Inelastic Electron Transport Research Articles

Enhancement of Graphene Phonon Excitation by a Chemically Engineered Molecular Resonance.

The abstraction of pyrrolic hydrogen from a single phthalocyanine on graphene turns the molecule into a sensitive probe for graphene phonons. The inelastic electron transport measured with a scanning tunneling microscope across the molecular adsorbate and graphene becomes strongly enhanced for a graphene out-of-plane acoustic phonon mode. Supporting density functional and transport calculations elucidate the underlying physical mechanism. A molecular orbital resonance close to the Fermi energy controls the inelastic current while specific phonon modes of graphene are magnified due to their coupling to symmetry-equivalent vibrational quanta of the molecule.

Extending the source-sink potential method to include electron-nucleus coupling.

The source-sink potential (SSP) method provides a simple tool for the qualitative analysis of the conductance of molecular electronic devices, and often analytical expressions for the conductance can be obtained. Here, we extend the SSP approach to account for decoherent, inelastic electron transport by including the non-adiabatic coupling between the electrons and the nuclei in the molecule. This coupling results in contributions to electron transport that can modify the qualitative structure-conductance relationships that we unraveled previously with SSP. In the approach proposed, electron-nucleus interactions are treated starting from the harmonic approximation for the nuclei, using a non-perturbative approach to account for the non-adiabatic coupling. Our method qualitatively describes experimentally observed phenomena and allows for a simple analysis that often provides analytical formulas in terms of the physical parameters of the junction, e.g., vibrational energies, non-adiabatic coupling, and molecule-contact coupling.

Inelastic Electron Tunneling Spectroscopic Analysis of Bias-Induced Structural Changes in a Solid-State Protein Junction.

A central issue in protein electronics is how far the structural stability of the protein is preserved under the very high electrical field that it will experience once a bias voltage is applied. This question is studied on the redox protein Azurin in the solid-state Au/protein/Au junction by monitoring protein vibrations during current transport under applied bias, up to ≈1 GV m-1 , by electrical detection of inelastic electron transport effects. Characteristic vibrational modes, such as CH stretching, amide (NH) bending, and AuS (of the bonds that connect the protein to an Au electrode), are not found to change noticeably up to 1.0V. At >1.0V, the NH bending and CH stretching inelastic features have disappeared, while the AuS features persist till ≈2 V,i.e., the proteins remain Au bound. Three possible causes for the disappearance of the NH and CH inelastic features at high bias, namely, i) resonance transport, ii) metallic filament formation, and iii) bond rupture leading to structural changes in the protein are proposed and tested. The results support the last option and indicate that spectrally resolved inelastic features can serve to monitor in operando structural stability of biological macromolecules while they serve as electronic current conduit.

Origin and mechanism analysis of asymmetric current fluctuations in single-molecule junctions

The measurements of molecular electronic devices usually suffer from serious noise. Although noise hampers the operation of electric circuits in most cases, current fluctuations in single-molecule junctions are essentially related to their intrinsic quantum effects in the process of electron transport. Noise analysis can reveal and understand these processes from the behavior of current fluctuations. Here, in this study we observe and analyze the faint asymmetric current distribution in single-molecule junctions, in which the asymmetric intensity is highly related to the applied biases. The exploration of high-order moments within bias and temperature dependent measurements, in combination with model Hamiltonian calculations, statistically prove that the asymmetric current distribution originates from the inelastic electron tunneling process. Such results demonstrate a potential noise analysis method based on the fine structures of the current distribution rather than the noise power, which has obvious advantages in the investigation of the inelastic electron tunneling process in single-molecule junctions.

Line shapes in inelastic electron tunneling spectroscopy of single-molecule junctions

Spectroscopic line-shape analyses for single-${\mathrm{C}}_{60}$ vibrational modes are presented for two kinds of scanning tunneling microscope experiments. Inelastic electron tunneling spectroscopy is performed for ${\mathrm{C}}_{60}$ molecules with different adsorption geometries on Pb(111). Depending on the ${\mathrm{C}}_{60}$ adsorption site and rotational orientation, the lowest unoccupied molecular orbital exhibits varying degrees of overlap with ${\mathrm{C}}_{60}$ vibrational energies. Concomitantly, the line shapes of vibrational modes are affected according to expectations for on-resonance inelastic electron tunneling. Inelastic electron transport is further studied for decreasing tip-${\mathrm{C}}_{60}$ distances covering tunneling and contact ranges. Line-shape changes signaling a conductance increase rather than the expected decrease upon exciting vibrational quanta are observed. A phenomenological approach is suggested to understand the dissimilar behavior of the junction conductance in the different electron transport ranges.

Diffraction effects and inelastic electron transport in angle-resolved microscopic imaging applications.

We analyse the signal formation process for scanning electron microscopic imaging applications on crystalline specimens. In accordance with previous investigations, we find nontrivial effects of incident beam diffraction on the backscattered electron distribution in energy and momentum. Specifically, incident beam diffraction causes angular changes of the backscattered electron distribution which we identify as the dominant mechanism underlying pseudocolour orientation imaging using multiple, angle-resolving detectors. Consequently, diffraction effects of the incident beam and their impact on the subsequent coherent and incoherent electron transport need to be taken into account for an in-depth theoretical modelling of the energy- and momentum distribution of electrons backscattered from crystalline sample regions. Our findings have implications for the level of theoretical detail that can be necessary for the interpretation of complex imaging modalities such as electron channelling contrast imaging (ECCI) of defects in crystals. If the solid angle of detection is limited to specific regions of the backscattered electron momentum distribution, the image contrast that is observed in ECCI and similar applications can be strongly affected by incident beam diffraction and topographic effects from the sample surface. As an application, we demonstrate characteristic changes in the resulting images if different properties of the backscattered electron distribution are used for the analysis of a GaN thin film sample containing dislocations.

Inelastic electron tunneling spectroscopy in molecular junctions showing quantum interference

Destructive quantum interference effect is implemented in large area molecular junctions to improve signatures of electron-phonon interaction. Vertical molecular junctions based on a cross-conjugated anthraquinone layer were fabricated and low-noise transport measurements were performed by acquiring simultaneously the current-voltage characteristics, its second derivative, and the differential conductance. Signatures of vibrational modes excited by inelastic events are present in the whole measured voltage range and superpose to the conductance suppression induced by destructive quantum interference. As a consequence vibrational modes have improved visibility in the low energy window $(<80\phantom{\rule{0.28em}{0ex}}\mathrm{meV})$. Inelastic electron transport spectroscopy data are compared to infrared attenuated total reflection spectroscopy on Au/anthraquinone thin films. Common vibrational modes can be clearly identified, but inelastic electron tunneling spectroscopy reveals the existence of vibrational modes in a wider energy range $(0--400\phantom{\rule{0.28em}{0ex}}\mathrm{meV})$ where infrared spectroscopy is lacking.

Dissipative time-dependent quantum transport theory: Quantum interference and phonon induced decoherence dynamics.

A time-dependent inelastic electron transport theory for strong electron-phonon interaction is established via the equations of motion method combined with the small polaron transformation. In this work, the dissipation via electron-phonon coupling is taken into account in the strong coupling regime, which validates the small polaron transformation. The corresponding equations of motion are developed, which are used to study the quantum interference effect and phonon-induced decoherence dynamics in molecular junctions. Numerical studies show clearly quantum interference effect of the transport electrons through two quasi-degenerate states with different couplings to the leads. We also found that the quantum interference can be suppressed by the electron-phonon interaction where the phase coherence is destroyed by phonon scattering. This indicates the importance of electron-phonon interaction in systems with prominent quantum interference effect.

Inelastic electron tunneling through degenerate and nondegenerate ground state polymeric junctions

The inelastic electron transport properties through two polymeric (trans-polyacetylene and polythiophene) molecular junctions are studied using Keldysh nonequilibrium Green function formalism. The Hamiltonian of the polymers is described via Su–Schrieffer–Heeger model and the metallic electrodes are modeled by the wide-band approximation. Results show that the step-like behavior of the current–voltage characteristics is deformed in presence of strong electron–phonon interaction. Also, the magnitude of current is slightly decreased in the phonon assistant electron transport regime. In addition, it is observed that the I–V curves are independent of temperature.

Effects of multiple reflection in the process of inelastic electron transport through an anisotropic magnetic atom

The effect of multiple reflection in the process of electron transport on the current-voltage characteristics of an adsorbed magnetic atom with single-ion anisotropy has been investigated. All orders of the perturbation theory with respect to the parameter of coupling between the contacts and the multilevel impurity have been taken into account by the Keldysh diagram technique with the use of Hubbard operators. It has been shown that the current-voltage characteristics of the system in a strongly nonequilibrium regime contains regions of negative differential conductance. The ways of enhancing this effect are discussed.

Inelastic electron transport through mesoscopic systems: Heating versus cooling and sequential tunneling versus cotunneling processes

Inelastic electron transport in quantum dot systems is studied via the hierarchical equations of motion combining a small polaron transformation approach, with differential conductance $dI/dV\ensuremath{\sim}V$ characteristics being evaluated accurately at the cotunneling level. We observe (i) the peak feature of phonon emission Franck-Condon sidebands to the zero-phonon peaks of both polaron and bipolaron in sequential electron transport; (ii) phonon absorption peaks occurring if the phonon temperature is sufficiently higher than that of the carrier electron; and (iii) the step feature of Raman sidebands in the cotunneling transport regime. We also evaluate the polaron transport response to a continuous-wave irradiation that induces bias-voltage oscillation. We observe, consistent with experimental results, that (iv) the photon-phonon-assisted tunneling enhances phonon absorptions while suppressing emissions. As the phonon absorption (emission) is associated with the process of absorbing (emitting) energy from (to) the phonon environment, an alternating or tailored field applied to contacts could be a practical means of cooling the mesoscopic quantum-transport device.

Nonequilibrium perturbation theory in Liouville–Fock space for inelastic electron transport

We use a superoperator representation of the quantum kinetic equation to develop nonequilibrium perturbation theory for an inelastic electron current through a quantum dot. We derive a Lindblad-type kinetic equation for an embedded quantum dot (i.e. a quantum dot connected to Lindblad dissipators through a buffer zone). The kinetic equation is converted to non-Hermitian field theory in Liouville–Fock space. The general nonequilibrium many-body perturbation theory is developed and applied to the quantum dot with electron–vibronic and electron–electron interactions. Our perturbation theory becomes equivalent to a Keldysh nonequilibrium Green’s function perturbative treatment provided that the buffer zone is large enough to alleviate the problems associated with approximations of the Lindblad kinetic equation.

Effects of inelastic spin-dependent electron transport through a spin nanostructure in a magnetic field

The transport properties and current-voltage (I–V) characteristics of a system of spin dimers with antiferromagnetic coupling arranged between metallic contacts are investigated in the tight binding approximation using the Landauer-Buttiker formalism. It is shown that the s-d(f) exchange interaction between the spin moments of the electrons being transported and the spins of the nanostructure leads to the formation of a potential profile as well as its variation due to spin-flip processes. As a result, the spin-dependent transport becomes inelastic, and the transmission coefficient and the I–V characteristic are strongly modified. It is found that the application of a magnetic field induces additional transparency peaks in the spectral characteristic of the system and causes the colossal magnetoresistance effect.

First-Principles Study for Detection of Inelastic Electron Transport in Molecular Junctions by Internal Substitution

The idea of doping and chemical substitutions for bridge molecules is one of promising techniques to control the transport properties and engineering of molecular devices. In the present article, we extend this concept and propose the use of internal substitutions to detect the mechanism of ballistic and inelastic transport through molecular junctions. By performing first-principles transport calculations for several internally substituted systems, we show systematic pathway analysis of tunneling electrons and vibronic states as well as electron−phonon couplings on bridge molecules. The correlation of inelastic electron tunneling spectroscopy (IETS) and Raman spectroscopy is also discussed.

Quantum and semiclassical inelastic electron transport

Quantum and semiclassical inelastic electron transport

Implications and Applications of Current-Induced Dynamics in Molecular Junctions

Instances of strongly nonadiabatic electronic-vibrational energy transfer have been studied since the early days of quantum mechanics and remain a topic of fundamental interest. Often such transfers are associated with electronic resonances, temporary states where transient localization of charge on the molecule provides a mechanism for channeling electronic energy into vibrational excitation. Extensively studied in the gas phase, electron resonance scattering also occurs with surface adsorbed molecules, where it manifests itself in broadened cross sections and desorption of adsorbates from metal surfaces. In this Account, we focus on a related topic: the implications of nonadiabatic, resonance-mediated scattering to the exciting field of molecular electronics. In this context, researchers can induce directed nuclear dynamics and control these processes in single molecules in contact with metallic and semiconducting electrodes. We discuss a variety of consequences and applications of current-driven nuclear excitation in molecular devices, ranging from the design of new forms of molecular machines to surface chemistry at the single-molecule level and atom-resolved lithography. We highlight two specific examples of molecular nanomachines. In the first, a Au-C(60)-Au transistor, the current induces the oscillatory motion of the center-of-mass coordinate of the C(60). The second, a zwitterion-based rattle, demonstrates excitation of intramolecular motion as the positively charged moiety is threaded back and forth through the negatively charged carbon ring. Finally, we discuss the current-induced desorption of organic molecules from Si(100) both to suggest the potential for controlled surface nanochemistry and to develop guidelines for the design of stable molecular junctions. Modeling the exchange of energy between tunneling electrons and the vibrational degrees of freedom of a target molecule subject to bias voltage, open boundary conditions in the electronic subspace, and the dissipative effects of the electrodes poses a fascinating challenge to contemporary theories of inelastic electron transport. A scattering theory of density matrices is motivated by the need to address large amplitude, chemically relevant dynamics in tandem with an appropriate treatment of the electronic scattering problem. We provide a qualitative discussion of the theory and note the limits in which it reduces to well-known approaches.

Vibration-induced inelastic effects in the electron transport through multisite molecular bridges

We theoretically analyzed inelastic effects in the electron transport through molecular junctions originating from electron-vibron interactions. The molecular bridge was simulated by a periodical chain of identical hydrogenlike atoms with the nearest neighbors interaction thus providing a set of energy states for the electron tunneling. To avoid difficulties inevitably arising when advanced computational techniques are employed to study inelastic electron transport through multilevel bridges, we propose and develop a semiphenomenological approach. The latter is based on Buttiker's dephasing model within the scattering matrix formalism. We apply the proposed approach to describe features associated with electron energy transfer to vibrational phonons that appear in the second derivative of the current in the junction with respect to the bias voltage. In the particular case of a single level bridge our results agree with those obtained by proper calculations carried out within the nonequilibrium Green's functions method indicating the usefulness of the suggested approach.

Alkaline Earth versus Noble Metal Particles on MgO Thin Films: Growth and Optical Properties

Nucleation and growth of Mg, Ca, and Au particles on 8 ML thick MgO/Mo(001) films have been investigated by scanning tunneling microscopy (STM). Whereas the alkaline earth metals strongly interact with the MgO surface and form islands that are in registry with the square oxide lattice, a reduced coupling is suggested for Au on the basis of the observed hexagonal particle shapes. Optical properties of the metal particles are probed by injecting electrons from the STM tip into individual deposits and detecting the resulting photon emission. The overall spectral shape is governed by a plasmon-mediated photon emission that is characteristic for the different particle materials. However, a distinct fine-structure that is superimposed on the plasmon response is found to be independent of the chemical identity and geometry of the particles. This spectral contribution is assigned to the discrete excitation behavior of particle plasmons via inelastic electron transport through the double-barrier STM junction.

Inelastic electron transport in polymer nanofibers

In this paper we present theoretical analysis of the electron transport in conducting polymers being in a metal-like state. We concentrate on the study of the effects of temperature on characteristics of the transport. We treat a conducting polymer in the metal state as a network of metalliclike grains embedded in poorly conducting environment, which consists of randomly distributed polymeric chains. We carry out the present studies assuming that the intergrain conduction is mostly provided by electron quantum tunneling via intermediate states localized on polymer chains between the grains. To analyze the effects of temperature on this kind of electron intergrain transport we represent the thermal environment as a phonon bath coupled to the intermediate state. The electron transmission is computed using the Buttiker model within the scattering matrix formalism. This approach is further developed, and the dephasing parameter is expressed in terms of relevant energies including the thermal energy. It is shown that temperature dependencies of both current and conductance associated with the above transport mechanism differ from those typical for other conduction mechanisms in conducting polymers. This could be useful to separate out the contribution from the intergrain electron tunneling to the net electric current in transport experiments on various polymer nanofibers. The proposed model could be used to analyze inelastic electron transport through molecular junctions.

Molecular modeling of inelastic electron transport in molecular junctions

A quantum chemical approach for the modeling of inelastic electron tunneling spectroscopyof molecular junctions based on scattering theory is presented. Within a harmonicapproximation, the proposed method allows us to calculate the electron–vibration couplingstrength analytically, which makes it applicable to many different systems. The calculatedinelastic electron transport spectra are often in very good agreement with theirexperimental counterparts, allowing the revelation of detailed information about molecularconformations inside the junction, molecule–metal contact structures, and intermolecularinteraction that is largely inaccessible experimentally.