of a model molecular junction weakly coupled to external electrodes in the case where charging effects do play an important role (Coulomb blockade regime). As a minimal model we consider a molecular junction with two spatially separated donor and acceptor sites. Depending on their mutual coupling to the electrodes, the resulting transport observables show well defined features such as rectification effects in the I-V characteristics and nesting of the stability diagrams. To be able to accomplish these results, we have developed a theory which allows to explore the charging regime via the nonequilibrium Green function formalism parallel to the widely used master equation technique. Our results, beyond their experimental relevance, offer a transparent framework for the systematic and modular inclusion of a richer physical phenomenology.