Quantitative Interpretations of Break Junction Conductance Histograms in Molecular Electron Transport

Microscopic theory, analysis, and interpretation of conductance histograms in molecular junctions

Molecular electronics break-junction experiments are widely used to investigate fundamental physics and chemistry at the nanoscale. Reproducibility in these experiments relies on measuring conductance on thousands of freshly formed molecular junctions, yielding a broad histogram of conductance events. Experiments typically focus on the most probable conductance, while the information content of the conductance histogram has remained unclear. Here we develop a microscopic theory for the conductance histogram by merging the theory of force-spectroscopy with molecular conductance. The procedure yields analytical equations that accurately fit the conductance histogram of a wide range of molecular junctions and augments the information content that can be extracted from them. Our formulation captures contributions to the conductance dispersion due to conductance changes during the mechanical elongation inherent to the experiments. In turn, the histogram shape is determined by the non-equilibrium stochastic features of junction rupture and formation. The microscopic parameters in the theory capture the junction's electromechanical properties and can be isolated from separate conductance and rupture force (or junction-lifetime) measurements. The predicted behavior can be used to test the range of validity of the theory, understand the conductance histograms, design molecular junction experiments with enhanced resolution and molecular devices with more reproducible conductance properties.

Single-molecule photoelectron tunnelling spectroscopy

Experimental mapping of transmission is essential for understanding and controlling charge transport through molecular devices and materials. Here we developed a single-molecule photoelectron tunnelling spectroscopy approach for mapping transmission beyond the HOMO-LUMO gap of the single diketopyrrolopyrrole molecule junction using an ultrafast-laser combined scanning tunnelling microscope-based break junction set-up at room temperature. Two resonant transport channels of ultrafast photocurrent are found by our photoelectron tunnelling spectroscopy, ranging from 1.31 eV to 1.77 eV, consistent with the LUMO + 1 and LUMO + 2 in the transmission spectrum obtained by density functional theory calculations. Moreover, we observed the modulation of resonant peaks by varying bias voltages, which demonstrates the ability to quantitatively characterize the effect of the electric field on frontier molecular orbitals. Our single-molecule photoelectron tunnelling spectroscopy offers an avenue that allows us to explore the nature of energy-dependent charge transport through single-molecule junctions.

Learning Conductance: Gaussian Process Regression for Molecular Electronics

Experimental studies of charge transport through single molecules often rely on break junction setups, where molecular junctions are repeatedly formed and broken while measuring the conductance, leading to a statistical distribution of conductance values. Modeling this experimental situation and the resulting conductance histograms is challenging for theoretical methods, as computations need to capture structural changes in experiments, including the statistics of junction formation and rupture. This type of extensive structural sampling implies that even when evaluating conductance from computationally efficient electronic structure methods, which typically are of reduced accuracy, the evaluation of conductance histograms is too expensive to be a routine task. Highly accurate quantum transport computations are only computationally feasible for a few selected conformations and thus necessarily ignore the rich conformational space probed in experiments. To overcome these limitations, we investigate the potential of machine learning for modeling conductance histograms, in particular by Gaussian process regression. We show that by selecting specific structural parameters as features, Gaussian process regression can be used to efficiently predict the zero-bias conductance from molecular structures, reducing the computational cost of simulating conductance histograms by an order of magnitude. This enables the efficient calculation of conductance histograms even on the basis of computationally expensive first-principles approaches by effectively reducing the number of necessary charge transport calculations, paving the way toward their routine evaluation.

Conductance modulation of metal-molecule-metal junction via extra acid addition and its mechanism investigation

The advance of single molecular device fabrication strongly relies on the understanding of the metal-molecule-metal junction that can response to the external stimulus. A model Lewis basic molecule DBP which can react with Lewis acid and protic acid was synthesized, then the molecular conducting behavior of the original molecule and the resulted Lewis acid-base pair were researched. Allowing for their identical physical paths for charge conducting, these results indicated that adjusting the molecular electronic structure, even not directly changing the conductive molecular backbone, could also tune the charge transporting ability by nearly one order of magnitude. Furthermore, the addition of another Lewis base - Triethylamine to Lewis acid-base pair brought the electrical properties back to that of single DBP junction, which establishs a basic understanding in the design and construction of reversible and controllable molecular device based on pyridine derived molecule.

Optimal in situ electromechanical sensing of molecular species

We investigate protocols for optimal molecular detection with electromechanical nanoscale sensors under ambient conditions. Our models are representative of suspended graphene nanoribbons, which due to their piezoelectric and electronic properties provide responsive and versatile sensors. In particular, we analytically account for the corrections in the electronic transmission function and signal-to-noise ratio originating in environmental perturbations, such as thermal fluctuations and solvation effects. We also investigate the role of the sampling time in the current statistics. As a result, we formulate a protocol for optimal sensing based on the modulation of the Fermi level at a fixed bias and provide approximate forms for the current, linear susceptibility, and current fluctuations. We show how the algebraic tails in the thermally broadened transmission function affect the behavior of the signal-to-noise ratio and optimal sensing. These results provide further insights into the operation of graphene deflectometers and other techniques for electromechanical sensing.

Generalized Voigt broadening due to thermal fluctuations of electromechanical nanosensors and molecular electronic junctions

Graphene and other 2D materials give a platform for electromechanical sensing of biomolecules in aqueous, room temperature environments. The electronic current changes in response to mechanical deflection, indicating the presence of forces due to interactions with, e.g., molecular species. We develop illustrative models of these sensors in order to give explicit, compact expressions for the current and signal-to-noise ratio. Electromechanical structures have an electron transmission function that follows a generalized Voigt profile, with thermal fluctuations giving a Gaussian smearing analogous to thermal Doppler broadening in solution/gas-phase spectroscopic applications. The Lorentzian component of the profile comes from the contact to the electrodes. After providing an accurate approximate form of this profile, we calculate the mechanical susceptibility for a representative two-level bridge and the current fluctuations for electromechanical detection. These results give the underlying mechanics of electromechanical sensing in more complex scenarios, such as graphene deflectometry.

The effect of nitrogen lone-pair interaction on the conduction in a single-molecule junction with amine-Au bonding

We have applied our previously developed three-dimensional dynamic probe method to analyze the conductance in a Au-/1,4-benzenediamine (BDA)/Au single molecule junction. This structure is a typically used example to demonstrate the high performance of the break junction (BJ) method for measuring conductance with small variations, however, details of the interaction of the nitrogen (N) lone-pair in the amine group with a Au electrode, which is considered to have a fundamental role in determining the conductance of the single molecule junction with the amine, have not yet been clarified and still remain an important issue to be resolved. In this study, we have succeeded, for the first time, in observing the site-dependent change in conductance of this system while the molecular conformation was accurately controlled, and the results were well reproduced by a simulation taking account of the effect of the N lone-pair in an amine bonding with a Au electrode.

Deep learning for single-molecule science

Exploring and making predictions based on single-molecule data can be challenging, not only due to the sheer size of the datasets, but also because a priori knowledge about the signal characteristics is typically limited and poor signal-to-noise ratio. For example, hypothesis-driven data exploration, informed by an expectation of the signal characteristics, can lead to interpretation bias or loss of information. Equally, even when the different data categories are known, e.g., the four bases in DNA sequencing, it is often difficult to know how to make best use of the available information content. The latest developments in machine learning (ML), so-called deep learning (DL) offer interesting, new avenues to address such challenges. In some applications, such as speech and image recognition, DL has been able to outperform conventional ML strategies and even human performance. However, to date DL has not been applied much in single-molecule science, presumably in part because relatively little is known about the 'internal workings' of such DL tools within single-molecule science as a field. In this Tutorial, we make an attempt to illustrate in a step-by-step guide how one of those, a convolutional neural network (CNN), may be used for base calling in DNA sequencing applications. We compare it with a SVM as a more conventional ML method, and discuss some of the strengths and weaknesses of the approach. In particular, a 'deep' neural network has many features of a 'black box', which has important implications on how we look at and interpret data.

Roles of vacuum tunnelling and contact mechanics in single-molecule thermopower

Molecular junction is a chemically-defined nanostructure whose discrete electronic states are expected to render enhanced thermoelectric figure of merit suitable for energy-harvesting applications. Here, we report on geometrical dependence of thermoelectricity in metal-molecule-metal structures. We performed simultaneous measurements of the electrical conductance and thermovoltage of aromatic molecules having different anchoring groups at room temperature in vacuum. We elucidated the mutual contributions of vacuum tunnelling on thermoelectricity in the short molecular bridges. We also found stretching-induced thermoelectric voltage enhancement in thiol-linked single-molecule bridges along with absence of the pulling effects in diamine counterparts, thereby suggested that the electromechanical effect would be a rather universal phenomenon in Au-S anchored molecular junctions that undergo substantial metal-molecule contact elongation upon stretching. The present results provide a novel concept for molecular design to achieve high thermopower with single-molecule junctions.

Gate-controlled conductance switching in DNA

Extensive evidence has shown that long-range charge transport can occur along double helical DNA, but active control (switching) of single-DNA conductance with an external field has not yet been demonstrated. Here we demonstrate conductance switching in DNA by replacing a DNA base with a redox group. By applying an electrochemical (EC) gate voltage to the molecule, we switch the redox group between the oxidized and reduced states, leading to reversible switching of the DNA conductance between two discrete levels. We further show that monitoring the individual conductance switching allows the study of redox reaction kinetics and thermodynamics at single molecular level using DNA as a probe. Our theoretical calculations suggest that the switch is due to the change in the energy level alignment of the redox states relative to the Fermi level of the electrodes.

Thanks to its base stacking structure, DNA can behave as an electric wire, but external control of its electronic properties has not been achieved yet. Here, the authors show that DNA conductance can be switched electrochemically when a DNA base is replaced by the redox molecule anthraquinone.

Estimating the Landauer-Büttiker transmission function from single molecule break junction experiments

When investigating the electronic response properties of molecules, experiments often measure conductance whereas computation predicts the transmission probability. Although Landauer-Büttiker theory usually relates the two, comparison between experiment and computation remains difficult because experimental data (specifically those from break junctions) are statistical and computational results are deterministic. In this work we develop tools to quantitatively estimate-with error bars-the shape of the Landauer-Büttiker transmission function directly from experimental statistics on conductance and thermopower (if the latter is also available). We subsequently apply these tools to existing data, demonstrating a rigorous statistical comparison between experimental and computational results on molecular electron transport.

Unsupervised vector-based classification of single-molecule charge transport data

The stochastic nature of single-molecule charge transport measurements requires collection of large data sets to capture the full complexity of a molecular system. Data analysis is then guided by certain expectations, for example, a plateau feature in the tunnelling current distance trace, and the molecular conductance extracted from suitable histogram analysis. However, differences in molecular conformation or electrode contact geometry, the number of molecules in the junction or dynamic effects may lead to very different molecular signatures. Since their manifestation is a priori unknown, an unsupervised classification algorithm, making no prior assumptions regarding the data is clearly desirable. Here we present such an approach based on multivariate pattern analysis and apply it to simulated and experimental single-molecule charge transport data. We demonstrate how different event shapes are clearly separated using this algorithm and how statistics about different event classes can be extracted, when conventional methods of analysis fail.