Controlling charge transport mechanisms in molecular junctions: Distilling thermally induced hopping from coherent-resonant conduction

Emergence of Boltzmann Subspaces in Open Quantum Systems Far from Equilibrium

Single molecule junctions are important examples of complex out-of-equilibrium many-body quantum systems. We identify a nontrivial clustering of steady state populations into distinctive subspaces with Boltzmann-like statistics, which persist far from equilibrium. Such Boltzmann subspaces significantly reduce the information needed to describe the steady state, enabling modeling of high-dimensional systems that are otherwise beyond the reach of current computations. The emergence of Boltzmann subspaces is demonstrated analytically and numerically for fermionic transport systems of increasing complexity.

A Method to Investigate the Mechanism of Charge Transport Across Bio-Molecular Junctions with Ferritin

To investigate the mechanisms of charge transport (CT) across biomolecular tunnel junctions, it is required to make electrical contacts by a non-invasive method that leaves the biomolecules unaltered. Although different methods to form biomolecular junctions are available, here we describe the EGaIn-method because it allows us to readily form electrical contacts to monolayers of biomolecules in ordinary laboratory settings and to probe CT as a function of voltage, temperature, or magnetic field. This method relies on a non-Newtonian liquid-metal ally of Ga and In with a few nm thin layer of GaOx floating on its surface giving this material non-Newtonian properties allowing it to be shaped in to cone-shaped tips or stabilized in microchannels. These EGaIn structures form stable contacts to monolayers making it possible to investigate CT mechanisms across biomolecules in great detail.

Temperature-Dependent Coherent Tunneling across Graphene-Ferritin Biomolecular Junctions

Understanding the mechanisms of charge transport (CT) across biomolecules in solid-state devices is imperative to realize biomolecular electronic devices in a predictive manner. Although it is well-accepted that biomolecule-electrode interactions play an essential role, it is often overlooked. This paper reveals the prominent role of graphene interfaces with Fe-storing proteins in the net CT across their tunnel junctions. Here, ferritin (AfFtn-AA) is adsorbed on the graphene by noncovalent amine-graphene interactions confirmed with Raman spectroscopy. In contrast to junctions with metal electrodes, graphene has a vanishing density of states toward its intrinsic Fermi level ("Dirac point"), which increases away from the Fermi level. Therefore, the amount of charge carriers is highly sensitive to temperature and electrostatic charging (induced doping), as deduced from a detailed analysis of CT as a function of temperature and iron loading. Remarkably, the temperature dependence can be fully explained within the coherent tunneling regime due to excitation of hot carriers. Graphene is not only demonstrated as an alternative platform to study CT across biomolecular tunnel junctions, but it also opens rich possibilities in employing interface electrostatics in tuning CT behavior.

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.

Verification and Temperature-Dependent Rectification by HBQ, the Smallest Unimolecular Donor-Acceptor Rectifier

Five years ago, rectification of electrical current was found in 4'-bromo-3,4-dicyano-2',5'-dimethoxy-[1,1'-biphenyl]-2,5-dione (1), a hemibiquinone (which we will call either 1 or HBQ) that has a very small working length (1.1 nm). Monolayers of HBQ on Au^TS were detected by "nanodozing" atomic force microscopy (AFM) and were contacted with two types of top electrodes: either cold Au or eutectic Ga-In. Here, we describe cyclic voltammetry of a self-assembled monolayer (SAM) of HBQ and its orientation on a gold substrate with angle-resolved X-ray photoelectron spectroscopy. New measurements of its rectification as a monolayer as a function of bias range and temperature confirm and prove that HBQ is truly the smallest donor-acceptor rectifier and provide some insight into the mechanism of rectification.

Empirical Parameter to Compare Molecule-Electrode Interfaces in Large-Area Molecular Junctions

This paper describes a simple model for comparing the degree of electronic coupling between molecules and electrodes across different large-area molecular junctions. The resulting coupling parameter can be obtained directly from current–voltage data or extracted from published data without fitting. We demonstrate the generalizability of this model by comparing over 40 different junctions comprising different molecules and measured by different laboratories. The results agree with existing models, reflect differences in mechanisms of charge transport and rectification, and are predictive in cases where experimental limitations preclude more sophisticated modeling. We also synthesized a series of conjugated molecular wires, in which embedded dipoles are varied systematically and at both molecule–electrode interfaces. The resulting current–voltage characteristics vary in nonintuitive ways that are not captured by existing models, but which produce trends using our simple model, providing insights that are otherwise difficult or impossible to explain. The utility of our model is its demonstrative generalizability, which is why simple observables like tunneling decay coefficients remain so widely used in molecular electronics despite the existence of much more sophisticated models. Our model is complementary, giving insights into molecule–electrode coupling across series of molecules that can guide synthetic chemists in the design of new molecular motifs, particularly in the context of devices comprising large-area molecular junctions.

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.

Kondo effect and RKKY interaction assisted by magnetic anisotropy in a frustrated magnetic molecular device at zero and finite temperature

Molecular magnetic compounds, which combine the advantages of nanoscale behaviors with the properties of bulk magnetic materials, are particularly attractive in the fields of high-density information storage and quantum computing. Before molecular electronic devices can be fabricated, a crucial task is the measurement and understanding of the transport behaviors. Herein, we consider a magnetic molecular trimer sandwiched between two metal electrodes, and, with the aid of the sophisticated full density matrix numerical renormalization group (FDM-NRG) technique, we study the effect of magnetic anisotropy on the charge transport properties, illustrated by the local density of states (LDOS, which is proportional to the differential conductance), the Kondo effect, and the temperature and inter-monomer hopping robustness. Three kinds of energy peaks are clarified in the LDOS: the Coulomb, the Kondo and the Ruderman-Kittel-Kasuya-Yosida (RKKY) peaks. The local magnetic moment and entropy go through four different regimes as the temperature decreases. The Kondo temperature TK could be described by a generalized Haldane's formula, revealing in detail the process where the local moment is partially screened by the itinerant electrons. A relationship between the width of the Kondo resonant peak WK and TK is built, ensuring the extraction of TK from WK in an efficient way. As the inter-monomer hopping integral varies, the ground state of the trimer changes from a spin quadruplet to a magnetically frustrated phase, then to an orbital spin singlet through two first order quantum phase transitions. In the first two phases, the Kondo peak in the transmission coefficient reaches its unitary limit, while in the orbital spin singlet, it is totally suppressed. We demonstrate that magnetic anisotropy may also induce the Kondo effect, even without Coulomb repulsion, hence it is replaceable in the many-body behaviours at low temperature.

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.

Tuning molecular fluctuation to boost the conductance in DNA based molecular wires

Inherent molecular fluctuations are known to have a significant influence on the charge transport properties of biomolecules like DNA, PNA and proteins. In this work, we show ways to control these fluctuations and further demonstrate their use to enhance the conductance of two widely studied molecular wires, namely dsDNA (DNA) and G4 Quadruplex (G4-Quad). We quantify the molecular fluctuation in terms of the root mean square deviation (RMSD) of the molecule. In the case of DNA, we use temperature to control the fluctuations, while in the case of G4-Quad the fluctuations are tuned by the ions inside the pore. The electronic coupling between the bases of dsDNA and G4-Quad, which measures the conductance of these molecular wires, shows a non-monotonic behaviour with the increase in fluctuation. We find values of fluctuation which give rise to maximum electronic coupling and hence high conductivity for both the cases. In the case of DNA, these optimal fluctuations (∼2.5 Å) are achieved at a temperature of 210 K, which gives rise to an electronic coupling of 0.135 eV between the DNA bases. The optimal fluctuations in G4-Quad are achieved (∼7 Å) in a 4 base pair long system with 2 Na⁺ ions inside the pore, giving rise to an electronic coupling of 0.09 eV.

Robust graphene-based molecular devices

One of the main challenges to upscale the fabrication of molecular devices is to achieve a mechanically stable device with reproducible and controllable electronic features that operates at room temperature^1,2. This is crucial because structural and electronic fluctuations can lead to significant changes in the transport characteristics at the electrode-molecule interface^3,4. In this study, we report on the realization of a mechanically and electronically robust graphene-based molecular junction. Robustness was achieved by separating the requirements for mechanical and electronic stability at the molecular level. Mechanical stability was obtained by anchoring molecules directly to the substrate, rather than to graphene electrodes, using a silanization reaction. Electronic stability was achieved by adjusting the π-π orbitals overlap of the conjugated head groups between neighbouring molecules. The molecular devices exhibited stable current-voltage (I-V) characteristics up to bias voltages of 2.0 V with reproducible transport features in the temperature range from 20 to 300 K.

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.

Why Are DNA and Protein Electron Transfer So Different?

The corpus of electron transfer (ET) theory provides considerable power to describe the kinetics and dynamics of electron flow at the nanoscale. How is it, then, that nucleic acid (NA) ET continues to surprise, while protein-mediated ET is relatively free of mechanistic bombshells? I suggest that this difference originates in the distinct electronic energy landscapes for the two classes of reactions. In proteins, the donor/acceptor-to-bridge energy gap is typically several-fold larger than in NAs. NA ET can access tunneling, hopping, and resonant transport among the bases, and fluctuations can enable switching among mechanisms; protein ET is restricted to tunneling among redox active cofactors and, under strongly oxidizing conditions, a few privileged amino acid side chains. This review aims to provide conceptual unity to DNA and protein ET reaction mechanisms. The establishment of a unified mechanistic framework enabled the successful design of NA experiments that switch electronic coherence effects on and off for ET processes on a length scale of multiple nanometers and promises to provide inroads to directing and detecting charge flow in soft-wet matter.

Formulation of Long-Range Transport Rates through Molecular Bridges: From Unfurling to Hopping

Weak fluctuations about the rigid equilibrium structure of ordered molecular bridges drive charge transfer in donor-bridge-acceptor systems via quantum unfurling, which differs from both hopping and ballistic transfer, yet static disorder (low frequency motions) in the bridge is shown to induce a change of mechanism from unfurling to hopping when local fluctuations along the molecular bridge are uncorrelated. Remarkably, these two different transport mechanisms manifest in similar charge-transfer rates, which are nearly independent of the molecular bridge length. We propose an experimental test for distinguishing unfurling from hopping in DNA models with different helix directionality. A unified formulation explains the apparent similarity in the length dependence of the transfer rate despite the difference in the underlying transport mechanisms.

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.