Understanding resonant charge transport through weakly coupled single-molecule junctions

Evaluating the interactions between vibrational modes and electronic transitions using frontier orbital energy derivatives

Vibrations affect molecular optoelectronic properties, even at zero kelvin. Accounting for these effects using computational modelling is costly, as it requires many calculations at geometries distorted from equilibrium. Here, we propose a low-cost method for identifying vibrations most strongly coupled to the electronic structure, based on using orbital energy derivatives as a diagnostic.

Quantum interference enhances the performance of single-molecule transistors

Quantum effects in nanoscale electronic devices promise to lead to new types of functionality not achievable using classical electronic components. However, quantum behaviour also presents an unresolved challenge facing electronics at the few-nanometre scale: resistive channels start leaking owing to quantum tunnelling. This affects the performance of nanoscale transistors, with direct source-drain tunnelling degrading switching ratios and subthreshold swings, and ultimately limiting operating frequency due to increased static power dissipation. The usual strategy to mitigate quantum effects has been to increase device complexity, but theory shows that if quantum effects can be exploited in molecular-scale electronics, this could provide a route to lower energy consumption and boost device performance. Here we demonstrate these effects experimentally, showing how the performance of molecular transistors is improved when the resistive channel contains two destructively interfering waves. We use a zinc-porphyrin coupled to graphene electrodes in a three-terminal transistor to demonstrate a >104 conductance-switching ratio, a subthreshold swing at the thermionic limit, a >7 kHz operating frequency and stability over >105 cycles. We fully map the anti-resonance interference features in conductance, reproduce the behaviour by density functional theory calculations and trace back the high performance to the coupling between molecular orbitals and graphene edge states. These results demonstrate how the quantum nature of electron transmission at the nanoscale can enhance, rather than degrade, device performance, and highlight directions for future development of miniaturized electronics.

Connections to the Electrodes Control the Transport Mechanism in Single-Molecule Transistors

When designing a molecular electronic device for a specific function, it is necessary to control whether the charge-transport mechanism is phase-coherent transmission or particle-like hopping. Here we report a systematic study of charge transport through single zinc-porphyrin molecules embedded in graphene nanogaps to form transistors, and show that the transport mechanism depends on the chemistry of the molecule-electrode interfaces. We show that van der Waals interactions between molecular anchoring groups and graphene yield transport characteristic of Coulomb blockade with incoherent sequential hopping, whereas covalent molecule-electrode amide bonds give intermediately or strongly coupled single-molecule devices that display coherent transmission. These findings demonstrate the importance of interfacial engineering in molecular electronic circuits.

Molecular Electronics: Creating and Bridging Molecular Junctions and Promoting Its Commercialization

Molecular electronics is driven by the dream of expanding Moore's law to the molecular level for next-generation electronics through incorporating individual or ensemble molecules into electronic circuits. For nearly 50 years, numerous efforts have been made to explore the intrinsic properties of molecules and develop diverse fascinating molecular electronic devices with the desired functionalities. The flourishing of molecular electronics is inseparable from the development of various elegant methodologies for creating nanogap electrodes and bridging the nanogap with molecules. This review first focuses on the techniques for making lateral and vertical nanogap electrodes by breaking, narrowing, and fixed modes, and highlights their capabilities, applications, merits, and shortcomings. After summarizing the approaches of growing single molecules or molecular layers on the electrodes, the methods of constructing a complete molecular circuit are comprehensively grouped into three categories: 1) directly bridging one-molecule-electrode component with another electrode, 2) physically bridging two-molecule-electrode components, and 3) chemically bridging two-molecule-electrode components. Finally, the current state of molecular circuit integration and commercialization is discussed and perspectives are provided, hoping to encourage the community to accelerate the realization of fully scalable molecular electronics for a new era of integrated microsystems and applications.

Graphene-molecule-graphene single-molecule junctions to detect electronic reactions at the molecular scale

The ability to measure the behavior of a single molecule during a reaction implies the detection of inherent dynamic and static disordered states, which may not be represented when measuring ensemble averages. Here, we describe the building of devices with graphene-molecule-graphene single-molecule junctions integrated into an electrical circuit. These devices are simple to build and are stable, showing tolerance to mechanical changes, solution environment and voltage stimulation. The design of a conductive channel based on a single molecule enables single-molecule detection and is sensitive to variations in physical properties and chemical structures of the detected molecules. The on-chip setup of single-molecule junctions further offers complementary metal-oxide-semiconductor (CMOS) compatibility, enabling logic functions in circuit elements, as well as deciphering of reaction intermediates. We detail the experimental procedure to prepare graphene transistor arrays as a basis for single-molecule junctions and the preparation of nanogapped carboxyl-terminal graphene electrodes by using electron-beam lithography and oxygen plasma etching. We describe the basic design of a molecular bridge with desired functions and terminals to form covalent bonds with electrode arrays, via a chemical reaction, to construct stably integrated single-molecule devices with a yield of 30-50% per chip. The immobilization of the single molecules is then characterized by using inelastic electron tunneling spectra, single-molecule imaging and fluorescent spectra. The whole protocol can be implemented within 2 weeks and requires users trained in using ultra-clean laboratory facilities and the aforementioned instrumentation.

Characterization and Application of Supramolecular Junctions

The convergence of supramolecular chemistry and single-molecule electronics offers a new perspective on supramolecular electronics, and provides a new avenue toward understanding and application of intermolecular charge transport at the molecular level. In this review, we will provide an overview of the advances in the characterization technique for the investigation of intermolecular charge transport, and summarize the experimental investigation of several non-covalent interactions, including π-π stacking interactions, hydrogen bonding, host-guest interactions and σ-σ interactions at the single-molecule level. We will also provide a perspective on supramolecular electronics and discuss the potential applications and future challenges.

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.

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.

Charge-State Dependent Vibrational Relaxation in a Single-Molecule Junction

The outcome of an electron-transfer process is determined by the quantum-mechanical interplay between electronic and vibrational degrees of freedom. Nonequilibrium vibrational dynamics are known to direct electron-transfer mechanisms in molecular systems; however, the structural features of a molecule that lead to certain modes being pushed out of equilibrium are not well understood. Herein, we report on electron transport through a porphyrin dimer molecule, weakly coupled to graphene electrodes, that displays sequential tunneling within the Coulomb-blockade regime. The sequential transport is initiated by current-induced phonon absorption and proceeds by rapid sequential transport via a nonequilibrium vibrational distribution of low-energy modes, likely related to torsional molecular motions. We demonstrate that this is an experimental signature of slow vibrational dissipation, and obtain a lower bound for the vibrational relaxation time of 8 ns, a value dependent on the molecular charge state.

Hopping or Tunneling? Tailoring the Electron Transport Mechanisms through Hydrogen Bonding Geometry in the Boron-Doped Diamond Molecular Junctions

Mechanisms of charge transport in molecular junctions involving hydrogen bonds are complex and remain mostly unclear. This study is focused on the elucidation of the electron transfer in a molecular device consisting of two boron-doped diamond interfaces bound with an aromatic linker and a hydrogen bonding surrogating molecule. The projected local density of states (PLODS) analysis coupled with transmission spectra and current-voltage (I-V) simulations show that hydrogen bonding through electron-donating hydroxyl groups in the aromatic linker facilitates electron transfer, while the electron-withdrawing carboxyl group inhibits electron transfer across the junction. Moreover, slight variations in the geometry of hydrogen bonding lead to significant changes in the alignment of the energy levels and positions of the transmission modes. As a result, we observe the switching of the electron transport mechanism from tunneling to hopping accompanied by a change in the shape of the I-V curves and current magnitudes. These results give important information on the tailoring of the electronic properties of molecular junctions.

Exchange-induced spin polarization in a single magnetic molecule junction

Many spintronic devices rely on the presence of spin-polarized currents at zero magnetic field. This is often obtained by spin exchange-bias, where an element with long-range magnetic order creates magnetized states and displaces the hysteresis loop. Here we demonstrate that exchange-split spin states are observable and usable in the smallest conceivable unit: a single magnetic molecule. We use a redox-active porphyrin as a transport channel, coordinating a dysprosium-based single-molecule-magnet inside a graphene nano-gap. Single-molecule transport in magnetic field reveals the existence of exchange-split channels with different spin-polarizations that depend strongly on the field orientation, and comparison with the diamagnetic isostructural compound and milikelvin torque magnetometry unravels the role of the single-molecule anisotropy and the molecular orientation. These results open a path to using spin-exchange in molecular electronics, and offer a method to quantify the internal spin structure of single molecules in multiple oxidation states.

The spin exchange, which is central to spintronics, has been restricted to devices with long-range magnetic ordering to date. Here, Pei et al. design a single-molecule-magnet and utilize its internal spin exchange to control the current through a single-molecule junction with high spin polarization (>95%).

Single-molecule nano-optoelectronics: insights from physics

Single-molecule optoelectronic devices promise a potential solution for miniaturization and functionalization of silicon-based microelectronic circuits in the future. For decades of its fast development, this field has made significant progress in the synthesis of optoelectronic materials, the fabrication of single-molecule devices and the realization of optoelectronic functions. On the other hand, single-molecule optoelectronic devices offer a reliable platform to investigate the intrinsic physical phenomena and regulation rules of matters at the single-molecule level. To further realize and regulate the optoelectronic functions toward practical applications, it is necessary to clarify the intrinsic physical mechanisms of single-molecule optoelectronic nanodevices. Here, we provide a timely review to survey the physical phenomena and laws involved in single-molecule optoelectronic materials and devices, including charge effects, spin effects, exciton effects, vibronic effects, structural and orbital effects. In particular, we will systematically summarize the basics of molecular optoelectronic materials, and the physical effects and manipulations of single-molecule optoelectronic nanodevices. In addition, fundamentals of single-molecule electronics, which are basic of single-molecule optoelectronics, can also be found in this review. At last, we tend to focus the discussion on the opportunities and challenges arising in the field of single-molecule optoelectronics, and propose further potential breakthroughs.

Charge transport through extended molecular wires with strongly correlated electrons

Electron–electron interactions are at the heart of chemistry and understanding how to control them is crucial for the development of molecular-scale electronic devices. Here, we investigate single-electron tunneling through a redox-active edge-fused porphyrin trimer and demonstrate that its transport behavior is well described by the Hubbard dimer model, providing insights into the role of electron–electron interactions in charge transport. In particular, we empirically determine the molecule's on-site and inter-site electron–electron repulsion energies, which are in good agreement with density functional calculations, and establish the molecular electronic structure within various oxidation states. The gate-dependent rectification behavior confirms the selection rules and state degeneracies deduced from the Hubbard model. We demonstrate that current flow through the molecule is governed by a non-trivial set of vibrationally coupled electronic transitions between various many-body ground and excited states, and experimentally confirm the importance of electron–electron interactions in single-molecule devices.

Experimental studies of electron transport through an edge-fused porphyrin oligomer in a graphene junction are interpreted within a Hubbard dimer framework.

Electrochemical Potential-Driven High-Throughput Molecular Electronic and Spintronic Devices: From Molecules to Applications

Molecules are fascinating candidates for constructing tunable and electrically conducting devices by the assembly of either a single molecule or an ensemble of molecules between two electrical contacts followed by current-voltage (I-V) analysis, which is often termed "molecular electronics". Recently, there has been also an upsurge of interest in spin-based electronics or spintronics across the molecules, which offer additional scope to create ultrafast responsive devices with less power consumption and lower heat generation using the intrinsic spin property rather than electronic charge. Researchers have been exploring this idea of utilizing organic molecules, organometallics, coordination complexes, polymers, and biomolecules (proteins, enzymes, oligopeptides, DNA) in integrating molecular electronics and spintronics devices. Although several methods exist to prepare molecular thin-films on suitable electrodes, the electrochemical potential-driven technique has emerged as highly efficient. In this Review we describe recent advances in the electrochemical potential driven growth of nanometric various molecular films on technologically relevant substrates, including non-magnetic and magnetic electrodes to investigate the stimuli-responsive charge and spin transport phenomena.

A review of oligo(arylene ethynylene) derivatives in molecular junctions

Oligo(arylene ethynylene) (OAE) derivatives are the "workhorse" molecules of molecular electronics. Their ease of synthesis and flexibility of functionalisation mean that a diverse array of OAE molecular wires have been designed, synthesised and studied theoretically and experimentally in molecular junctions using both single-molecule and ensemble methods. This review summarises the breadth of molecular designs that have been investigated with emphasis on structure-property relationships with respect to the electronic conductance of OAEs. The factors considered include molecular length, connectivity, conjugation, (anti)aromaticity, heteroatom effects and quantum interference (QI). Growing interest in the thermoelectric properties of OAE derivatives, which are expected to be at the forefront of research into organic thermoelectric devices, is also explored.

Quantum transport in a single molecular transistor at finite temperature

We study quantum transport in a single molecular transistor in which the central region consists of a single-level quantum dot and is connected to two metallic leads that act as a source and a drain respectively. The quantum dot is considered to be under the influence of electron-electron and electron-phonon interactions. The central region is placed on an insulating substrate that acts as a heat reservoir that interacts with the quantum dot phonon giving rise to a damping effect to the quantum dot. The electron-phonon interaction is decoupled by applying a canonical transformation and then the spectral density of the quantum dot is calculated from the resultant Hamiltonian by using Keldysh Green function technique. We also calculate the tunneling current density and differential conductance to study the effect of quantum dissipation, electron correlation and the lattice effects on quantum transport in a single molecular transistor at finite temperature.

Quantum Algorithm for Simulating Single-Molecule Electron Transport

An accurate description of electron transport at a molecular level requires a precise treatment of quantum effects. These effects play a crucial role in determining the electron transport properties of single molecules, which can be challenging to simulate classically. Here we introduce a quantum algorithm to efficiently calculate electronic current through single-molecule junctions in the weak-coupling regime. We show that a quantum computer programmed to simulate vibronic transitions between different charge states of a molecule can be used to compute electron-transfer rates and electronic current. In the harmonic approximation, the algorithm can be implemented using Gaussian boson sampling devices, which are a near-term platform for photonic quantum computing. We apply the algorithm to simulate the current and conductance of a magnesium porphine molecule. The algorithm provides a means for better understanding the mechanism of electron transport at a molecular level, which paves the way for building practical molecular electronic devices.

Voltage-Induced Single-Molecule Junction Planarization

Probing structural changes of a molecule induced by charge transfer is important for understanding the physicochemical properties of molecules and developing new electronic devices. Here, we interrogate the structural changes of a single diketopyrrolopyrrole (DPP) molecule induced by charge transport at a high bias using scanning tunneling microscope break junction (STM-BJ) techniques. Specifically, we demonstrate that application of a high bias increases the average nonresonant conductance of single Au-DPP-Au junctions. We infer from the increased conductance that resonant charge transport induces planarization of the molecular backbone. We further show that this conformational planarization is assisted by thermally activated junction reorganization. The planarization only occurs under specific electronic conditions, which we rationalize by ab initio calculations. These results emphasize the need for a comprehensive view of single-molecule junctions which includes both the electronic properties and structure of the molecules and the electrodes when designing electrically driven single-molecule motors.

Long-lived charged states of single porphyrin-tape junctions under ambient conditions

The ability to control the charge state of individual molecules wired in two-terminal single-molecule junctions is a key challenge in molecular electronics, particularly in relation to the development of molecular memory and other computational componentry. Here we demonstrate that single porphyrin molecular junctions can be reversibly charged and discharged at elevated biases under ambient conditions due to the presence of a localised molecular eigenstate close to the Fermi edge of the electrodes. In particular, we can observe long-lived charge-states with lifetimes upwards of 1-10 seconds after returning to low bias and large changes in conductance, in excess of 100-fold at low bias. Our theoretical analysis finds charge-state lifetimes within the same time range as the experiments. The ambient operation demonstrates that special conditions such as low temperatures or ultra-high vacuum are not essential to observe hysteresis and stable charged molecular junctions.

Reversal of the Direction of Rectification Induced by Fermi Level Pinning at Molecule-Electrode Interfaces in Redox-Active Tunneling Junctions

Control over the energy level alignment in molecular junctions is notoriously difficult, making it challenging to control basic electronic functions such as the direction of rectification. Therefore, alternative approaches to control electronic functions in molecular junctions are needed. This paper describes switching of the direction of rectification by changing the bottom electrode material M = Ag, Au, or Pt in M-S(CH₂)₁₁S-BTTF//EGaIn junctions based on self-assembled monolayers incorporating benzotetrathiafulvalene (BTTF) with EGaIn (eutectic alloy of Ga and In) as the top electrode. The stability of the junctions is determined by the choice of the bottom electrode, which, in turn, determines the maximum applied bias window, and the mechanism of rectification is dominated by the energy levels centered on the BTTF units. The energy level alignments of the three junctions are similar because of Fermi level pinning induced by charge transfer at the metal-thiolate interface and by a varying degree of additional charge transfer between BTTF and the metal. Density functional theory calculations show that the amount of electron transfer from M to the lowest unoccupied molecular orbital (LUMO) of BTTF follows the order Ag > Au > Pt. Junctions with Ag electrodes are the least stable and can only withstand an applied bias of ±1.0 V. As a result, no molecular orbitals can fall in the applied bias window, and the junctions do not rectify. The junction stability increases for M = Au, and the highest occupied molecular orbital (HOMO) dominates charge transport at a positive bias resulting in a positive rectification ratio of 83 at ±1.5 V. The junctions are very stable for M = Pt, but now the LUMO dominates charge transport at a negative bias resulting in a negative rectification ratio of 912 at ±2.5 V. Thus, the limitations of Fermi level pinning can be bypassed by a judicious choice of the bottom electrode material, making it possible to access selectively HOMO- or LUMO-based charge transport and, as shown here, associated reversal of rectification.

Functional Redox-Active Molecular Tunnel Junctions

Redox-active molecular junctions have attracted considerable attention because redox-active molecules provide accessible energy levels enabling electronic function at the molecular length scales, such as, rectification, conductance switching, or molecular transistors. Unlike charge transfer in wet electrochemical environments, it is still challenging to understand how redox-processes proceed in solid-state molecular junctions which lack counterions and solvent molecules to stabilize the charge on the molecules. In this minireview, we first introduce molecular junctions based on redox-active molecules and discuss their properties from both a chemistry and nanoelectronics point of view, and then discuss briefly the mechanisms of charge transport in solid-state redox-junctions followed by examples where redox-molecules generate new electronic function. We conclude with challenges that need to be addressed and interesting future directions from a chemical engineering and molecular design perspectives.

Multifaceted aspects of charge transfer

Charge transfer and charge transport are by far among the most important processes for sustaining life on Earth and for making our modern ways of living possible. Involving multiple electron-transfer steps, photosynthesis and cellular respiration have been principally responsible for managing the energy flow in the biosphere of our planet since the Great Oxygen Event. It is impossible to imagine living organisms without charge transport mediated by ion channels, or electron and proton transfer mediated by redox enzymes. Concurrently, transfer and transport of electrons and holes drive the functionalities of electronic and photonic devices that are intricate for our lives. While fueling advances in engineering, charge-transfer science has established itself as an important independent field, originating from physical chemistry and chemical physics, focusing on paradigms from biology, and gaining momentum from solar-energy research. Here, we review the fundamental concepts of charge transfer, and outline its core role in a broad range of unrelated fields, such as medicine, environmental science, catalysis, electronics and photonics. The ubiquitous nature of dipoles, for example, sets demands on deepening the understanding of how localized electric fields affect charge transfer. Charge-transfer electrets, thus, prove important for advancing the field and for interfacing fundamental science with engineering. Synergy between the vastly different aspects of charge-transfer science sets the stage for the broad global impacts that the advances in this field have.

Crucial effect of transverse vibrations on the transport through polymer chains

The low temperature transport of electron, or vibrational or electronic exciton toward polymer chains, turns out to be dramatically sensitive to its interaction with transverse acoustic vibrations. We show that this interaction leads to a substantial polaron effect and decoherence, which are generally stronger than those associated with longitudinal vibrations. For site-dependent interactions, transverse phonons form subohmic bath leading to the quantum phase transition accompanied by full suppression of the transport at zero temperature and fast decoherence characterized by temperature dependent rate k₂ ∝ T^3/4 at low temperature, while k₂ ∝ T² for site-independent interactions. The latter dependence was used to interpret recent measurements of temperature dependent vibrational energy transport in polyethylene glycol oligomers.

Large Increase in the Dielectric Constant and Partial Loss of Coherence Increases Tunneling Rates across Molecular Wires

Although the dielectric behavior of monolayers is important in a large range of applications, its role in charge transport studies involving molecular junctions is largely ignored. This paper describes a large increase in the relative static dielectric constant (ε_r) by simply increasing the thickness of well-organized monolayers of oligoglycine and oligo(ethylene glycol) from 7 up to 14. The resulting large capacitance of 3.5-5.1 μF/cm² is thickness-independent, which is highly attractive for field-effect transistor applications. This increase of ε_r results in a linear increase of the thermal activation energy by a factor of 6, which suggests that the mechanism of charge transport gradually changes from coherent to (partially) incoherent tunneling. The comparisons of oligoglycine (which readily forms hydrogen bonds with neighboring molecules) and methyl terminated oligo(ethylene glycol) (which lacks hydrogen bond donors) monolayers, kinetic isotope effects, and relative humidity-dependent measurements all indicate the importance of strong hydrogen bonds involving ionic species and strongly bonded water in the unusual dielectric behavior and the incoherent tunneling mechanism. This partial loss of coherence of the charge carriers can explain the unusually small tunneling decay coefficients across long molecular wires, and the length-dependent increase of ε_r of monolayers opens up interesting new applications.

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.