The role of multimode vibrational dynamics in electron transport through single molecule junctions is investigated. The study is based on a generic model, which describes charge transport through a single molecule that is attached to metal leads. To address vibrationally-coupled electron transport, we employ a nonequilibrium Green's function approach that extends a method recently proposed by Galperin et al. [Phys. Rev. B 73, 045314 (2006)] to multiple vibrational modes. The methodology is applied to two systems: a generic model with two vibrational degrees of freedom and benzenedibutanethiolate covalently bound to gold electrodes. The results show that the coupling to multiple vibrational modes can have a significant effect on the conductance of a molecular junction. In particular, we demonstrate the effect of electronically induced coupling between different vibrational modes and study nonequilibrium vibrational effects by calculating the current-induced excitation of vibrational modes.
Vibrational nonequilibrium effects in charge transport through single-molecule junctions are investigated. Focusing on molecular bridges with multiple electronic states, it is shown that electronic-vibrational coupling triggers a variety of vibronic emission and absorption processes, which influence the conductance properties and mechanical stability of single-molecule junctions profoundly. Employing a master equation and a nonequilibrium Green's function approach, these processes are analyzed in detail for a generic model of a molecular junction and for benzenedibutanethiolate bound to gold e…
Within the hierarchical quantum master equation (HQME) framework, an approach is presented, which allows a numerically exact description of nonequilibrium charge transport in nanosystems with strong electronic-vibrational coupling. The method is applied to a generic model of vibrationally coupled transport considering a broad spectrum of parameters ranging from the nonadiabatic to the adiabatic regime and including both resonant and off-resonant transport. We show that nonequilibrium effects are important in all these regimes. In particular in the off-resonant transport regime, the inelastic c…
In a nanoscale molecular junction at finite bias voltage,the intra-molecular distribution of vibrational energy can strongly deviate from the thermal equilibrium distribution and specific vibrational modes can be selectively excited in a controllable way,regardless of the corresponding mode frequency. This is demonstrated for generic models of asymmetric molecular junctions with localized electronic states, employing a master equation as well as a nonequilibrium Green's function approach. It is shown that the applied bias voltage controls the excitation of specific vibrational modes coupled to…
We present a novel hierarchical quantum master equation (HQME) approach which provides a numerically exact description of nonequilibrium charge transport in nanosystems with electronic-vibrational coupling. In contrast to previous work [Phys. Rev. B $\bf{94}$, 201407 (2016)], the active vibrational degrees of freedom are treated in the reservoir subspace and are integrated out. This facilitates applications to systems with very high excitation levels, for example due to current-induced heating, while properties of the vibrational degrees of freedom, such as the excitation level and other momen…
We calculate the nonequilibrium local density of states on a vibrational quantum dot coupled to two electrodes at T=0 using a numerically exact diagrammatic Monte Carlo method. Our focus is on the interplay between the electron-phonon interaction strength and the bias voltage. We find that the spectral density exhibits a significant voltage dependence if the voltage window includes one or more phonon sidebands. A comparison with well-established approximate approaches indicates that this effect could be attributed to the nonequilibrium distribution of the phonons. Moreover, we discuss the long…
We investigate electron transport through a mixed-valence molecular complex in which an excess electron can tunnel between hetero-valent transition metal ions, each having a fixed localized spin. We show that in this class of molecules the interplay of the spins and the vibrational breathing modes of the ionic ligand-shells allows the total molecular spin to be detected as well as controlled by nonequilibrium transport. Due to a spin-dependent pseudo Jahn-Teller effect electronic transitions with different spin values can be distinguished by their vibronic conductance side peaks, without using…
We have derived a general formula describing current noise in multimode ballistic channels connecting source and drain electrodes with Fermi electron gas. In particular (at $eV\gg k_{B}T$), the expression describes the nonequilibrium ''shot'' noise, which may be suppressed by both Fermi correlations and space charge screening. The general formula has been applied to an approximate model of a 2D nanoscale, ballistic MOSFET. At large negative gate voltages, when the density of electrons in the channel is small, shot noise spectral density $S_{I}(0)$ approaches the Schottky value $2eI$, where $I$…
Quantum interference effects and decoherence mechanisms in single-molecule junctions are analyzed employing a nonequilibrium Green's function approach. Electrons tunneling through quasi-degenerate states of a nanoscale molecular junction exhibit interference effects. We show that electronic-vibrational coupling, inherent to any molecular junction, strongly quenches such interference effects. As a result, the electrical current can be significantly larger than without electronic-vibrational coupling. The analysis reveals that the quenching of quantum interference is particularly pronounced if t…
As a step towards a more realistic modeling of vibrations in single-molecule devices, we investigate the effects of charge-dependent vibrational frequencies and anharmonic potentials on electronic transport. For weak phonon relaxation, we find that in both cases vibrational steps split into a multitude of substeps. This effectively leads to a bias-dependent broadening of vibrational features in current-voltage and conductance characteristics, which provides a fingerprint of nonequilibrium vibrations whenever other broadening mechanisms are secondary. In the case of an asymmetric molecule-lead …
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 w…
We investigate the interplay of quantum interference effects and electronic-vibrational coupling in electron transport through single-molecule junctions, employing a nonequilibrium Green's function approach. Our findings show that inelastic processes lead, in general, to a quenching of quantum interference effects. This quenching is more pronounced for increasing bias voltages and levels of vibrational excitation. As a result of this vibrationally induced decoherence, vibrational signatures in the transport characteristics of a molecular contact may strongly deviate from a simple Franck-Condon…
We investigate the effects of alternating voltage on nonequilibrium quantum systems with localised phonon modes. Nonequilibrium Green's functions are utilised, with electron-phonon coupling being considered with the $GD$ approximation (self-consistent Born approximation). Using a Floquet approach, we assume periodicity of the dynamics. This approach allows us to investigate the influence of the driven electronic component on the nonequilibrium occupation of the vibrations. It was found that signatures of inelastic transport gained photon-assisted peaks. A simplistic model was proposed and foun…
We present a hierarchical quantum master equation (HQME) approach, which allows the numerically exact evaluation of higher-order current cumulants in the framework of full counting statistics for nonequilibrium charge transport in nanosystems. The novel methodology is exemplarily applied to a model of vibrationally coupled electron transport in a molecular nanojunction. We investigate the influence of cotunneling on avalanche-like transport, in particular in the nonresonant transport regime, where we find that inelastic cotunneling acts as trigger process for resonant avalanches. In this regim…
We investigate the transient nonequilibrium dynamics of a molecular junction biased by a finite voltage and strongly coupled to internal vibrational degrees of freedom. Using two different, numerical exact techniques, diagrammatic Monte Carlo and the multilayer multiconfiguration time-dependent Hartree method, we show that the steady state current through the junction may depend sensitively on the initial preparation of the system, thus revealing signatures of bistability. The influence of the bias voltage and the transient dynamics on the phenomenon of bistability is analyzed. Furthermore, a …
We study vibrational statistics in current-carrying model molecular junctions using master equation approach. Especially, we concentrate on the validity of using an effective temperature $T_{\rm eff}$ to characterize the nonequilibrium steady state of a vibrational mode. We identify cases where a single $T_{\rm eff}$ can not 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 …
Inelastic effects in the Coulomb blockade and Kondo regimes of electron transport through molecular junctions are considered within a simple nonequilibrium equation-of-motion (EOM) approach. The scheme is self-consistent, and can qualitatively reproduce the main experimental observations of vibrational features in Coulomb blockade [H.Park et al., Nature 407, 57 (2000)] and Kondo [L.H.Yu et al., Phys. Rev. Lett. 93, 266802 (2004)] regimes. Considerations similar to the equilibrium EOM approach by Meir et al. [Phys. Rev. Lett. 66, 3048 (1991); ibid. 70, 2601 (1993)] are used on the Keldysh conto…
In nanoscale junctions the interaction between charge carriers and the local vibrations results in renormalization, damping and heating of the vibrational modes. We here formulate a nonequilibrium Green's functions based theory to describe such effects. Studying a generic junction model with an off-resonant electronic level, we find a strong bias dependence of the frequency renormalization and vibrational damping accompanied by pronounced nonlinear vibrational heating in junctions with intermediate values of the coupling to the leads. Combining our theory with ab-initio calculations we further…
We analyze the effects of a distortion of the nuclear potential of a molecular quantum dot (QD), as well as a shift of its equilibrium position, on nonequilibrium-vibration-assisted tunneling through the QD with a single level ($ε_d$) coupled to the vibrational mode. For this purpose, we derive an explicit analytical expression for the Franck-Condon (FC) factor for a displaced-distorted oscillator surface of the molecule and establish rate equations in the joint electron-phonon representation to examine the current-voltage characteristics and zero-frequency shot noise, and skewness as well. Ou…
The coupling of the charge carriers passing through a molecule bridging two bulky conductors with local vibrational modes of the molecule, gives rise to distinct features in the electronic transport properties on one hand, and to nonequilibrium features in the vibrations' properties, e.g., their population, on the other. Here we explore theoretically a generic model for a molecular junction biased by an arbitrary dc voltage in the weak-coupling regime. We analyze the signature of the electron-vibration interaction on the full-counting statistics of the current fluctuations (i.e., the cumulant …
We investigate the nonequilibrium population of a vibrational mode in the steady state of a biased molecular junction, using a rate equation approach. We focus on the limit of weak electronic-vibrational coupling and show that, in the resonant transport regime and for sufficiently high bias voltages, the level of vibrational excitation increases with decreasing coupling strength, assuming a finite and non-zero value. An analytic behavior with respect to the electronic-vibrational coupling strength is only observed if the influence of environmental degrees of freedom is explicitly taken into ac…
We investigate chemical bond formation and conductance in a molecular C60-junction under finite bias voltage using first-principles calculations based on density functional theory and nonequilibrium Green's functions (DFT-NEGF). At the point of contact formation we identify a remarkably strong coupling between the C60-motion and the molecular electronic structure. This is only seen for positive sample bias, although the conductance itself is not strongly polarity dependent. The nonequilibrium effect is traced back a sudden shift in the position of the voltage drop with a small C60-displacement…
We study the quantum transport and the nonequilibrium vibrational states of a quantum dot embedded between a normal and a superconducting lead with the charge on the quantum dot linearly coupled to a harmonic oscillator of frequency $ω$. To the leading order in the charge-vibration interaction, we calculate the current and the nonequilibrium phonon occupation by the Keldsyh Green's function technique. We analyze the inelastic, vibration-assisted tunneling processes in the regime $ω<Δ$, with the superconducting energy gap $Δ$, and for sharp resonant transmission through the dot. When the energy…
We show that individual vibrational modes in single-molecule junctions with asymmetric molecule-lead coupling can be selectively excited by applying an external bias voltage. Thereby, a non-statistical distribution of vibrational energy can be generated, that is, a mode with a high frequency can be stronger excited than a mode with a lower frequency. This is of particular interest in the context of mode-selective chemistry, where one aims to break specific (not necessarily the weakest) chemical bond in a molecule. Such mode-selective vibrational excitation is demonstrated for two generic model…
We expand iterative numerically-exact influence functional path-integral tools and present a method capable of following the nonequilibrium time evolution of subsystems coupled to multiple bosonic and fermionic reservoirs simultaneously. Using this method, we study the real-time dynamics of charge transfer and vibrational mode excitation in an electron conducting molecular junction. We focus on nonequilibrium vibrational effects, particularly, the development of vibrational instability in a current-rectifying junction. Our simulations are performed by assuming large molecular vibrational anhar…
The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory within second quantization representation of the Fock space, a novel numerically exact methodology to treat many-body quantum dynamics for systems containing identical particles, is applied to study the effect of vibrational motion on electron transport in a generic model for single-molecule junctions. The results demonstrate the importance of electronic-vibrational coupling for the transport characteristics. For situations where the energy of the bridge state is located close to the Fermi energy, the simulations show t…
A compact scheme for the preparation of macroscopic multipartite entanglement is proposed and analyzed. In this scheme the vibrational modes of a mechanical resonator constitute continuous variable (CV) subsystems that entangle to each other as a result of their interaction with a two-level system (TLS). By properly driving the TLS, we show that a selected set of modes can be activated and prepared in a multipartite entangled state. We first study entanglement properties of a three-mode system by evaluating the genuine multipartite entanglement. And investigate its usefulness as a quantum reso…
We develop a classical mapping approach suitable to describe vibrationally coupled charge transport in molecular junctions based on the Cartesian mapping for many-electron systems [J. Chem. Phys. 137, 154107 (2012)]. To properly describe vibrational quantum effects in the transport characteristics, we introduce a simple transformation rewriting the Hamiltonian in terms of occupation numbers and use a binning function to facilitate quantization. The approach provides accurate results for the nonequilibrium Holstein model for a range of bias voltages, vibrational frequencies and temperatures. It…
The calculation of the nonlinear conductance of a single-molecule junction is revisited. The self energy on the junction resulting from the electron-phonon interaction has at low temperatures logarithmic singularities (in the real part) and discontinuities (in the imaginary one) at the frequencies corresponding to the opening of the inelastic channels. These singularities generate discontinuities and logarithmic divergences (as a function of the bias voltage) in the low-temperature differential conductance around the inelastic thresholds. The self energy also depends on the population of the v…
We study spin-dependent transport in a suspended carbon nanotube quantum dot in contact with two ferromagnetic leads and with the dot's spin coupled to the flexural mechanical modes. The spin-vibration interaction induces spin-flip processes between the two energy levels of the dot. This interaction arises from the spin-orbit coupling or a magnetic field gradient. The inelastic vibration-assisted spin flips give rise to a mechanical damping and, for an applied bias voltage, to a steady nonequilibrium occupation of the harmonic oscillator. We analyze these effects as function of the energy-leve…
The interaction between electronic and vibrational degrees of freedom is an important mechanism in nonequilibrium charge transport through molecular nanojunctions. While adiabatic polaron-type coupling has been studied in great detail, new transport phenomena arise for nonadiabatic coupling scenarios corresponding to a breakdown of the Born-Oppenheimer approximation. Employing the numerically exact hierarchical equations of motion approach, we analyze the effect of nonadiabatic electronic-vibrational coupling on electron transport in molecular junctions considering a series of models with incr…
Electronic current flowing in a molecular electronic junction dissipates significant amounts of energy to vibrational degrees of freedom, straining and rupturing chemical bonds and often quickly destroying the integrity of the molecular device. The infamous mechanical instability of molecular electronic junctions critically limits performance, lifespan, and raises questions as to the technological viability of single-molecule electronics. Here we propose a practical scheme for cooling the molecular vibrational temperature via application of an AC voltage over a large, static operational DC vol…
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.
By using nonequilibrium Green's functions and the equation of motion method, we formulate a self-consistent field theory for the electron transport through a single molecular junction (SMJ) coupled with a vibrational mode. We show that the nonequilibrium dynamics of the phonons in strong electron-phonon coupling regime can be taken into account appropriately in this self-consistent perturbation theory, and the self-energy of phonons is connected with the current fluctuations in the molecular junction. We calculate the finite-frequency nonsymmetrized noise spectra and the ac conductance, which …
In the present work, we theoretically analyze the steady-state thermoelectric transport through a single-molecule junction with a vibrating bridge. Thermally induced charge current in the system is explored using a nonequilibrium Green's functions formalism. We study combined effects of Coulomb interactions between charge carriers on the bridge and electron-phonon interactions on the thermocurrent beyond the linear response regime. It is shown that electron-vibron interactions may significantly affect both magnitude and direction of the thermocurrent, and vibrational signatures may appear.
We explore the mechanism for the long-lived quantum coherence by considering the discrete phonon modes: these vibrational modes effectively weaken the exciton-environment interaction, due to the new composite (polaron) formed by excitons and vibrons. This subsequently demonstrates the role of vibrational coherence which greatly contributes to long-lived feature of the excitonic coherence that has been observed in femtosecond experiments. The estimation of the timescale of coherence elongated by vibrational modes is given in an analytical manner. To test the validity of our theory, we study the…
The effect of molecular vibrations on electronic transport is investigated with the smallest fullerene C20 bridge, utilizing the Keldysh nonequilibrium Green's function techniques combined with the tight-binding molecular-dynamics method. Large discontinuous steps appear in the differential conductance when the applied bias-voltage matches particular vibrational energies. The magnitude of the step is found to vary considerably with the vibrational mode and to depend on the local electronic states besides the strength of electron-vibration coupling. On the basis of this finding, a novel way to …
We study the quantum dynamics of the cavity optomechanical system formed by a Fabry-Perot cavity with a thin vibrating membrane at its center. We first derive the general multimode Hamiltonian describing the radiation pressure interaction between the cavity modes and the vibrational modes of the membrane. We then restrict the analysis to the standard case of a single cavity mode interacting with a single mechanical resonator and we determine to what extent optical absorption by the membrane hinder reaching a quantum regime for the cavity-membrane system. We show that membrane absorption does n…
We discuss two theoretical proposals for controlling the nonequilibrium steady state of nanomechanical resonators using quantum electronic transport. Specifically?, we analyse two approaches to achieve the ground-state cooling of the mechanical vibration coupled to a quantum dot embedded between (i) spin-polarised contacts or (ii) a normal metal and a superconducting contact. Assuming a suitable coupling between the vibrational modes and the charge or spin of the electrons in the quantum dot, we show that ground-state cooling of the mechanical oscillator is within the state of the art for susp…
Using the atomistic nonequilibrium Green's function, we find that thermal conductance of carbon nanotubes with presence of topological lattice imperfects is remarkably reduced, due to the strong Rayleigh scattering of high-frequency phonons. Phonon transmission across multiple defects behaves as a cascade scattering based with the random phase approximation. We elucidate that phonon scattering by structural defects is related to the spatial fluctuations of local vibrational density of states (LVDOS). An effective method of tuning thermal transport in low-dimensional systems through the modulat…
We describe a first-principles method for calculating electronic structure, vibrational modes and frequencies, electron-phonon couplings, and inelastic electron transport properties of an atomic-scale device bridging two metallic contacts under nonequilibrium conditions. The method extends the density-functional codes SIESTA and TranSIESTA that use atomic basis sets. The inelastic conductance characteristics are calculated using the nonequilibrium Green's function formalism, and the electron-phonon interaction is addressed with perturbation theory up to the level of the self-consistent Born ap…
We present an ab-initio method to simulate the current noise in the presence of electron-vibration interactions in atomic and molecular junctions at finite temperature. Using a combination of nonequilibrium Keldysh Green's function techniques and density functional theory, we study the elastic and inelastic contributions to electron current and shot noise within a wide range of transmission values in systems exhibiting multiple electronic levels and vibrational modes. Within our model we find the upper threshold, at which the inelastic noise contribution changes sign, at a total transmission b…
In a current-carrying single-molecular junction (SMJ), a hierarchy of hybrid energy transport processes takes place under a highly nonequilibrium situation, including energy transfer from electrons to molecular vibrations via electron-vibration interaction, energy redistribution within different vibrational modes via anharmonic coupling, and eventual energy transport to surrounding electrodes. A comprehensive understanding of such processes is a prerequisite for their potential applications as single-molecular devices. $Ab$ $initio$ current-induced molecular dynamics (MD) is an ideal approach …
