Phonon-assisted current noise in molecular junctions

Quantum Flicker Noise in Atomic and Molecular Junctions

We report on a quantum form of electronic flicker noise in nanoscale conductors that contains valuable information on quantum transport. This noise is experimentally identified in atomic and molecular junctions and theoretically analyzed by considering quantum interference due to fluctuating scatterers. Using conductance, shot-noise, and flicker-noise measurements, we show that the revealed quantum flicker noise uniquely depends on the distribution of transmission channels, a key characteristic of quantum conductors. This dependence opens the door for the application of flicker noise as a diagnostic probe for fundamental properties of quantum conductors and many-body quantum effects, a role that up to now has been performed by the experimentally less-accessible shot noise.

Identification of vibration modes in single-molecule junctions by strong inelastic signals in noise

Conductance measurements in single-molecule junctions (SMJs) are on many occasions accompanied by inelastic spectroscopy and shot-noise measurements in order to obtain information about different vibration modes (or vibrons) and channels involved in the transport respectively. We have extended the single-molecule shot-noise measurements, which were previously performed at low bias, to high bias and we have studied the effects of these vibrons on the noise for a Deuterium (D₂) molecule between Pt leads. We report here two important findings from these measurements. First, we find in our noise measurements that at the vibron energies of the molecule, a two-level fluctuation (TLF) is excited in the junction. Second, we show that in the presence of this TLF, a form of enhanced noise spectroscopy can be performed to detect inelastic electron-vibron interactions, by studying the third derivative of the noise (d³S_I/dV³). This is possible because TLFs are insensitive to elastic scattering of electrons from defects, which nevertheless leave their signature in the usual inelastic electron tunnelling spectroscopy (IETS) measurements.

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.

The asymmetric current noise in a single-molecule device was observed, which is relevant to an inelastic electron transport process.

Fast and accurate shot noise measurements on atomic-size junctions in the MHz regime

Shot noise measurements on atomic and molecular junctions provide rich information about the quantum transport properties of the junctions and on the inelastic scattering events taking place in the process. Dissipation at the nanoscale, a problem of central interest in nano-electronics, can be studied in its most explicit and simplified form. Here, we describe a measurement technique that permits extending previous noise measurements to a much higher frequency range, and to much higher bias voltage range, while maintaining a high accuracy in noise and conductance. We also demonstrate the advantages of having access to the spectral information for diagnostics.

Towards Noise Simulation in Interacting Nonequilibrium Systems Strongly Coupled to Baths

Progress in experimental techniques at nanoscale makes measurements of noise in molecular junctions possible. These data are important source of information not accessible through average flux measurements. The emergence of optoelectronics, the recently shown possibility of strong light-matter couplings, and developments in the field of quantum thermodynamics are making measurements of transport statistics even more important. Theoretical methods for noise evaluation in first principles simulations can be roughly divided into approaches for weak intra-system interactions, and those treating strong interactions for systems weakly coupled to baths. We argue that due to structure of its diagrammatic expansion, and the use of many-body states as a basis of its formulation, the recently introduced nonequilibrium diagrammatic technique for Hubbard Green functions is a relatively inexpensive method suitable for evaluation of noise characteristics in first principles simulations over a wide range of parameters. We illustrate viability of the approach by simulations of noise and noise spectrum within generic models for non-, weakly and strongly interacting systems. Results of the simulations are compared to exact data (where available) and to simulations performed within approaches best suited for each of the three parameter regimes.

Current noise enhancement: channel mixing and possible nonequilibrium phonon backaction in atomic-scale Au junctions

We report measurements of the bias dependence of the Fano factor in ensembles of atomic-scale Au junctions at 77 K. Previous measurements of shot noise at room temperature and low biases have found good agreement of the Fano factor with the expectations of the Landauer-Büttiker formalism, while enhanced Fano factors have been observed at biases of hundreds of mV (Chen et al 2014 Sci. Rep. 4 4221). We find even stronger enhancement of shot noise at 77 K with an 'excess' Fano factor up to ten times the low bias value. We discuss the observed ensemble Fano factor bias dependence in terms of candidate models. The results are most consistent with either a bias-dependent channel mixing picture or a model incorporating noise enhancement due to current-driven, nonequilibrium phonon populations, though a complete theoretical treatment of the latter in the ensemble average limit is needed.

Evolution of shot noise in suspended lithographic gold break junctions with bias and temperature

Shot noise is a powerful tool to probe correlations and microscopic transport details that conductance measurements alone cannot reveal. Even in atomic-scale Au devices that are well described by Landauer-Büttiker physics, complications remain such as local heating and electron-phonon interactions. We report systematic rf measurements of shot noise in individual atomic-scale gold break junctions at multiple temperatures, with most bias voltages well above the energy of the Au optical phonon mode. Motivated by the previous experimental evidence that electron-phonon interactions can modify Fano factors and result in kinked features in bias dependence of shot noise, we find that the temperature dependence of shot noise from 4.2 to 100 K is minimal. Enhanced Fano factors near [Formula: see text] and features beyond simply linear bias dependence of shot noise near the [Formula: see text] plateau are observed. Both are believed to have non-interacting origins and the latter likely results from slightly bias-dependent transmittance of the dominant quantum channel.

Large-voltage behavior of charge transport characteristics in nanosystems with weak electron-vibration coupling

We study analytically the Full Counting Statistics of the charge transport through a nanosystem consisting of a few electronic levels weakly coupled to a discrete vibrational mode. In the limit of large transport voltage bias the cumulant generating function can be evaluated explicitly based solely on the intuitive physical arguments and classical master equation description of the vibration mode. We find that for the undamped vibrational modes mutual dynamical interplay between electronic and vibronic degrees of freedom leads to strongly nonlinear (in voltage) transport characteristics of the nanosystem. In particular, we find that for large voltages the k-th cumulant of the current grows as V (2k) to be contrasted with the linear dependence in case of more strongly externally damped and thus thermalized vibrational modes.

Thermoelectric effect in Aharonov-Bohm structures

The thermoelectric effects of a single Aharonov-Bohm (SAB) ring and coupled double Aharonov-Bohm (DAB) rings have been investigated on a theoretical basis, taking into account the contributions of both electrons and phonons to the transport process by using the nonequilibrium Green's function technique. The thermoelectric figure of merit of the coupled DAB rings cannot be predicted directly by combining the values of two SAB ring systems due to the contribution of electron-phonon interaction to coupling between the two sites connecting the rings. We find that thermoelectric efficiency can be optimized by modulating the phases of the magnetic flux threading the two rings.

Phonon effects on the current noise spectra and the ac conductance of a single molecular junction

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-molecule junction (SMJ) coupled with a vibrational mode. We show that the nonequilibrium dynamics of the phonons in a strong electron-phonon coupling regime can be taken into account appropriately in this self-consistent perturbation theory, and the self-energy of the phonons is connected with the current fluctuations in the molecular junction. We calculate the finite-frequency nonsymmetrized noise spectra and the ac conductance, which reveal a wealth of inelastic electron tunneling characteristics on the absorption and emission properties of this SMJ. In the presence of a finite bias voltage and the electron tunneling current, the vibration mode of the molecular junction is heated and driven to an unequilibrated state. The influences of unequilibrated phonons on the current and the noise spectra are investigated.

Enhanced noise at high bias in atomic-scale Au break junctions

Heating in nanoscale systems driven out of equilibrium is of fundamental importance, has ramifications for technological applications, and is a challenge to characterize experimentally. Prior experiments using nanoscale junctions have largely focused on heating of ionic degrees of freedom, while heating of the electrons has been mostly neglected. We report measurements in atomic-scale Au break junctions, in which the bias-driven component of the current noise is used as a probe of the electronic distribution. At low biases (<150 mV) the noise is consistent with expectations of shot noise at a fixed electronic temperature. At higher biases, a nonlinear dependence of the noise power is observed. We consider candidate mechanisms for this increase, including flicker noise (due to ionic motion), heating of the bulk electrodes, nonequilibrium electron-phonon effects, and local heating of the electronic distribution impinging on the ballistic junction. We find that flicker noise and bulk heating are quantitatively unlikely to explain the observations. We discuss the implications of these observations for other nanoscale systems, and experimental tests to distinguish vibrational and electron interaction mechanisms for the enhanced noise.

Electron-vibration interaction in multichannel single-molecule junctions

The effect of electron-vibration interaction in atomic-scale junctions with a single conduction channel was widely investigated both theoretically and experimentally. However, the more general case of junctions with several conduction channels has received very little attention. Here we study electron-vibration interaction in multichannel molecular junctions, formed by introduction of either benzene or carbon dioxide between platinum electrodes. By combining shot noise and differential conductance measurements, we analyze the effect of vibration activation on conductance in view of the distribution of conduction channels. Based on the shift of vibration energy while the junction is stretched, we identify vibration modes with transverse and longitudinal symmetry. The detection of different vibration modes is ascribed to efficient vibration coupling to different conduction channels according to symmetry considerations. While most of our observations can be explained in view of the theoretical models for a single conduction channel, the appearance of conductance enhancement, induced by electron-vibration interaction, at high conductance values indicates either unexpected high electron-vibration coupling or interchannel scattering.

Fundamental quantum noise mapping with tunnelling microscopes tested at surface structures of subatomic lateral size

We present a measurement scheme that enables quantitative detection of the shot noise in a scanning tunnelling microscope while scanning the sample. As test objects we study defect structures produced on an iridium single crystal at low temperatures. The defect structures appear in the constant current images as protrusions with curvature radii well below the atomic diameter. The measured power spectral density of the noise is very near to the quantum limit with Fano factor F = 1. While the constant current images show detailed structures expected for tunnelling involving d-atomic orbitals of Ir, we find the current noise to be without pronounced spatial variation as expected for shot noise arising from statistically independent events.

Cooperative effects in inelastic tunneling

Several aspects of intermolecular effects in molecular conduction have been studied in recent years. These experimental and theoretical studies, made on several setups of molecular conduction junctions, have focused on the current-voltage characteristic that is usually dominated by the elastic transmission properties of such junctions. In this paper, we address cooperative intermolecular effects in the inelastic tunneling signal calculated for simple generic models of such systems. We find that peak heights in the inelastic (d(2)I/dE(2) vs E) spectrum may be affected by such cooperative effects even when direct intermolecular interactions can be disregarded. This finding suggests that comparing experimental results to calculations made on single-molecule junctions should be done with care.

P-wave Cooper pair splitting

BACKGROUND

Splitting of Cooper pairs has recently been realized experimentally for s-wave Cooper pairs. A split Cooper pair represents an entangled two-electron pair state, which has possible application in on-chip quantum computation. Likewise the spin-activity of interfaces in nanoscale tunnel junctions has been investigated theoretically and experimentally in recent years. However, the possible implications of spin-active interfaces in Cooper pair splitters so far have not been investigated.

RESULTS

We analyze the current and the cross correlation of currents in a superconductor-ferromagnet beam splitter, including spin-active scattering. Using the Hamiltonian formalism, we calculate the cumulant-generating function of charge transfer. As a first step, we discuss characteristics of the conductance for crossed Andreev reflection in superconductor-ferromagnet beam splitters with s-wave and p-wave superconductors and no spin-active scattering. In a second step, we consider spin-active scattering and show how to realize p-wave splitting using only an s-wave superconductor, through the process of spin-flipped crossed Andreev reflection. We present results for the conductance and cross correlations.

CONCLUSION

Spin-activity of interfaces in Cooper pair splitters allows for new features in ordinary s-wave Cooper pair splitters, that can otherwise only be realized by using p-wave superconductors. In particular, it provides access to Bell states that are different from the typical spin singlet state.

Single molecule electronics and devices

The manufacture of integrated circuits with single-molecule building blocks is a goal of molecular electronics. While research in the past has been limited to bulk experiments on self-assembled monolayers, advances in technology have now enabled us to fabricate single-molecule junctions. This has led to significant progress in understanding electron transport in molecular systems at the single-molecule level and the concomitant emergence of new device concepts. Here, we review recent developments in this field. We summarize the methods currently used to form metal-molecule-metal structures and some single-molecule techniques essential for characterizing molecular junctions such as inelastic electron tunnelling spectroscopy. We then highlight several important achievements, including demonstration of single-molecule diodes, transistors, and switches that make use of electrical, photo, and mechanical stimulation to control the electron transport. We also discuss intriguing issues to be addressed further in the future such as heat and thermoelectric transport in an individual molecule.

Detection of vibration-mode scattering in electronic shot noise

We present shot noise measurements on Au nanowires showing very pronounced vibration-mode features. In accordance to recent theoretical predictions the sign of the inelastic signal, i.e., the signal due to vibration excitations, depends on the transmission probability becoming negative below a certain transmission value. We argue that the negative contribution to noise arises from coherent two-electron processes mediated by electron-phonon scattering and the Pauli exclusion principle. These signals can provide unique information on the local phonon population and lattice temperature of the nanoscale system.

Unsymmetrical hot electron heating in quasi-ballistic nanocontacts

Electrons are allowed to pass through a single atom connected to two electrodes without being scattered as the characteristic size is much smaller than the inelastic mean free path. In this quasi-ballistic regime, it is difficult to predict where and how power dissipation occurs in such current-carrying atomic system. Here, we report direct assessment of electrical heating in a metallic nanocontact. We find asymmetric electrical heating effects in the essentially symmetric single-atom contact. We simultaneously identified the voltage polarity independent onset of the local heating by conducting the inelastic noise spectroscopy. As a result, we revealed significant heat dissipation by hot electrons transmitting ballistically through the junction that creates a hot spot at the current downstream. This technique can be used as a platform for studying heat dissipation and transport in atomic/molecular systems.

Unified description of charge transfer mechanisms and vibronic dynamics in nanoscale junctions

We propose a general framework that unifies the description of counting statistics of transmitted (fermionic) charges as it is commonly used in the quantum transport community with the description of counting statistics of phonons (bosons). As a particular example, we study on the same footing the counting statistics of electrons transferred through a molecular junction and the corresponding population dynamics of the associated molecular vibrational mode. In the tunnel limit, non-perturbative results in the electron-phonon interaction are derived that unify complementary approaches based on rate equations or on the use of non-equilibrium Green functions.

Single-molecule identification via electric current noise

Label-free and real-time single-molecule detection may aid the development of high-throughput biosensing platforms. Molecular fluctuations are a source of noise that often hinders single-molecule identification by obscuring the fine details of molecular identity. In this study, we report molecular identification through direct observation of quantum-fluctuation-induced inelastic noise in single organic molecules. We investigated current fluctuations flowing through a single molecule that is chemically connected to two electrodes. We found increased current oscillations synchronous to electric field excitations of characteristic molecular vibrational modes that contribute to inelastic electron tunnelling. This finding demonstrates a large contribution of charge interaction with nuclear dynamics on noise properties of single-molecule bridges and suggests a potential use of inelastic noise as a valuable molecular signature for single-molecule identification.