Charge transport in molecular junctions: From tunneling to hopping with the probe technique

Thermodynamics of a continuously monitored double-quantum-dot heat engine in the repeated interactions framework

Understanding the thermodynamic role of measurement in quantum mechanical systems is a burgeoning field of study. In this article, we study a double quantum dot (DQD) connected to two macroscopic fermionic thermal reservoirs. We assume that the DQD is continuously monitored by a quantum point contact (QPC), which serves as a charge detector. Starting from a minimalist microscopic model for the QPC and reservoirs, we show that the local master equation of the DQD can alternatively be derived in the framework of repeated interactions and that this framework guarantees a thermodynamically consistent description of the DQD and its environment (including the QPC). We analyze the effect of the measurement strength and identify a regime in which particle transport through the DQD is both assisted and stabilized by dephasing. We also find that in this regime the entropic cost of driving the particle current with fixed relative fluctuations through the DQD is reduced. We thus conclude that under continuous measurement a more constant particle current may be achieved at a fixed entropic cost.

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.

Nanoscale molecular rectifiers

The use of molecules bridged between two electrodes as a stable rectifier is an important goal in molecular electronics. Until recently, however, and despite extensive experimental and theoretical work, many aspects of our fundamental understanding and practical challenges have remained unresolved and prevented the realization of such devices. Recent advances in custom-designed molecular systems with rectification ratios exceeding 10⁵ have now made these systems potentially competitive with existing silicon-based devices. Here, we provide an overview and critical analysis of recent progress in molecular rectification within single molecules, self-assembled monolayers, molecular multilayers, heterostructures, and metal-organic frameworks and coordination polymers. Examples of conceptually important and best-performing systems are discussed, alongside their rectification mechanisms. We present an outlook for the field, as well as prospects for the commercialization of molecular rectifiers.

Long-range charge transport in homogeneous and alternating-rigidity chains

We study the interplay of intrinsic-electronic and environmental factors in long-range charge transport across molecular chains with up to N ∼ 80 monomers. We describe the molecular electronic structure of the chain with a tight-binding Hamiltonian. Thermal effects in the form of electron decoherence and inelastic scattering are incorporated with the Landauer–Büttiker probe method. In short chains of up to ten units, we observe the crossover between coherent (tunneling, ballistic) motion and thermally-assisted conduction, with thermal effects enhancing the current beyond the quantum coherent limit. We further show that unconventional (nonmonotonic with size) transport behavior emerges when monomer-to-monomer electronic coupling is made large. In long chains, we identify a different behavior, with thermal effects suppressing the conductance below the coherent-ballistic limit. With the goal to identify a minimal model for molecular chains displaying unconventional and effective long-range transport, we simulate a modular polymer with alternating regions of high and low rigidity. Simulations show that, surprisingly, while charge correlations are significantly affected by structuring environmental conditions, reflecting charge delocalization, the electrical resistance displays an averaging effect, and it is not sensitive to this patterning. We conclude by arguing that efficient long-range charge transport requires engineering both internal electronic parameters and environmental conditions.

Coherent and incoherent contributions to molecular electron transport

We numerically isolate the limits of validity of the Landauer approximation to describe charge transport along molecular junctions in condensed phase environments. To do so, we contrast Landauer with exact time-dependent non-equilibrium Green’s function quantum transport computations in a two-site molecular junction subject to exponentially correlated noise. Under resonant transport conditions, we find Landauer accuracy to critically depend on intramolecular interactions. By contrast, under nonresonant conditions, the emergence of incoherent transport routes that go beyond Landauer depends on charging and discharging processes at the electrode–molecule interface. In both cases, decreasing the rate of charge exchange between the electrodes and molecule and increasing the interaction strength with the thermal environment cause Landauer to become less accurate. The results are interpreted from a time-dependent perspective where the noise prevents the junction from achieving steady-state and from a fully quantum perspective where the environment introduces dephasing in the dynamics. Using these results, we analyze why the Landauer approach is so useful to understand experiments, isolate regimes where it fails, and propose schemes to chemically manipulate the degree of transport coherence.

Quantum Plasmonics: Energy Transport Through Plasmonic Gap

At the interfaces of metal and dielectric materials, strong light-matter interactions excite surface plasmons; this allows electromagnetic field confinement and enhancement on the sub-wavelength scale. Such phenomena have attracted considerable interest in the field of exotic material-based nanophotonic research, with potential applications including nonlinear spectroscopies, information processing, single-molecule sensing, organic-molecule devices, and plasmon chemistry. These innovative plasmonics-based technologies can meet the ever-increasing demands for speed and capacity in nanoscale devices, offering ultrasensitive detection capabilities and low-power operations. Size scaling from the nanometer to sub-nanometer ranges is consistently researched; as a result, the quantum behavior of localized surface plasmons, as well as those of matter, nonlocality, and quantum electron tunneling is investigated using an innovative nanofabrication and chemical functionalization approach, thereby opening a new era of quantum plasmonics. This new field enables the ultimate miniaturization of photonic components and provides extreme limits on light-matter interactions, permitting energy transport across the extremely small plasmonic gap. In this review, a comprehensive overview of the recent developments of quantum plasmonic resonators with particular focus on novel materials is presented. By exploring the novel gap materials in quantum regime, the potential quantum technology applications are also searched for and mapped out.

Delocalization-Assisted Transport through Nucleic Acids in Molecular Junctions

The flow of charge through molecules is central to the function of supramolecular machines, and charge transport in nucleic acids is implicated in molecular signaling and DNA repair. We examine the transport of electrons through nucleic acids to understand the interplay of resonant and nonresonant charge carrier transport mechanisms. This study reports STM break junction measurements of peptide nucleic acids (PNAs) with a G-block structure and contrasts the findings with previous results for DNA duplexes. The conductance of G-block PNA duplexes is much higher than that of the corresponding DNA duplexes of the same sequence; however, they do not display the strong even-odd dependence conductance oscillations found in G-block DNA. Theoretical analysis finds that the conductance oscillation magnitude in PNA is suppressed because of the increased level of electronic coupling interaction between G-blocks in PNA and the stronger PNA-electrode interaction compared to that in DNA duplexes. The strong interactions in the G-block PNA duplexes produce molecular conductances as high as 3% G₀, where G₀ is the quantum of conductance, for 5 nm duplexes.

Molecular bridge-mediated ultralow-power gas sensing

We report the electrical detection of captured gases through measurement of the quantum tunneling characteristics of gas-mediated molecular junctions formed across nanogaps. The gas-sensing nanogap device consists of a pair of vertically stacked gold electrodes separated by an insulating 6 nm spacer (~1.5 nm of sputtered α-Si and ~4.5 nm ALD SiO₂), which is notched ~10 nm into the stack between the gold electrodes. The exposed gold surface is functionalized with a self-assembled monolayer (SAM) of conjugated thiol linker molecules. When the device is exposed to a target gas (1,5-diaminopentane), the SAM layer electrostatically captures the target gas molecules, forming a molecular bridge across the nanogap. The gas capture lowers the barrier potential for electron tunneling across the notched edge region, from ~5 eV to ~0.9 eV and establishes additional conducting paths for charge transport between the gold electrodes, leading to a substantial decrease in junction resistance. We demonstrated an output resistance change of >10⁸ times upon exposure to 80 ppm diamine target gas as well as ultralow standby power consumption of <15 pW, confirming electron tunneling through molecular bridges for ultralow-power gas sensing.

Toward a First-Principles Evaluation of Transport Mechanisms in Molecular Wires

Understanding charge transport through molecular wires is important for nanoscale electronics and biochemistry. Our goal is to establish a simple first-principles protocol for predicting the charge transport mechanism in such wires, in particular the crossover from coherent tunneling for short wires to incoherent hopping for longer wires. This protocol is based on a combination of density functional theory with a polarizable continuum model introduced by Kaupp et al. for mixed-valence molecules, which we had previously found to work well for length-dependent charge delocalization in such systems. We combine this protocol with a new charge delocalization measure tailored for molecular wires, and we show that it can predict the tunneling-to-hopping transition length with a maximum error of one subunit in five sets of molecular wires studied experimentally in molecular junctions at room temperature. This suggests that the protocol is also well suited for estimating the extent of hopping sites as relevant, for example, for the intermediate tunneling-hopping regime in DNA.

Thermally activated charge transport in carbon atom chains

Charge transport through single molecules is at the heart of molecular electronics for realizing the practical use of the rich quantum characteristics of electrode-molecule-electrode systems. Despite the extensive studies reported in the past, little experimental efforts have been focused on the electron transport mechanism at a temperature higher than the ambient temperature. In this work, we have reported the observation of the subtle interplay between electron tunneling and charge hopping in carbon chains connected to two Au electrodes at elevated temperatures. We measured the single-molecule conductance of Au-alkanedithiol-Au molecular junctions at various temperatures from 300 K to 420 K in vacuum. The temperature dependence of conductance suggested substantial roles of superexchange with inter-chain charge hopping under elevated temperatures for alkane chains longer than heptane. This finding provides a guide to design functional molecular junctions under practical conditions.

Ballistic transport and quantum unfurling in molecular junctions via minimal representations of quantum master equations

Quantum furling and unfurling are inelastic transitions between localized and delocalized electronic states. We predict scenarios where these processes govern charge transport through donor-bridge-acceptor molecular junctions. Like in the case of ballistic transport, the resulting currents are nearly independent of the molecular bridge length. However, currents involving quantum furling and unfurling processes can be controlled by the coupling to vibrations in the intra-molecular and the extra-molecular environment, which can be experimentally tuned. Our study is based on rate equations for exchange of energy (bosons) and particles (fermions) between the molecular bridge and its environment. An efficient algorithm is introduced for a compact representation of the relevant rate equations, which utilizes the redundancies in the rate matrix and the sparsity of the creation and annihilation operators in the molecular Fock space.

Beyond Marcus theory and the Landauer-Büttiker approach in molecular junctions. II. A self-consistent Born approach

Marcus and Landauer-Büttiker approaches to charge transport through molecular junctions describe two contrasting mechanisms of electronic conduction. In previous work, we have shown how these charge transport theories can be unified in the single-level case by incorporating lifetime broadening into the second-order quantum master equation. Here, we extend our previous treatment by incorporating lifetime broadening in the spirit of the self-consistent Born approximation. By comparing both theories to numerically converged hierarchical-equations-of-motion results, we demonstrate that our novel self-consistent approach rectifies shortcomings of our earlier framework, which are present especially in the case of relatively strong electron-vibrational coupling. We also discuss circumstances under which the theory developed here simplifies to the generalized theory developed in our earlier work. Finally, by considering the high-temperature limit of our new self-consistent treatment, we show how lifetime broadening can also be self-consistently incorporated into Marcus theory. Overall, we demonstrate that the self-consistent approach constitutes a more accurate description of molecular conduction while retaining most of the conceptual simplicity of our earlier framework.

Single-molecule functionality in electronic components based on orbital resonances

A gateable single-molecule diode and resonant tunneling diode are realized using molecular orbital engineering in multi-site molecules.

Introducing mesoscopic charge transfer rates into molecular electronics

It has been demonstrated that the concept of mesoscopic rate is able to establish a bridge between electrochemical and molecular electronic concepts.

Machine Learning Prediction of DNA Charge Transport

First-principles calculations of charge transfer in DNA molecules are computationally expensive given that conducting charge carriers interact with intra- and intermolecular atomic motion. Screening sequences, for example, to identify excellent electrical conductors, is challenging even when adopting coarse-grained models and effective computational schemes that do not explicitly describe atomic dynamics. We present a machine learning (ML) model that allows the inexpensive prediction of the electrical conductance of millions of long double-stranded DNA (dsDNA) sequences, reducing computational costs by orders of magnitude. The algorithm is trained on short DNA nanojunctions with n = 3-7 base pairs. The electrical conductance of the training set is computed with a quantum scattering method, which captures charge-nuclei scattering processes. We demonstrate that the ML method accurately predicts the electrical conductance of varied dsDNA junctions tracing different transport mechanisms: coherent (short-range) quantum tunneling, on-resonance (ballistic) transport, and incoherent site-to-site hopping. Furthermore, the ML approach supports physical observations that clusters of nucleotides regulate DNA transport behavior. The input features tested in this work could be used in other ML studies of charge transport in complex polymers in the search for promising electronic and thermoelectric materials.

Microbial nanowires - Electron transport and the role of synthetic analogues

Electron transfer is central to cellular life, from photosynthesis to respiration. In the case of anaerobic respiration, some microbes have extracellular appendages that can be utilised to transport electrons over great distances. Two model organisms heavily studied in this arena are Shewanella oneidensis and Geobacter sulfurreducens. There is some debate over how, in particular, the Geobacter sulfurreducens nanowires (formed from pilin nanofilaments) are capable of achieving the impressive feats of natural conductivity that they display. In this article, we outline the mechanisms of electron transfer through delocalised electron transport, quantum tunnelling, and hopping as they pertain to biomaterials. These are described along with existing examples of the different types of conductivity observed in natural systems such as DNA and proteins in order to provide context for understanding the complexities involved in studying the electron transport properties of these unique nanowires. We then introduce some synthetic analogues, made using peptides, which may assist in resolving this debate. Microbial nanowires and the synthetic analogues thereof are of particular interest, not just for biogeochemistry, but also for the exciting potential bioelectronic and clinical applications as covered in the final section of the review.

STATEMENT OF SIGNIFICANCE

Some microbes have extracellular appendages that transport electrons over vast distances in order to respire, such as the dissimilatory metal-reducing bacteria Geobacter sulfurreducens. There is significant debate over how G. sulfurreducens nanowires are capable of achieving the impressive feats of natural conductivity that they display: This mechanism is a fundamental scientific challenge, with important environmental and technological implications. Through outlining the techniques and outcomes of investigations into the mechanisms of such protein-based nanofibrils, we provide a platform for the general study of the electronic properties of biomaterials. The implications are broad-reaching, with fundamental investigations into electron transfer processes in natural and biomimetic materials underway. From these studies, applications in the medical, energy, and IT industries can be developed utilising bioelectronics.

Environment-assisted quantum transport through single-molecule junctions

Single-molecule electronics has been envisioned as the ultimate goal in the miniaturisation of electronic circuits. While the aim of incorporating single-molecule junctions into modern technology still proves elusive, recent developments in this field have begun to enable experimental investigation of fundamental concepts within the area of chemical physics. One such phenomenon is the concept of environment-assisted quantum transport which has emerged from the investigation of exciton transport in photosynthetic complexes. Here, we study charge transport through a two-site molecular junction coupled to a vibrational environment. We demonstrate that vibrational interactions can significantly enhance the current through specific molecular orbitals. Our study offers a clear pathway towards finding and identifying environment-assisted transport phenomena in charge transport settings.

Plasmonic tunnel junctions for single-molecule redox chemistry

Nanoparticles attached just above a flat metallic surface can trap optical fields in the nanoscale gap. This enables local spectroscopy of a few molecules within each coupled plasmonic hotspot, with near thousand-fold enhancement of the incident fields. As a result of non-radiative relaxation pathways, the plasmons in such sub-nanometre cavities generate hot charge carriers, which can catalyse chemical reactions or induce redox processes in molecules located within the plasmonic hotspots. Here, surface-enhanced Raman spectroscopy allows us to track these hot-electron-induced chemical reduction processes in a series of different aromatic molecules. We demonstrate that by increasing the tunnelling barrier height and the dephasing strength, a transition from coherent to hopping electron transport occurs, enabling observation of redox processes in real time at the single-molecule level.

Effects of the Backbone and Chemical Linker on the Molecular Conductance of Nucleic Acid Duplexes

Scanning tunneling microscope break junction measurements are used to examine how the molecular conductance of nucleic acids depends on the composition of their backbone and the linker group to the electrodes. Molecular conductances of 10 base pair long homoduplexes of DNA, aeg-PNA, γ-PNA, and a heteroduplex of DNA/aeg-PNA with identical nucleobase sequence were measured. The molecular conductance was found to vary by 12 to 13 times with the change in backbone. Computational studies show that the molecular conductance differences between nucleic acids of different backbones correlate with differences in backbone structural flexibility. The molecular conductance was also measured for duplexes connected to the electrode through two different linkers, one directly to the backbone and one directly to the nucleobase stack. While the linker causes an order-of-magnitude increase in the overall conductance for a particular duplex, the differences in the electrical conductance with backbone composition are preserved. The highest molecular conductance value, 0.06G₀, was measured for aeg-PNA duplexes with a base stack linker. These findings reveal an important new strategy for creating longer and more complex electroactive, nucleic acid assemblies.

Protocol for disentangling the thermally activated contribution to the tunneling-assisted charge transport. Analytical results and experimental relevance

In this paper we present results demonstrating that the charge transport by tunneling in molecular junctions can exhibit a substantial temperature dependence.

Conductance and activation energy for electron transport in series and parallel intramolecular circuits

We investigate electron transport through series and parallel intramolecular circuits in the framework of the multi-level Redfield theory.