Electron-vibron Coupling Research Articles

Enantioselectivity from inelastic electron tunnelling through a chiral sensor

The vibration theory of olfaction, which explains it as the sensing of odorant molecules by their vibrational energies through inelastic electron tunnelling spectroscopy (IETS) has inspired olfactory sensor ideas. However, this theory has been presumed inadequate to explain the difference in smell between enantiomers (chiral molecules, which are mirror images of each other), since these have identical vibrational spectra. Going beyond phenomenological assumptions of enantioselective tunnelling, we show on the basis of ab initio modelling of real chiral molecules, that this drawback is indeed obviated for IETS-based olfactory sensors if they are chiral. Our treatment unifies IETS with chirality induced spin selectivity, which explains that charge polarization in chiral molecules by accompanied by spin polarization. First, we apply ab initio symmetry adapted perturbation theory to explain and illustrate enantioselective coupling of chiral odorant molecules and chiral olfactory sensors. This naturally leads to enantioselective coupling of the vibrational mode of an odorant to electron transport (electron-vibron coupling) in an IETS-based sensor when both odorant and sensor are chiral. Finally, we show, from phenomenological quantum transport calculations, that that in turn results in enantioselective IET spectra. Thus, we have demonstrated the feasibility of enantioselective sensing within a vibration framework. Our work also limns the possibility of quantum biomimetic electronic nose sensors that are enantioselective, a feature which could open up new sensing applications.

Exceptionally clean single-electron transistors from solutions of molecular graphene nanoribbons

Only single-electron transistors with a certain level of cleanliness, where all states can be properly accessed, can be used for quantum experiments. To reveal their exceptional properties, carbon nanomaterials need to be stripped down to a single element: graphene has been exfoliated into a single sheet, and carbon nanotubes can reveal their vibrational, spin and quantum coherence properties only after being suspended across trenches1–3. Molecular graphene nanoribbons4–6 now provide carbon nanostructures with single-atom precision but suffer from poor solubility, similar to carbon nanotubes. Here we demonstrate the massive enhancement of the solubility of graphene nanoribbons by edge functionalization, to yield ultra-clean transport devices with sharp single-electron features. Strong electron–vibron coupling leads to a prominent Franck–Condon blockade, and the atomic definition of the edges allows identifying the associated transverse bending mode. These results demonstrate how molecular graphene can yield exceptionally clean electronic devices directly from solution. The sharpness of the electronic features opens a path to the exploitation of spin and vibrational properties in atomically precise graphene nanostructures.

Intrinsic Vibrational Angular Momentum from Nonadiabatic Effects in Noncollinear Magnetic Molecules.

We show that in noncollinear magnetic molecules, nonadiabatic (dynamical) effects due to the electron-vibron coupling are time-reversal symmetry breaking interactions for the vibrational field. Because the electronic wave function cannot be chosen as real in these molecules, a nonzero geometric vector potential (Berry connection) arises. As a result, an intrinsic nonzero vibrational angular momentum occurs even for nondegenerate modes and in the absence of external probes. The vibronic modes can then be seen as elementary quantum particles carrying a sizeable angular momentum. As a proof of concept, we demonstrate the magnitude of this topological effect by performing nonadiabatic first principles calculations on platinum clusters and by showing that these molecules host sizeable intrinsic phonon angular momenta comparable to the orbital electronic ones in itinerant ferromagnets.

Vibrational Frequency Used as Internal Clock Reference to Access Molecule-Metal Charge-Transfer Times.

Dynamical charge transfer processes at molecule-metal interfaces proceed in the few fs timescale that renders them highly relevant to electronic excitations in optoelectronic devices. Yet, knowledge thereof is limited when electronic ground state situations are considered that implicate charge transfer directly at the fermi energy. Here we show that such processes can be accessed by means of vibrational excitations, with nonadiabatic electron-vibron coupling leading to distinct asymmetric line shapes. Thereby the characteristic timescale of this interfacial dynamical charge transfer can be derived by using the vibrational oscillation period as an internal clock reference.

Interference and shot noise in a degenerate Anderson-Holstein model

We study the transport properties of an Anderson-Holstein model with orbital degeneracies and a tunneling phase that allows for the formation of dark states. The resulting destructive interference yields a characteristic pattern of positive and negative differential conductance features with enhanced shot noise, without further asymmetry requirements in the coupling to the leads. The transport characteristics are strongly influenced by the Lamb-shift renormalization of the system Hamiltonian. Thus, the electron-vibron coupling cannot be extracted by a simple fit of the current steps to a Poisson distribution. For strong vibronic relaxation, a simpler effective model with analytical solution allows for a better understanding and moreover demonstrates the robustness of the described effects.

Magnetic field control of the Franck-Condon coupling of few-electron quantum states

Suspended carbon nanotubes display at cryogenic temperatures a distinct interaction between the quantized longitudinal vibration of the macromolecule and its embedded quantum dot, visible via Franck-Condon conductance side bands in transport spectroscopy. We present data on such side bands at known absolute number N=1 and N=2 of conduction band electrons and consequently well-defined electronic ground and excited states in a clean nanotube device. The interaction evolves only at a finite axial magnetic field and displays a distinct magnetic field dependence of the Franck-Condon coupling, different for different electronic base states and indicating a valley-dependent electron-vibron coupling. A tentative cause of these effects, reshaping of the electronic wavefunction by the magnetic field, is discussed and demonstrated in a model.

Terahertz dynamics of electron–vibron coupling in single molecules with tunable electrostatic potential

Clarifying electronic and vibronic properties at individual molecule level provides key insights to future chemistry, nanoelectronics, and quantum information technologies. The single electron tunneling spectroscopy has been used to study the charging/discharging process in single molecules. The obtained information was, however, mainly on static electronic properties, and access to their dynamical properties was very indirect. Here, we report on the terahertz (THz) spectroscopy of single fullerene molecules by using a single molecule transistor (SMT) geometry. From the time-domain THz autocorrelation measurements, we have obtained THz spectra associated with the THz-induced center-of-mass oscillation of the molecules. The observed peaks are finely split into two, reflecting the difference in the van der Waals potential profile experienced by the molecule on the metal surface when the number of electrons on the molecule fluctuates by one during the single electron tunneling process. Such an ultrahigh-sensitivity to the electronic/vibronic structures of a single molecule upon adding/removing a single electron has been achieved by using the THz spectroscopy in the SMT geometry. This novel scheme provides a new opportunity for investigating ultrafast THz dynamics of sub-nm scale systems.

Lifting the Franck-Condon blockade in driven quantum dots

Electron-vibron coupling in quantum dots can lead to a strong suppression of the average current in the sequential tunneling regime. This effect is known as Franck-Condon blockade and can be traced back to an overlap integral between vibron states with different electron numbers which becomes exponentially small for large electron-vibron coupling strength. Here, we investigate the effect of a time-dependent drive on this phenomenon, in particular the effect of an oscillatory gate voltage acting on the electronic dot level. We employ two different approaches: perturbation theory based on nonequilibrium Keldysh Green's functions and a master equation in Born-Markov approximation. In both cases, we find that the drive can lift the blockade by exciting vibrons. As a consequence, the relative change in average current grows exponentially with the drive strength.

Structural and Vibrational Properties of CuPc/Ag(111) Ultrathin Films

The initial stages of copper(II)–phthalocyanine (CuPc) thin film growth on Ag(111) have been investigated using Fourier transform infrared absorption spectroscopy (FT-IRAS), spot profile analysis low-energy electron diffraction (SPA-LEED), and thermal desorption spectroscopy (TDS). Starting at (sub)monolayer coverages up to 5 monolayers (ML), a number of ordered overlayers are found. Vibrational spectroscopy shows characteristic spectroscopic signatures for the individual submonolayer phases as well as for the bilayer, trilayer, and multilayers. Highly asymmetric line shapes of the in-plane vibrational modes of submonolayer CuPc provide unequivocal evidence for interfacial dynamical charge transfer between the metal electronic states and CuPc molecular orbitals, indicative for a partially filled LUMO at the Fermi energy as well as the prevalence of severe nonadiabaticity in the electron–vibron coupling. Growth of the second and third CuPc layers proceeds in a layer-by-layer fashion (Frank van der Merwe gr...

Electron-Vibron Coupling at Metal-Organic Interfaces from Theory and Experiment.

We study the significance and characteristics of interfacial dynamical charge transfer at metal-organic interfaces for the organic semiconductor model system 1,4,5,8-naphthalene-tetra-carboxylic dianhydride (NTCDA) on Ag(111) quantitatively. We combine infrared absorption spectroscopy and dispersion-corrected density functional theory calculations to analyze dynamic dipole moments and electron-vibron coupling at the interface. We demonstrate that interfacial dynamical charge transfer is the dominant cause of infrared activity in these systems and that it correlates with results from partial charge and density of states analysis. Nuclear motion generates an additional dynamic dipole moment but represents a minor effect except for modes with significant out-of-plane amplitudes.

Redox-Dependent Franck-Condon Blockade and Avalanche Transport in a Graphene-Fullerene Single-Molecule Transistor.

We report transport measurements on a graphene-fullerene single-molecule transistor. The device architecture where a functionalized C60 binds to graphene nanoelectrodes results in strong electron-vibron coupling and weak vibron relaxation. Using a combined approach of transport spectroscopy, Raman spectroscopy, and DFT calculations, we demonstrate center-of-mass oscillations, redox-dependent Franck-Condon blockade, and a transport regime characterized by avalanche tunnelling in a single-molecule transistor.

Electron-vibron coupling effects on electron transport via a single-molecule magnet

We investigate how the electron-vibron coupling influences electron transport via an anisotropic magnetic molecule, such as a single-molecule magnet (SMM) Fe$_4$, by using a model Hamiltonian with parameter values obtained from density-functional theory (DFT). Magnetic anisotropy parameters, vibrational energies, and electron-vibron coupling strengths of the Fe$_4$ are computed using DFT. A giant spin model is applied to the Fe$_4$ with only two charge states, specifically a neutral state with the total spin $S=5$ and a singly charged state with $S=9/2$, which is consistent with our DFT result and experiments on Fe$_4$ single-molecule transistors. In sequential electron tunneling, we find that the magnetic anisotropy gives rise to new features in conductance peaks arising from vibrational excitations. In particular, the peak height shows a strong, unusual dependence on the direction as well as magnitude of applied B field. The magnetic anisotropy also introduces vibrational satellite peaks whose position and height are modified with the direction and magnitude of applied B field. Furthermore, when multiple vibrational modes with considerable electron-vibron coupling have energies close to one another, a low-bias current is suppressed, independently of gate voltage and applied B field, although that is not the case for a single mode with the similar electron-vibron coupling. In the former case, the conductance peaks reveal a stronger B-field dependence than in the latter case. The new features appear because the magnetic anisotropy barrier is of the same order of magnitude as the energies of vibrational modes with significant electron-vibron coupling. Our findings clearly show the interesting interplay between magnetic anisotropy and electron-vibron coupling in electron transport via the Fe$_4$. The similar behavior can be observed in transport via other anisotropic magnetic molecules.

The image charge effect and vibron-assisted processes in Coulomb blockade transport: a first principles approach.

We present a combination of density functional theory and of both non-equilibrium Green's function formalism and a Master equation approach to accurately describe quantum transport in molecular junctions in the Coulomb blockade regime. We apply this effective first-principles approach to reproduce the experimental results of Perrin et al., [Nat. Nanotechnol., 2013, 8, 282] for the transport properties of a Au-(Zn)porphyrin-Au molecular junction. We demonstrate that energy level renormalization due to the image charge effect is crucial to the prediction of the current onset in the current-voltage, I-V, curves as a function of electrode separation. Furthermore, we show that for voltages beyond that setting the current onset, the slope of the I-V characteristics is determined by the interaction of the charge carriers with molecular vibrations. This corresponds to current-induced local heating, which may also lead to an effective reduced electronic coupling. Overall our scheme provides a fully ab initio description of quantum transport in the Coulomb blockade regime in the presence of electron-vibron coupling.

Franck-Condon blockade in a single-molecule transistor.

We investigate vibron-assisted electron transport in single-molecule transistors containing an individual Fe4 Single-Molecule Magnet. We observe a strong suppression of the tunneling current at low bias in combination with vibron-assisted excitations. The observed features are explained by a strong electron-vibron coupling in the framework of the Franck-Condon model supported by density-functional theory.

Generation and coherent control of pure spin currents via terahertz pulses

We inspect the time and spin-dependent, inelastic tunneling in engineered semiconductor-based double quantum well driven by time-structured terahertz pulses. An essential ingredient is an embedded spin-active structure with vibrational modes that scatter the pulse driven carriers. Due to the different time scales of the charge and spin dynamics, the spin-dependent electron-vibron coupling may result in pure net spin current (with negligible charge current). Heating the vibrational site may affect the resulting spin current. Furthermore, by controlling the charge dynamics, the spin dynamics and the generated spin current can be manipulated and switched on and off coherently.

Probing Wigner correlations in a suspended carbon nanotube

The influence of electron–vibron coupling on the transport properties of a strongly interacting quantum dot built in a suspended carbon nanotube (CNT) is analyzed. The latter is probed by a charged atomic force microscope tip scanned along the axis of the CNT which induces oscillations of the chemical potential and of the linear conductance. These oscillations are due to the competition between finite-size effects and the formation of a Wigner molecule for strong interactions. Such oscillations are shown to be suppressed by the electron–vibron coupling. The suppression is more pronounced in the regime of weak Coulomb interactions, which ensures that probing Wigner correlations in such a system is in principle possible.

Suppression of electron–vibron coupling in graphene nanoribbons contacted via a single atom

Graphene nanostructures, where quantum confinement opens an energy gap in the band structure, hold promise for future electronic devices. To realize the full potential of these materials, atomic-scale control over the contacts to graphene and the graphene nanostructure forming the active part of the device is required. The contacts should have a high transmission and yet not modify the electronic properties of the active region significantly to maintain the potentially exciting physics offered by the nanoscale honeycomb lattice. Here we show how contacting an atomically well-defined graphene nanoribbon to a metallic lead by a chemical bond via only one atom significantly influences the charge transport through the graphene nanoribbon but does not affect its electronic structure. Specifically, we find that creating well-defined contacts can suppress inelastic transport channels.

Vibrational distortion effects in transport through single molecular magnets

We study the transport through an isotropic single molecular magnet (S=1) with electron–vibron coupling using Keldysh's non-equilibrium Green function based on Hubbard operator. Electron–vibron coupling smooths the current steps due to the broadening of effective channel levels and shifts the elastic resonance peaks in differential conductance down in energy. At low temperature vibron-assisted peaks appear only at energies above the elastic resonance due to the absence of vibron excitation. The electron–vibron coupling also leads to the increase of shot noise, which gets more evident with increasing electron–vibron coupling.

Symmetry Dependence of Vibration-Assisted Tunneling

We present spatially resolved vibronic spectroscopy of individual pentacene molecules in a double-barrier tunneling junction. It is observed that even for this effective single-level system the energy dissipation associated with electron attachment varies spatially by more than a factor of 2. This is in contrast to the usual treatment of electron-vibron coupling in the Franck-Condon picture. Our experiments unambiguously prove that the local symmetry of initial and final wave function determines the dissipation in electron transport.

Stability and Nonadiabatic Effects of the Endohedral Clusters X@Al12 (X = B, C, N, Al, Si, P) with 39, 40, and 41 Valence Electrons

Metallic nanoclusters, with one electron or hole difference from closed shell, might end up in a degenerate state undergoing a Jahn–Teller distortion as a result of nonadiabatic effects, which are a manifestation of the electron–vibron coupling. Here, we report a theoretical study on the stability and nonadiabaticity of the neutral and charged endohedral clusters X@Al12 (X = B, C, N, Al, Si, P) around icosahedral symmetry, for 39, 40, and 41 valence electrons. The nonadiabatic effects are evaluated through the Jahn–Teller gain for the distorted cluster and their effect on the calculated electronic density of states is analyzed. For the 40 electron valence systems, we present the full vibrational spectra. Our results are discussed within the framework of the superatom model, and show that not all systems are well described by the spherical jellium model and that nonadiabaticity is better represented by ellipsoidal models. We present a detail discussion of the Al13–1 electron detachment process and show how...