Regular atomic narrowing of Ni, Fe, and V nanowires resolved by two-dimensional correlation analysis

Regulation of π-π interactions between single aromatic molecules by bias voltage

π-stacking interaction, as a fundamental type of intermolecular interaction, plays a crucial role in generating new functional molecules, altering the optoelectronic properties of materials, and maintaining protein structural stability. However, regulating intermolecular π-π interactions at the single-molecule level without altering the molecular conformation as well as the chemical properties remains a significant challenge. To this end, via conductance measurement with thousands of single molecular junctions employing a series of aromatic molecules, we demonstrate that the π-π coupling between neighboring aromatic molecules with rigid structures in a circuit can be greatly enhanced by increasing the bias voltage. We further reveal that this universal regulating effect of bias voltage without molecular conformational variation originates from the increases of the molecular dipole upon an applied electric field. These findings not only supply a non-destructive method to regulate the intermolecular interactions offering an approach to modulate the electron transport through a single molecular junction, but also deepen the understanding of the mechanism of π-π interactions.

Structural Memory Effects in Gold-4,4'-Bipyridine-Gold Single-Molecule Nanowires

We study the vulnerability of single-molecule nanowires against a temporary disconnection of the junction. To this end, we compare the room and low-temperature junction formation trajectories along the opening and closing of gold-4,4'-bipyridine-gold single-molecule nanowires. In the low-temperature measurements, the cross-correlations between the opening and subsequent closing conductance traces demonstrate a strong structural memory effect: around half of the molecular opening traces exhibit similar, statistically dependent molecular features as the junction is closed again. This means that the junction stays rigid and the molecule remains protruding from one electrode even after the rupture of the junction, and therefore, the same single-molecule junction can be reestablished if the electrodes are closed again. In the room-temperature measurements, however, weak opening-closing correlations are found, indicating a significant rearrangement of the junction after the rupture and the related loss of structural memory effects.

Unsupervised feature recognition in single-molecule break junction data

Single-molecule break junction measurements deliver a huge number of conductance vs. electrode separation traces. During such measurements, the target molecules may bind to the electrodes in different geometries, and the evolution and rupture of the single-molecule junction may also follow distinct trajectories. The unraveling of the various typical trace classes is a prerequisite to the proper physical interpretation of the data. Here we exploit the efficient feature recognition properties of neural networks to automatically find the relevant trace classes. To eliminate the need for manually labeled training data we apply a combined method, which automatically selects training traces according to the extreme values of principal component projections or some auxiliary measured quantities. Then the network captures the features of these characteristic traces and generalizes its inference to the entire dataset. The use of a simple neural network structure also enables a direct insight into the decision-making mechanism. We demonstrate that this combined machine learning method is efficient in the unsupervised recognition of unobvious, but highly relevant trace classes within low and room temperature gold-4,4' bipyridine-gold single-molecule break junction data.

Fast and straightforward analysis approach of charge transport data in single molecule junctions

In this study, we introduce an efficient data sorting algorithm, including filters for noisy signals, conductance mapping for analyzing the most dominant conductance group and sub-population groups. The capacity of our data analysis process has also been corroborated on real experimental data sets of Au-1,6-hexanedithiol-Au and Au-1,8-octanedithiol-Au molecular junctions. The fully automated and unsupervised program requires less than one minute on a standard PC to sort the data and generate histograms. The resulting one-dimensional and two-dimensional log histograms give conductance values in good agreement with previous studies. Our algorithm is a straightforward, fast and user-friendly tool for single molecule charge transport data analysis. We also analyze the data in a form of a conductance map which can offer evidence for diversity in molecular conductance. The code for automatic data analysis is openly available, well-documented and ready to use, thereby offering a useful new tool for single molecule electronics.

Fast Data Sorting with Modified Principal Component Analysis to Distinguish Unique Single Molecular Break Junction Trajectories

A simple and fast analysis method to sort large data sets into groups with shared distinguishing characteristics is described and applied to single molecular break junction conductance versus electrode displacement data. The method, based on principal component analysis, successfully sorts data sets based on the projection of the data onto the first or second principal component of the correlation matrix without the need to assert any specific hypothesis about the expected features within the data. This is an improvement on the current correlation matrix analysis approach because it sorts data automatically, making it more objective and less time consuming, and our method is applicable to a wide range of multivariate data sets. Here the method is demonstrated on two systems. First, it is demonstrated on mixtures of two molecules with identical anchor groups and similar lengths, but either a π (high conductance) or a σ (low conductance) bridge. The mixed data are automatically sorted into two groups containing one molecule or the other. Second, it is demonstrated on break junction data measured with the π bridged molecule alone. Again, the method distinguishes between two groups. These groups are tentatively assigned to different geometries of the molecule in the junction.

DFT and two-dimensional correlation analysis methods for evaluating the Pu(3+)-Pu(4+) electronic transition of plutonium-doped zircon

Understanding how plutonium (Pu) doping affects the crystalline zircon structure is very important for risk management. However, so far, there have been only a very limited number of reports of the quantitative simulation of the effects of the Pu charge and concentration on the phase transition. In this study, we used density functional theory (DFT), virtual crystal approximation (VCA), and two-dimensional correlation analysis (2D-CA) techniques to calculate the origins of the structural and electronic transitions of Zr1-cPucSiO4 over a wide range of Pu doping concentrations (c=0-10mol%). The calculations indicated that the low-angular-momentum Pu-fxy-shell electron excites an inner-shell O-2s(2) orbital to create an oxygen defect (VO-s) below c=2.8mol%. This oxygen defect then captures a low-angular-momentum Zr-5p(6)5s(2) electron to form an sp hybrid orbital, which exhibits a stable phase structure. When c>2.8mol%, each accumulated VO-p defect captures a high-angular-momentum Zr-4dz electron and two Si-pz electrons to create delocalized Si(4+)→Si(2+) charge disproportionation. Therefore, we suggest that the optimal amount of Pu cannot exceed 7.5mol% because of the formation of a mixture of ZrO8 polyhedral and SiO4 tetrahedral phases with the orientation (10-1). This study offers new perspective on the development of highly stable zircon-based solid solution materials.

Alternative types of molecule-decorated atomic chains in Au-CO-Au single-molecule junctions

We investigate the formation and evolution of Au-CO single-molecule break junctions. The conductance histogram exhibits two distinct molecular configurations, which are further investigated by a combined statistical analysis. According to conditional histogram and correlation analysis these molecular configurations show strong anticorrelations with each other and with pure Au monoatomic junctions and atomic chains. We identify molecular precursor configurations with somewhat higher conductance, which are formed prior to single-molecule junctions. According to detailed length analysis two distinct types of molecule-affected chain-formation processes are observed, and we compare these results to former theoretical calculations considering bridge- and atop-type molecular configurations where the latter has reduced conductance due to destructive Fano interference.

First principles simulation of temperature dependent electronic transition of FM-AFM phase BFO

Understanding how temperature affects the electronic transitions of BFO is important for design of BiFeO3 (BFO)-based temperature-sensitive device. Hitherto, however, there have been only very limited reports of the quantitative simulation. Here, we used density functional theory (DFT) and two-dimensional correlation analysis (2D-CA) techniques to calculate the systematic variations in electronic transitions of BFO crystal, over a range of temperature (50~1500 K). The results suggest that the heat accumulation accelerates the O-2p(4) orbital splitting, inducing the Fe(3+)-3d(5) → Fe(2+)-3d(5)d(0) charge disproportionation. The origin is observed as the temperature-dependent electron transfer process changes from threefold degeneracy to twofold degeneracy. Additionally, the crystallographic orientation (111) can be used to control the 2p-hole-induced electronic transition as O → unoccupied Fe(3+)-3d(5), in comparison to the O → Bi-6p(3) + Fe(3+)-3d(5)d(0) on the orientations (001) and (101). This study offers new perspective on the improvement of BFO-based temperature-sensitive device.

DFT and two-dimensional correlation analysis for evaluating the oxygen defect mechanism of low-density 4f (or 5f) elements interacting with Ca-Mt

Existence states of f-shell electrons in Ca-Mt is calculatedviaDFT with 2D-CA techniques. Reasons of f-shell electrons influencing on electronic and optical properties are discussed. Electronic transitions are systematically analyzed.

Precursor configurations and post-rupture evolution of Ag-CO-Ag single-molecule junctions

Experimental correlation analysis and first-principles theory are used to probe the structure and evolution of Ag-CO-Ag single-molecule junctions both before the formation and after the rupture of the junctions. Two dimensional correlation histograms and conditional histograms demonstrate that prior to the single-molecule bridge configuration the CO molecule is already bound parallel to the Ag single-atom contact. This molecular precursor configuration is accompanied by the opening of additional conductance channels compared to the single-channel transport in pure Ag monoatomic junctions. To investigate the post-rupture evolution of the junction we introduce a cross-correlation analysis between the opening and the subsequent closing conductance traces. This analysis implies that the molecule is bound rigidly to the apex of one electrode, and so the same single-molecule configuration is re-established as the junction is closed. The experimental results are confirmed by ab initio simulations of the evolution of contact geometries, transmission eigenvalues and scattering wavefunctions.

Shot noise variation within ensembles of gold atomic break junctions at room temperature

Atomic-scale junctions are a powerful tool to study quantum transport, and are frequently examined through the mechanically controllable break junction technique. The junction-to-junction variation of atomic configurations often leads to a statistical approach, with ensemble-averaged properties providing access to the relevant physics. However, the full ensemble contains considerable additional information. We report a new analysis of shot noise over entire ensembles of junction configurations using scanning tunneling microscope-style gold break junctions at room temperature in ambient conditions, and compare these data with simulations based on molecular dynamics, a sophisticated tight-binding model, and nonequilibrium Green's functions. The experimental data show a suppression in the variation of the noise near conductances dominated by fully transmitting channels, and a surprising participation of multiple channels in the nominal tunneling regime. Comparison with the simulations, which agree well with published work at low temperatures and ultrahigh vacuum conditions, suggests that these effects likely result from surface contamination and disorder in the electrodes. We propose additional experiments that can distinguish the relative contributions of these factors.

Force and conductance molecular break junctions with time series crosscorrelation

Force and conductance, measured across 4,4'-bipyridine simultaneously, are crosscorrelated using a two dimensional (2D) histogram method. The result is a 2D multivariate statistical analysis superior to current one dimensional histogram techniques for exploring significant conductance and force modulations within SMBJs. This method is sensitive enough to crosscorrelate signal modulations between force and conductance traces associated with contact geometry perturbations predicted in literature such as Au-molecule contact twisting and slipping during junction elongation.

Correlating structure, conductance, and mechanics of silver atomic-scale contacts

We measure simultaneously force and conductance of Ag metal point-contacts under ambient conditions at room temperature. We observe the formation of contacts with a conductance close to 1 G0, the quantum of conductance, which can be attributed to a single-atom contact, similar to those formed by Au. We also find two additional conductance features at ∼0.4 G0 and ∼1.3 G0, which have been previously ascribed to contacts with oxygen contaminations. Here, using a conductance cross-correlation technique, we distinguish three different atomic-scale structural motifs and analyze their rupture forces and stiffness. Our results allow us to assign the ∼0.4 G0 conductance feature to an Ag-O-Ag contact and the ∼1.3 G0 feature to an Ag-Ag single-atom contact with an oxygen atom in parallel. Utilizing complementary information from force and conductance, we thus demonstrate the correlation of conductance with the structural evolution at the atomic scale.

The self-breaking mechanism of atomic scale Au nanocontacts

We have investigated the self-breaking mechanism of atomic scale Au nanocontacts at room temperature in air. In the conductance traces, we frequently observed traces showing both a 1G(0) (2e(2)/h) and 3G(0) plateaux, or only a 2G(0) plateau in the conductance regime below 3G(0). The statistical analysis showed a negative correlation between the appearance of 1G(0) and 2G(0) peaks, and a positive correlation between 1G(0) and 3G(0) peaks. This conductance behavior suggested that the symmetric triple atomic rows changed into a symmetric single row, while the asymmetric double rows broke without changing into a symmetric single row. The regular self-breaking process can be explained by the breaking of the thermodynamically stable Au nanocontacts which were formed during the self-breaking of the contacts.

Pulling platinum atomic chains by carbon monoxide molecules

The interaction of carbon monoxide molecules with atomic-scale platinum nanojunctions is investigated by low temperature mechanically controllable break junction experiments. Combining plateau length analysis, two-dimensional conductance-displacement histograms and conditional correlation analysis a comprehensive microscopic picture is proposed about the formation and evolution of Pt-CO-Pt single-molecule configurations. Our analysis implies that before pure Pt monoatomic chains are formed a CO molecule infiltrates the junction, first in a configuration that is perpendicular to the contact axis. This molecular junction is strong enough to pull a monoatomic platinum chain with the molecule being incorporated in the chain. Along the chain formation the molecule can either stay in the perpendicular configuration, or rotate to a parallel configuration. The evolution of the single-molecule configurations along the junction displacement shows quantitative agreement with theoretical predictions, justifying the interpretation in terms of perpendicular and parallel molecular alignment. Our analysis demonstrates that the combination of two-dimensional conductance-displacement histograms with conditional correlation analysis is a useful tool to analyze separately fundamentally different types of junction trajectories in single molecule break junction experiments.

Signatures of cooperative effects and transport mechanisms in conductance histograms

We present a computational investigation into the line shapes of peaks in conductance histograms, finding that they possess high information content. In particular, the histogram peak associated with conduction through a single molecule elucidates the electron transport mechanism and is generally well-described by beta distributions. A statistical analysis of the peak corresponding to conduction through two molecules reveals the presence of cooperative effects between the molecules and also provides insight into the underlying conduction channels. This work describes tools for extracting additional interpretations from experimental statistical data, helping us better understand electron transport processes.

Correlation analysis of atomic and single-molecule junction conductance

The break-junction technique is widely used to measure electronic properties of nanoscale junctions including metal point-contacts and single-molecule junctions. In these measurements, conductance is measured as a function of electrode displacement yielding data that is analyzed by constructing conductance histograms to determine the most frequently observed conductance values in the nanoscale junctions. However much of the rich physics in these measurements is lost in this simple analysis technique. Conductance histograms cannot be used to study the statistical relation of distinct junction configurations, to distinguish structurally different configurations that have similar conductance values, or to obtain information on the relation between conductance and junction elongation. Here, we give a detailed introduction to a novel statistical analysis method based on the two-dimensional cross-correlation histogram (2DCH) analysis of conductance traces and show that this method provides new information about the relation of different junction configurations that occur during the formation and evolution of metal and single-molecule junctions. We first illustrate the different types of correlation effects by using simulated conductance traces. We then apply this analysis method to several different experimental examples. We show from break-junction measurements of different metal point-contacts that in aluminum, the first conductance histogram peak corresponds to two different junction structures. In tantalum, we identify the frequent absence of adhesive instability. We show that conductance plateaus shift in a correlated manner in iron and vanadium junctions. Finally, we highlight the applicability of the correlation analysis to single-molecule platinum-CO-platinum and gold-4,4'-bipyridine-gold junctions.

Mechanical break junctions: enormous information in a nanoscale package

Mechanical break junctions, particularly those in which a metal tip is repeatedly moved in and out of contact with a metal film, have provided many insights into electronic conduction at the atomic and molecular scale, most often by averaging over many possible junction configurations. This averaging throws away a great deal of information, and Makk et al. in this issue of ACS Nano demonstrate that, with both simulated and real experimental data, more sophisticated two-dimensional analysis methods can reveal information otherwise obscured in simple histograms. As additional measured quantities come into play in break junction experiments, including thermopower, noise, and optical response, these more sophisticated analytic approaches are likely to become even more powerful. While break junctions are not directly practical for useful electronic devices, they are incredibly valuable tools for unraveling the electronic transport physics relevant for ultrascaled nanoelectronics.

Advanced simulation of conductance histograms validated through channel-sensitive experiments on indium nanojunctions

We demonstrate a self-contained methodology for predicting conductance histograms of atomic and molecular junctions. Fast classical molecular-dynamics simulations are combined with accurate density functional theory calculations predicting both quantum transport properties and molecular-dynamics force field parameters. The methodology is confronted with experiments on atomic-sized indium nanojunctions. Beside conductance histograms the distribution of individual channel transmission eigenvalues is also determined by fitting the superconducting subgap features in the I-V curves. The remarkable agreement in the evolution of the channel transmissions demonstrates that the simulated ruptures are able to reproduce a realistic statistical ensemble of contact configurations, whereas simulations on selected ideal geometries show strong deviations from the experimental observations.