Electron-vibron Coupling Research Articles

Functionality in single-molecule devices: Model calculations and applications of the inelastic electron tunneling signal in molecular junctions

We analyze how functionality could be obtained within single-molecule devices by using a combination of non-equilibrium Green's functions and ab initio calculations to study the inelastic transport properties of single-molecule junctions. First, we apply a full non-equilibrium Green's function technique to a model system with electron-vibration coupling. We show that the features in the inelastic electron tunneling spectra (IETS) of the molecular junctions are virtually independent of the nature of the molecule-lead contacts. Since the contacts are not easily reproducible from one device to another, this is a very useful property. The IETS signal is much more robust versus modifications at the contacts and hence can be used to build functional nanodevices. Second, we consider a realistic model of a organic conjugated molecule. We use ab initio calculations to study how the vibronic properties of the molecule can be controlled by an external electric field which acts as a gate voltage. The control, through the gate voltage, of the vibron frequencies and (more importantly) of the electron-vibron coupling enables the construction of functionality: nonlinear amplification and/or switching is obtained from the IETS signal within a single-molecule device.

Ultra-short suspended single-wall carbon nanotube transistors

We describe a method to fabricate clean suspended single-wall carbon nanotube (SWCNT) transistors hosting a single quantum dot ranging in length from a few 10 s of nm down to ≈3 nm. We first align narrow gold bow-tie junctions on top of individual SWCNTs and suspend the devices. We then use a feedback-controlled electromigration to break the gold junctions and expose nm-sized sections of SWCNTs. We measure electron transport in these devices at low temperature and show that they form clean and tunable single-electron transistors. These ultra-short suspended transistors offer the prospect of studying THz oscillators with strong electron-vibron coupling.

Dynamical symmetry breaking in vibration-assisted transport through nanostructures

A theoretical model of a single molecule coupled to many vibronic modes is presented. At low energies, transport is dominated by electron-vibron processes where transfer of an electron through the dot is accompanied by the excitation/emission of quanta (vibrons). Because the frequency of the $n$th mode is taken as an $n$th multiple of the frequency of the fundamental mode, several energetically degenerate or quasi-degenerate vibronic configurations can contribute to transport. We investigate the consequences of strong electron-vibron coupling in a fully \emph{symmetric} set-up. Several striking features are predicted. In particular, a gate-asymmetry and pronounced negative differential conductance features are observed. We attribute these features to the presence of slow channels originating from the interplay of Franck-Condon suppression of transport channels and spin/orbital degeneracies.

Nonequilibrium inelastic electronic transport: Polarization effects and vertex corrections to the self-consistent Born approximation

We study the effect of electron-vibron interactions on the inelastic transport properties of single-molecule nanojunctions. We use the non-equilibrium Green's functions technique and a model Hamiltonian to calculate the effects of second-order diagrams (double-exchange DX and dressed-phonon DPH diagrams) on the electron-vibration interaction and consider their effects across the full range of parameter space. The DX diagram, corresponding to a vertex correction, introduces an effective dynamical renormalization of the electron-vibron coupling in both the purely inelastic and the inelastic-resonant features of the IETS. The purely inelastic features correspond to an applied bias around the energy of a vibron, while the inelastic-resonant features correspond to peaks (resonance) in the conductance. The DPH diagram affects only the inelastic resonant features. We also discuss the circumstances in which the second-order diagrams may be approximated in the study of more complex model systems.

Franck–Condon physics in a single trapped ion

We propose a way to explore the Franck–Condon (FC) physics using a single ion confined in a spin-dependent potential, formed by the combination of a Paul trap and a magnetic field gradient. A correlation between electronic and vibrational degrees of freedom, called electron–vibron coupling, is induced by a non-zero gradient. In the case of a sufficiently strong electron–vibron coupling, FC blockade of low-lying vibronic transitions takes place. We examine the feasibility of observing FC physics in a single trapped ion and demonstrate many potential applications of ionic FC physics in quantum state engineering and quantum information processing.

Chemical Raman Enhancement of Organic Adsorbates on Metal Surfaces

Using first-principles theory and experiments, chemical contributions to surface-enhanced Raman spectroscopy for a well-studied organic molecule, benzene thiol, chemisorbed on planar Au(111) surfaces are explained and quantified. Density functional theory calculations of the static Raman tensor demonstrate a strong mode-dependent modification of benzene thiol Raman spectra by Au substrates. Raman active modes with the largest enhancements result from stronger contributions from Au to their electron-vibron coupling, as quantified through a deformation potential. A straightforward and general analysis is introduced to extract chemical enhancement from experiments for specific vibrational modes; measured values are in excellent agreement with our calculations.

Valence band photoemission from the Zn-phthalocyanine/Ag(110) interface: Charge transfer and scattering of substrate photoelectrons

The electronic properties of Zn-phthalocyanine vacuum deposited on Ag(110) are studied by high-resolution valence-band photoelectron spectroscopy. Submonolayer, one ordered monolayer, and molecular layers of increasing thickness present spectral features that can be related to the molecule-substrate interaction as well as to the effect of the overlayer on the escape conditions of the substrate photoelectrons. For the first-ordered molecular layer, an interface state related to a charge transfer from the substrate to the molecules is detected through the appearance of a new feature at low binding energy. Such feature, appearing already at submonolayer coverage, is interpreted as the partial filling of the lowest unoccupied molecular orbital (LUMO) and to possible hybridization of the LUMO with substrate states. Because it is the major change observed in the molecular electronic structure after adsorption, the filling of the LUMO is likely to have a major role in the molecular chemisorption. The spectral line shape of the filled part of the LUMO is discussed in terms of electron-vibron coupling and electron correlation effects. Molecular states lying at higher binding energy show spectral modifications as a function of coverage implying a weaker contribution in the molecule-substrate interaction. Important changes are found in the spectral region of the $\text{Ag}\text{ }4d$ band after the deposition of a submonolayer and as a function of coverage although no interface states are detected. It is shown that these features can be entirely explained by considering the effect of the molecular overlayer on the escape conditions of the substrate photoelectrons. The major effect is the emerging of the substrate three-dimensional density of states. Such evidence is not simply related to the present case but it is expected to apply to other systems where an organic layer is deposited on a single-crystal substrate.

Nonequilibrium electronic structure of interacting single-molecule nanojunctions: Vertex corrections and polarization effects for the electron-vibron coupling

We consider the interaction between electrons and molecular vibrations in the context of electronic transport in nanoscale devices. We present a method based on nonequilibrium Green's functions to calculate both equilibrium and nonequilibrium electronic properties of a single-molecule junction in the presence of electron-vibron interactions. We apply our method to a model system consisting of a single electronic level coupled to a single vibration mode in the molecule, which is in contact with two electron reservoirs. Higher-order diagrams beyond the usual self-consistent Born approximation (SCBA) are included in the calculations. In this paper we consider the effects of the double-exchange diagram and the diagram in which the vibron propagator is renormalized by one electron-hole bubble. We study in detail the effects of the first- and second-order diagrams on the spectral functions for a large set of parameters and for different transport regimes (resonant and off-resonant cases), both at equilibrium and in the presence of a finite applied bias. We also study the linear response (linear conductance) of the nanojunction for all the different regimes. We find that it is indeed necessary to go beyond the SCBA in order to obtain correct results for a wide range of parameters.

Electromechanical instability in vibrating quantum dots with effectively negative charging energy

In quantum dots or molecules with vibrational degrees of freedom the electron-vibron coupling renormalizes the electronic charging energy. For sufficiently strong coupling, the renormalized charging energy can become negative. Here, we discuss an instability toward adding or removing an arbitrary number of electrons when the magnitude of the renormalized charging energy exceeds the single-particle level spacing. We show that the instability is regularized by the anharmonic contribution to the vibron energy. The resulting effective charging energy as a function of the electron number has a double-well structure causing a variety of novel features in the Coulomb-blockade properties.

Electron-vibron coupling in suspended carbon nanotube quantum dots

Motivated by recent experiments, we investigate the electron-vibron coupling in suspended carbon nanotube quantum dots, starting with the electron-phonon coupling of the underlying graphene layer. We show that the coupling strength depends sensitively on the type of vibron and is strongly sample dependent. The coupling strength becomes particularly strong when inhomogeneity-induced electronic quantum dots are located near regions where the vibronic mode is associated with large strain. Specifically, we find that the longitudinal stretching mode and the radial breathing mode are coupled via the strong deformation potential, while twist modes couple more weakly via a mechanism involving modulation of the electronic hopping amplitudes between carbon sites. A special case are bending modes: for symmetry reasons, their coupling is only quadratic in the vibron coordinate. Our results can explain recent experiments on suspended carbon nanotube quantum dots which exibit vibrational sidebands accompanied by the Franck-Condon blockade with strong electron-vibron coupling.

Franck–Condon blockade in suspended carbon nanotube quantum dots

Understanding the influence of vibrational motion of the atoms on electronic transitions in molecules constitutes a cornerstone of quantum physics, as epitomized by the Franck–Condon principle1,2 of spectroscopy. Recent advances in building molecular-electronics devices3 and nanoelectromechanical systems4 open a new arena for studying the interaction between mechanical and electronic degrees of freedom in transport at the single-molecule level. The tunnelling of electrons through molecules or suspended quantum dots5,6 has been shown to excite vibrational modes, or vibrons6,7,8,9. Beyond this effect, theory predicts that strong electron–vibron coupling strongly suppresses the current flow at low biases, a collective behaviour known as Franck–Condon blockade10,11. Here, we show measurements on quantum dots formed in suspended single-wall carbon nanotubes revealing a remarkably large electron–vibron coupling that, owing to the high quality and unprecedented tunability of our samples, allow a quantitative analysis of vibron-mediated electronic transport in the regime of strong electron–vibron coupling. This enables us to unambiguously demonstrate the Franck–Condon blockade in a suspended nanostructure. The large observed electron–vibron coupling could ultimately be a key ingredient for the detection of quantized mechanical motion12,13. It also emphasizes the unique potential for nanoelectromechanical device applications based on suspended graphene sheets and carbon nanotubes.

Bonding and vibrational dynamics of a largeπ-conjugated molecule on a metal surface

The interplay between the substrate bonding of a largeπ-conjugated semiconductor molecule and the dynamical properties of the metal–organicinterface is studied, employing the prototypical PTCDA/Ag(111) monolayer as an example.Both the coupling of molecular vibrations to the electron–hole-pair continuum of themetal surface and the inelastic scattering of tunnelling electrons by the molecularvibrations on their passage through the molecule are considered. The results ofboth types of experiment are consistent with the findings of measurements whichprobe the geometric and electronic structure of the adsorbate–substrate complexdirectly; generally speaking, they can be understood in the framework of standardtheories for the electron–vibron coupling. While the experiments reported herein fact provide additional qualitative insights into the substrate bonding of ourπ-conjugated model molecule, their detailed quantitative understanding would require a fullcalculation of the dynamical interface properties, which is currently not available.

Nonequilibrium resonant spectroscopy of molecular vibrons

Quantum transport through single molecules is essentially affected by molecular vibrations. We investigate the behavior of the prototype single-level model with intermediate electron-vibron coupling and arbitrary coupling to the leads. We have developed a theory which allows to explore this regime via the nonequilibrium Green function formalism. We show that the nonequilibrium resonant spectroscopy is able to determine the energies of molecular orbitals and the spectrum of molecular vibrations. Our results are relevant to scanning tunneling spectroscopy experiments, and demonstrate the importance of the systematic and self-consistent investigation of the effects of the vibronic dynamics onto the transport through single molecules.

Influence of vibrational modes on the electronic properties of DNA

We investigate the electron (hole) transport through short double-stranded DNA wires in which the electrons are strongly coupled to the specific vibrational modes (vibrons) of the DNA. We analyze the problem starting from a tight-binding model of DNA, with parameters derived from ab initio calculations, and describe the dissipative transport by equation-of-motion techniques. For homogeneous DNA sequences like poly-(guanine-cytosine), we find the transport to be quasiballistic with an effective density of states which is modified by the electron-vibron coupling. At low temperatures, the linear conductance is strongly enhanced, but above the ``semiconducting'' gap it is much less affected. In contrast, for inhomogeneous (``natural'') sequences, almost all states are strongly localized and transport is dominated by dissipative processes. In this case, a nonlocal electron-vibron coupling influences the conductance in a qualitative and sequence-dependent way.

Nonequilibrium molecular vibrons: An approach based on the nonequilibrium Green function technique and the self-consistent Born approximation

We consider the nonequilibrium quantum vibrations of a molecule clamped between two macroscopic leads in a current-carrying state at finite voltages. Our approach is based on the nonequilibrium Green function technique and the self-consistent Born approximation. Kinetic equations for the average populations of electrons and vibrons are formulated in the weak electron-vibron coupling case and self-consistent solutions are obtained. The effects of vibron emission and vibronic instability are demonstrated using few-orbital models. The importance of the electron-vibron resonance is shown.

Electron–vibron coupling in suspended nanotubes

We consider electron–vibron coupling in suspended nanotube quantum dots. Modelling the tube as an elastic medium, we study the possible coupling mechanism for exciting the stretching mode in a single-electron-transistor setup. Both the forces due to the longitudinal and the transverse fields are included. The effect of the longitudinal field is found to be too small to be seen in experiment. In contrast, the transverse field which couple to the stretching mode via the bending of the tube can in some cases give sizeable Franck–Condon factors. However, the length dependence is not compatible with recent experiments (Sapmaz et al 2005 New J. Phys. 7 243).

A comparison of fine structures in high-resolution x-ray-absorption spectra of various condensed organic molecules

We report on a high-resolution C-K and O-K near-edge x-ray-absorption fine-structure (NEXAFS) study of large aromatic molecules in condensed thin films, namely, anhydrides 1,4,5,8-naphthalene-tetracarboxylic acid dianhydride, 3,4,9,10-perylene-tetracarboxylic acid dianhydride, benzoperylene-(1,2)-dicarboxylic acid anhydride, and 1,8-naphthalene-dicarboxylic acid anhydride and the quinoic acenaphthenequinone. Due to the high-energy resolution of the third-generation synchrotron source BESSY II we observe large differences in the NEXAFS fine structures even for very similar molecules, resulting in a wealth of new information. The rich fine structure can unambiguously be assigned to the coupling of electronic transitions to vibronic excitations. Backed by ab initio calculations we present a detailed analysis of the spectra that allows the complete interpretation of the near-edge features. It also yields information on the vibronic properties in the electronically excited state as well as on the response of the electronic system upon core excitation. The strong differences in the electron-vibron coupling for different molecules are discussed.

Vibrational Sidebands and the Kondo Effect in Molecular Transistors

Electron transport through molecular quantum dots coupled to a single vibrational mode is studied in the Kondo regime. We apply a generalized Schrieffer-Wolff transformation to determine the effective low-energy spin-spin-vibron interaction. From this model we calculate the nonlinear conductance and find Kondo sidebands located at bias voltages equal to multiples of the vibron frequency. Because of selection rules, the side peaks are found to have strong gate-voltage dependences, which can be tested experimentally. In the limit of weak electron-vibron coupling, we employ a perturbative renormalization group scheme to calculate analytically the nonlinear conductance.

Rectification in single molecular dimers with strong polaron effect

We study theoretically the transport properties of a molecular two-level system with large electron-vibron coupling in the Coulomb blockade regime. We show that when the electron-vibron coupling induces polaron states, the current-voltage characteristic becomes strongly asymmetric because, in one current direction, one of the polaron state blocks the current through the other. This situation occurs when the coupling between the polaron states is smaller than the coupling to the leads. We discuss the relevance of our calculation for experiments on ${C}_{140}$ molecules.

Electron-Vibron Coupling in High-Resolution X-Ray Absorption Spectra of Organic Materials: NTCDA on Ag(111)

We report additional rich fine structures in high-resolution near-edge x-ray-absorption fine structure (NEXAFS) spectra of large organic molecules using NTCDA on Ag(111) as an example. These fine structures are completely interpreted as vibronic coupling to electronic core excitations. The coupling is mode selective; predominantly one vibronic mode couples to each excitation. The fit results suggest the occurrence of a Davydov splitting, first observed for core excitons. Morphological differences substantially influence the electron-vibron coupling, indicating a strong intermolecular interaction. Thus NEXAFS becomes a more subtle probe for organic solids.