arXiv subjects

R. Härtle

Publications and source records attributed to R. Härtle.

17 recordsLinked to original sources

arXiv2018

Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems: Reservoir formulation and application to vibrational instabilities

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 moments of the vibrational distribution function, are still accessible. The method is applied to a generic model of a nanosystem, which comprises a single electronic level that is coupled to fermionic leads and a vibrational degree of freedom. Converged results are obtained in a broad spectrum of parameters, ranging from the nonadiabatic to the adiabatic transport regime. We specifically investigate the phenomenon of vibrational instability, that is, the increase of current-induced vibrational excitation for decreasing electronic-vibrational coupling. The novel HQME approach allows us to analyze the influence of level broadening due to both molecule-lead coupling and thermal effects. Results obtained for the first two moments suggest that the vibrational excitation is always described by a geometric distribution in the weak electronic-vibrational coupling limit.

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arXiv2018

Cooling by heating in nonequilibrium nanosystems

We demonstrate the possiblity to cool nanoelectronic systems in nonequilibrium situations by increasing the temperature of the environment. Such cooling by heating is possible for a variety of experimental conditions where the relevant transport-induced excitation processes become quenched and deexcitation processes are enhanced upon an increase of temperature. The phenomenon turns out to be robust with respect to all relevant parameters. It is especially pronounced for higher bias voltages and weak to moderate coupling. Our findings have implications for open quantum systems in general, where electron transport is coupled to mechanical (phononic) or photonic degrees of freedom. In particular, molecular junctions with rigid tunneling pathways or quantum dot circuit QED systems meet the required conditions.

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arXiv2016

Hierarchical Quantum Master Equation Approach to Electronic-Vibrational Coupling in Nonequilibrium Transport through Nanosystems

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 co-tunneling signal is analyzed for a vibrational mode in full nonequilibrium, revealing a complex interplay of different transport processes and deviations from the commonly used $G_0/2$-thumb-rule. In addition, the HQME-approach is used to benchmark approximate master equation and nonequilibrium Green's function methods.

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arXiv2015

Transport through an Anderson impurity: Current ringing, non-linear magnetization and a direct comparison of continuous-time quantum Monte Carlo and hierarchical quantum master equations

We give a detailed comparison of the hierarchical quantum master equation (HQME) method to a continuous-time quantum Monte Carlo (CT-QMC) approach, assessing the usability of these numerically exact schemes as impurity solvers in practical nonequilibrium calculations. We review the main characteristics of the methods and discuss the scaling of the associated numerical effort. We substantiate our discussion with explicit numerical results for the nonequilibrium transport properties of a single-site Anderson impurity. The numerical effort of the HQME scheme scales linearly with the simulation time but increases (at worst exponentially) with decreasing temperature. In contrast, CT-QMC is less restricted by temperature at short times, but in general the cost of going to longer times is also exponential. After establishing the numerical exactness of the HQME scheme, we use it to elucidate the influence of different ways to induce transport through the impurity on the initial dynamics, discuss the phenomenon of coherent current oscillations, known as current ringing, and explain the non-monotonic temperature dependence of the steady-state magnetization as a result of competing broadening effects. We also elucidate the pronounced non-linear magnetization dynamics, which appears on intermediate time scales in the presence of an asymmetric coupling to the electrodes.

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arXiv2014

The formation of nonequilibrium steady states in interacting double quantum dots: When coherences dominate the charge distribution

We theoretically investigate the full time evolution of a nonequilibrium double quantum dot structure from initial conditions corresponding to different product states (no entanglement between dot and lead) to a nonequilibrium steady state. The structure is described by a two-level spinless Anderson model where the levels are coupled to two leads held at different chemical potentials. The problem is solved by a numerically exact hierarchical master equation technique and the results are compared to approximate ones obtained from Born-Markov theory. The methods allow us to study the time evolution up to times of order $10^4$ of the bare hybridization time, enabling eludication of the role of the initial state on the transient dynamics, coherent charge oscillations and an interaction-induced renormalization of energy levels. We find that when the system carries a single electron on average the formation of the steady state is strongly influenced by the coherence between the dots. The latter can be sizeable and indeed larger in the presence of a bias voltage than it is in equilibrium. Moreover, the interdot coherence is shown to lead to a pronounced difference in the population of the dots.

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arXiv2014

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 quasi-degenerate 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 coupling, are analyzed in some detail.

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arXiv2014

Current Noise in Single-Molecule Junctions Induced by Electronic-Vibrational Coupling

The influence of multiple vibrational modes on current fluctuations in electron transport through single-molecule junctions is investigated. Our analysis is based on a generic model of a molecular junction, which comprises a single electronic state on the molecular bridge coupled to multiple vibrational modes and fermionic leads, and employs a master equation approach. The results reveal that in molecular junctions with multiple vibrational modes already weak to moderate electronic-vibrational coupling may result in high noise levels, especially at the onset of resonant transport, in accordance with experimental findings of Secker et al..[1] The underlying mechanisms are analyzed in some detail. [1] D. Secker et al., Phys. Rev. Lett. 106, 136807 (2011).

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arXiv2014

Switching the Conductance of a Molecular Junction using a Proton Transfer Reaction

A novel mechanism for switching a molecular junction based on a proton transfer reaction triggered by an external electrostatic field is proposed. As a specific example to demonstrate the feasibility of the mechanism, the tautomers [2,5-(4-hydroxypyridine)] and {2,5-[4(1H)-pyridone]} are considered. Employing a combination of first-principles electronic structure calculations and Landauer transport theory, we show that both tautomers exhibit very different conductance properties and realize the "on" and "off" states of a molecular switch. Moreover, we provide a proof of principle that both forms can be reversibly converted into each other using an external electrostatic field.

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arXiv2013

Decoherence and lead induced inter-dot coupling in nonequilibrium electron transport through interacting quantum dots: A hierarchical quantum master equation approach

The interplay between interference effects and electron-electron interactions in electron transport through an interacting double quantum dot system is investigated using a hierarchical quantum master equation approach which becomes exact if carried to infinite order and converges well if the temperature is not too low. Decoherence due to electron-electron interactions is found to give rise to pronounced negative differential resistance, enhanced broadening of structures in current-voltage characteristics and an inversion of the electronic population. Dependence on gate voltage is shown to be a useful method of distinguishing decoherence-induced phenomena from effects induced by other mechanisms such as the presence of a blocking state. Comparison of results obtained by the hierarchical quantum master equation approach to those obtained from the Born-Markov approximation to the Nakajima-Zwanzig equation and from the non-crossing approximation to the nonequilibrium Green's function reveals the importance of an inter-dot coupling that originates from the energy dependence of the conduction bands in the leads and the need for a systematic perturbative expansion.

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arXiv2013

Vibrationally coupled electron transport in single-molecule junctions: The importance of electron-hole pair creation processes

Vibrationally coupled electron transport through single-molecule junctions is considered. Reviewing our recent theoretical work, we show that electron-hole pair creation processes represent the key to understand the vibrational excitation characteristic of a single-molecule contact. Moreover, these processes can lead to a number of interesting transport phenomena such as, for example, negative differential resistance, rectification, mode-selective vibrational excitation and a pronounced temperature dependence of the electrical current. Thus, electron-hole pair creation processes are crucial to elucidate the basic mechanisms of vibrationally coupled electron transport through a single-molecule contact, despite the fact that these processes do not directly contribute to the electrical current that is flowing through the junction.

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arXiv2013

Vibrationally Induced Decoherence in Single-Molecule Junctions

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 picture. This includes signatures in both the resonant and the non-resonant transport regime. Moreover, it is shown that local cooling by electron-hole pair creation processes can influence the transport characteristics profoundly, giving rise to a significant temperature dependence of the electrical current.

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arXiv2011

Bias-Controlled Selective Excitation of Vibrational Modes in Molecular Junctions: A Route Towards Mode-Selective Chemistry

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 systems representing asymmetric molecular junctions and/or scanning tunneling microscopy experiments. To this end, we employ two complementary theoretical approaches, a nonequilibrium Green's function approach and a master equation approach. The comparison of both methods reveals good agreement in describing resonant electron transport through a single-molecule contact, but also highlights the role of non-resonant transport processes, in particular co-tunneling and off-resonant electron-hole pair creation processes.

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arXiv2011

Quantum Interference and Decoherence in Single-Molecule Junctions: How Vibrations Induce Electrical Current

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 the junction is vibrationally highly excited, e.g. due to current-induced nonequilibrium effects in the resonant transport regime.

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arXiv2011

Vibrational Instabilities in Resonant Electron Transport through Single-Molecule Junctions

We analyze various limits of vibrationally coupled resonant electron transport in single-molecule junctions. Based on a master equation approach, we discuss analytic and numerical results for junctions under a high bias voltage or weak electronic-vibrational coupling. It is shown that in these limits the vibrational excitation of the molecular bridge increases indefinitely, i.e. the junction exhibits a vibrational instability. Moreover, our analysis provides analytic results for the vibrational distribution function and reveals that these vibrational instabilities are related to electron-hole pair creation processes.

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arXiv2010

Resonant Electron Transport in Single-Molecule Junctions: Vibrational Excitation, Rectification, Negative Differential Resistance and Local Cooling

Vibronic effects in resonant electron transport through single-molecule junctions are analyzed. The study is based on generic models for molecular junctions, which include electronic states on the molecular bridge that are vibrationally coupled and exhibit Coulomb interaction. The transport calculations employ a master equation approach. The results, obtained for a series of models with increasing complexity, show a multitude of interesting transport phenomena, including vibrational excitation, rectification, negative differential resistance (NDR) as well as local cooling. While some of these phenomena have been observed or proposed before, the present analysis extends previous studies and allows a more detailed understanding of the underlying transport mechanisms. In particular, it is shown that many of the observed phenomena can only be explained if electron-hole pair creation processes at the molecule-lead interface are taken into account. Furthermore, vibronic effects in sytems with multiple electronic states and their role for the stability of molecular junctions are analyzed.

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arXiv2008

Vibrational nonequilibrium effects in the conductance of single-molecules with multiple electronic states

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 electrodes.

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arXiv2008

Multimode vibrational effects in single molecule conductance: A nonequilibrium Green's function approach

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.

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