Probing the conductance superposition law in single-molecule circuits with parallel paths

Symmetry-Like Relation of Relative Entropy Measure of Quantum Coherence

Quantum coherence is an important physical resource in quantum information science, and also as one of the most fundamental and striking features in quantum physics. To quantify coherence, two proper measures were introduced in the literature, the one is the relative entropy of coherence Cr(ρ)=S(ρdiag)−S(ρ) and the other is the ℓ1-norm of coherence Cℓ1(ρ)=∑i≠j|ρij|. In this paper, we obtain a symmetry-like relation of relative entropy measure Cr(ρA1A2⋯An) of coherence for an n-partite quantum states ρA1A2⋯An, which gives lower and upper bounds for Cr(ρ). As application of our inequalities, we conclude that when each reduced states ρAi is pure, ρA1⋯An is incoherent if and only if the reduced states ρAi and trAiρA1⋯An(i=1,2,…,n) are all incoherent. Meanwhile, we discuss the conjecture that Cr(ρ)≤Cℓ1(ρ) for any state ρ, which was proved to be valid for any mixed qubit state and any pure state, and open for a general state. We observe that every mixture η of a state ρ satisfying the conjecture with any incoherent state σ also satisfies the conjecture. We also observe that when the von Neumann entropy is defined by the natural logarithm ln instead of log2, the reduced relative entropy measure of coherence C¯r(ρ)=−ρdiaglnρdiag+ρlnρ satisfies the inequality C¯r(ρ)≤Cℓ1(ρ) for any state ρ.

Nonmagnetic single-molecule spin-filter based on quantum interference

Key spin transport phenomena, including magnetoresistance and spin transfer torque, cannot be activated without spin-polarized currents, in which one electron spin is dominant. At the nanoscale, the relevant length-scale for modern spintronics, spin current generation is rather limited due to unwanted contributions from poorly spin-polarized frontier states in ferromagnetic electrodes, or too short length-scales for efficient spin splitting by spin-orbit interaction and magnetic fields. Here, we show that spin-polarized currents can be generated in silver-vanadocene-silver single molecule junctions without magnetic components or magnetic fields. In some cases, the measured spin currents approach the limit of ideal ballistic spin transport. Comparison between conductance and shot-noise measurements to detailed calculations reveals a mechanism based on spin-dependent quantum interference that yields very efficient spin filtering. Our findings pave the way for nanoscale spintronics based on quantum interference, with the advantages of low sensitivity to decoherence effects and the freedom to use non-magnetic materials.

Electronic Communication as a Transferable Property of Molecular Bridges?

Electronic communication through molecular bridges is important for different types of experiments, such as single-molecule conductance, electron transfer, superexchange spin coupling, and intramolecular singlet fission. In many instances, the chemical structure of the bridge determines how the two parts it is connecting communicate, and does so in ways that are transferable between these different manifestations (for example, high conductance often correlates with strong antiferromagnetic spin coupling, and low conductance due to destructive quantum interference correlates with ferromagnetic coupling). Defining electronic communication as a transferable property of the bridge can help transfer knowledge between these different areas of research. Examples and limits of such transferability are discussed here, along with some possible directions for future research, such as employing spin-coupled and mixed-valence systems as structurally well-controlled proxies for understanding molecular conductance and for validating first-principles theoretical methodologies, building conceptual understanding for the growing experimental work on intramolecular singlet fission, and developing measures for the transferability of electronic communication as a bridge property.

Effect of electrophilic substitution and destructive quantum interference on the thermoelectric performance in molecular devices

Using density function theory combined with the non-equilibrium Green's function method, the thermoelectric properties of para-Xylene-based molecular devices are investigated. It is found that destructive quantum interference can be triggered in n-type of para-connected para-Xylene-based molecular device and can obviously enhance the thermoelectric performance of the devices. Moreover, bridge atom electrophilic substitution can significantly improve the thermoelectric properties of p-type monolayer molecular device. The ZT value of p-type monolayer molecular device with doped electrodes can be optimized to 2.2 at 300 K and 2.8 at 500 K, and n-type bilayer molecular device can achieve the value of 1.2 at 300 K and 2.0 at 500 K. These results offer the information to design the complete molecular thermoelectric device with p-type and n-type of components and to promote the thermoelectric properties of bilayer molecular junctions by employing destructive quantum interference effects.

Tuning the contact conductance of anchoring groups in single molecule junctions by molecular design

A tetraphenylmethane tripod functionalized with three thiol moieties in the para position can serve as a supporting platform for functional molecular electronic elements. A combined experimental scanning tunneling microscopy break junction technique with theoretical approaches based on density functional theory and non-equilibrium Green's function formalism was used for detailed charge transport analysis to find configurations, geometries and charge transport pathways in the molecular junctions of single molecule oligo-1,4-phenylene conductors containing this tripodal anchoring group. The effect of molecular length (n = 1 to 4 repeating phenylene units) on the charge transport properties and junction configurations is addressed. The number of covalent attachments between the electrode and the tripodal platform changes with n affecting the contact conductance of the junction. The longest homologue n = 4 adopts an upright configuration with all three para thiolate moieties of the tripod attached to the gold electrode. The contact conductance of the tetraphenylmethane tripod substituted by thiols in the para position is higher than that substituted in the meta position. Such molecular arrangement is highly conducting and allows well-defined directional positioning of a variety of functional groups.

Quantum coherence in ultrafast photo-driven charge separation

Coherent interactions are prevalent in photodriven processes, ranging from photosynthetic energy transfer to superexchange-mediated electron transfer, resulting in numerous studies aimed towards identifying and understanding these interactions. A key motivator of this interest is the non-statistical scaling laws that result from coherently traversing multiple pathways due to quantum interference. To that end, we employed ultrafast transient absorption spectroscopy to measure electron transfer in two donor-acceptor molecular systems comprising a p-(9-anthryl)-N,N-dimethylaniline chromophore/electron donor and either one or two equivalent naphthalene-1,8:4,5-bis(dicarboximide) electron acceptors at both ambient and cryogenic temperatures. The two-acceptor compound shows a statistical factor of 2.1 ± 0.2 rate enhancement at room temperature and a non-statistical factor of 2.6 ± 0.2 rate enhancement at cryogenic temperatures, suggesting correlated interactions between the two acceptors with the donor and with the bath modes. Comparing the charge recombination rates indicates that the electron is delocalized over both acceptors at low temperature but localized on a single acceptor at room temperature. These results highlight the importance of shielding the system from bath fluctuations to preserve and ultimately exploit the coherent interactions.

Evolution of local conductance pathways in a single-molecule junction studied using the three-dimensional dynamic probe method

Understanding of the dynamics of the bonding states of molecules with electrodes while the molecular conformation is changed is particularly important for elucidating the details of electrochemical devices as well as molecular devices in which the reaction dynamics of the electrodes and molecules plays an important role, such as in fuel cells, catalysis and bioelectrochemical devices. However, it has been difficult to make measurements when the distance between counter electrodes is short, namely, the molecule is raised from a lying form, almost parallel and close to the electrodes, toward a standing form and vice versa. We previously have developed a method called the three-dimensional (3D) dynamic probe method, which enables conductance measurement while the conformation of a single-molecule junction is precisely controlled by scanning tunneling microscopy (STM) techniques. Here, by combining this method with density functional theory (DFT) calculations, it has become possible to simultaneously consider the effects of the dynamics of molecular structures and the bonding states at the electrodes on the local transmission pathways, local-bond contributions to conductance. Here, by performing an analysis on 1,4-benzenediamine (BDA) and 1,4-benzenedithiol (BDT) single molecule junctions, we have observed, for the first time, the effect of a change in the molecular conformations and bonding states on the local transmission pathways for a short Au electrode distance condition.

Detection and Characterization of Anharmonic Overtone Vibrations of Single Molecules on a Metal Surface

Inelastic electron tunneling spectroscopy (IETS) with the scanning tunneling microscope (STM) is a powerful technique used to characterize the vibration and spin states at the single-molecule level. While IETS lacks hard selection rules, historically it has been assumed that vibrational overtones are rarely seen or even absent. Here we provide definitive experimental evidence that the hindered rotation overtone excitation of carbon monoxide molecules adsorbed on Ag(110) can be detected with STM-IETS via isotope substitution. We also demonstrate that the anharmonicity of the overtone excitation can be characterized and compared between adsorption sites and find evidence of anisotropy in the vibrational anharmonicity for CO adsorbed on the [11[over ¯]0] step edge.

On the resilience of magic number theory for conductance ratios of aromatic molecules

If simple guidelines could be established for understanding how quantum interference (QI) can be exploited to control the flow of electricity through single molecules, then new functional molecules, which exploit room-temperature QI could be rapidly identified and subsequently screened. Recently it was demonstrated that conductance ratios of molecules with aromatic cores, with different connectivities to electrodes, can be predicted using a simple and easy-to-use "magic number theory." In contrast with counting rules and "curly-arrow" descriptions of destructive QI, magic number theory captures the many forms of constructive QI, which can occur in molecular cores. Here we address the question of how conductance ratios are affected by electron-electron interactions. We find that due to cancellations of opposing trends, when Coulomb interactions and screening due to electrodes are switched on, conductance ratios are rather resilient. Consequently, qualitative trends in conductance ratios of molecules with extended pi systems can be predicted using simple 'non-interacting' magic number tables, without the need for large-scale computations. On the other hand, for certain connectivities, deviations from non-interacting conductance ratios can be significant and therefore such connectivities are of interest for probing the interplay between Coulomb interactions, connectivity and QI in single-molecule electron transport.

Charge transfer complexation boosts molecular conductance through Fermi level pinning

Interference features in the transmission spectra can dominate charge transport in metal-molecule-metal junctions when they occur close to the contact Fermi energy (E F). Here, we show that by forming a charge-transfer complex with tetracyanoethylene (TCNE) we can introduce new constructive interference features in the transmission profile of electron-rich, thiophene-based molecular wires that almost coincide with E F. Complexation can result in a large enhancement of junction conductance, with very efficient charge transport even at relatively large molecular lengths. For instance, we report a conductance of 10-3 G 0 (∼78 nS) for the ∼2 nm long α-quaterthiophene:TCNE complex, almost two orders of magnitude higher than the conductance of the bare molecular wire. As the conductance of the complexes is remarkably independent of features such as the molecular backbone and the nature of the contacts to the electrodes, our results strongly suggest that the interference features are consistently pinned near to the Fermi energy of the metallic leads. Theoretical studies indicate that the semi-occupied nature of the charge-transfer orbital is not only important in giving rise to the latter effect, but also could result in spin-dependent transport for the charge-transfer complexes. These results therefore present a simple yet effective way to increase charge transport efficiency in long and poorly conductive molecular wires, with important repercussions in single-entity thermoelectronics and spintronics.

Topology-Driven Single-Molecule Conductance of Carbon Nanothreads

Highly conductive single-molecule junctions typically involve π-conjugated molecular bridges, whose frontier molecular orbital energy levels can be fine-tuned to best match the Fermi level of the leads. Fully saturated wires, e.g., alkanes, are typically thought of as insulating rather than highly conductive. However, in this work, we demonstrate in silico that significant zero-bias conductance can be achieved in such systems by means of topology. Specifically, caged saturated hydrocarbons offering multiple σ-conductance channels afford transmission far beyond what could be expected based upon conventional superposition laws, particularly if these pathways are composed entirely from quaternary carbon atoms. Computed conductance of molecular bridges based on carbon nanothreads, e.g., polytwistane, is not only of appreciable magnitude; it also shows a very slow decay with increasing nanogap, similarly to the case of π-conjugated wires. These findings offer a way to manipulate the transport properties of molecular systems by means of their topology, alternatively to the traditionally invoked electronic structure.

Coherent population trapping by dark state formation in a carbon nanotube quantum dot

Illumination of atoms by resonant lasers can pump electrons into a coherent superposition of hyperfine levels which can no longer absorb the light. Such superposition is known as a dark state, because fluorescent light emission is then suppressed. Here we report an all-electric analogue of this destructive interference effect in a carbon nanotube quantum dot. The dark states are a coherent superposition of valley (angular momentum) states which are decoupled from either the drain or the source leads. Their emergence is visible in asymmetric current−voltage characteristics, with missing current steps and current suppression which depend on the polarity of the applied source-drain bias. Our results demonstrate coherent-population trapping by all-electric means in an artificial atom.

Transport in quantum systems is complex and can be suppressed by coherent superposition of the involved states. Here, the authors find all-electronic suppression of transport in a carbon nanotube originating from coherent population trapping and give criteria for the presence of such a dark state.

Quantum Interference Effects in Charge Transport through Single-Molecule Junctions: Detection, Manipulation, and Application

Quantum interference effects (QIEs), which offer unique opportunities for the fine-tuning of charge transport through molecular building blocks by constructive or destructive quantum interference, have become an emerging area in single-molecule electronics. Benefiting from the QIEs, charge transport through molecular systems can be controlled through minor structural and environmental variations, which cause various charge transport states to be significantly changed from conductive to insulative states and offer promising applications in future functional single-molecule devices. Although QIEs were predicted by theoreticians more than two decades ago, only since 2011 have the challenges in ultralow conductance detection originating from destructive quantum interference been overcome experimentally. Currently, a series of single-molecule conductance investigations have been carried out experimentally to detect constructive and destructive QIEs in charge transport through various types of molecular junctions by altering molecular patterns and connectivities. Furthermore, the use of QIEs to tune the properties of charge transport through single-molecule junctions using external gating shows vital potential in future molecular electronic devices. The experimental and theoretical investigations of QIEs offer new fundamental understanding of the structural-electronic relationships in molecular devices and materials at the nanoscale. In this Account, we discuss our progress toward the experimental detection, manipulation, and further application of QIEs in charge transport through single-molecule junctions. These experiments were carried out continuously in our previous group at the University of Bern and in our lab at Xiamen University. As a result of the development of mechanically controllable break junction (MCBJ) and scanning tunneling microscope break junction (STM-BJ) techniques, we could detect ultralow charge transport through the cross-conjugated anthraquinone center, which was one of the earliest experimental studies of QIEs. In close cooperation with organic chemists and theoretical physicists, we systematically investigated charge transport through single-molecule junctions originating from QIEs in conjugated centers ranging from simple single benzene to polycyclic aromatic hydrocarbons (PAHs), heteroaromatics, and even complicated metalla-aromatics at room temperature. Then we further investigated the quantitative correlation between molecular structure and quantum interference by altering different molecular patterns and connectivities in homologous series of PAHs and heteroatom systems. Additionally, external chemical and electrochemical gating of single-molecule devices can be used for direct QIE manipulation via not only tuning molecular conjugation but also shifting the electrode Fermi level. Our study further suggested that distinguishable differences in conductance resulting from QIEs offer opportunities to detect photothermal reaction kinetics and to recognize isomers at the single-molecule scale. These investigations demonstrate the universality of QIEs in charge transport through various molecular building blocks. Moreover, effective manipulation of QIEs leads to various novel phenomena and promising applications in molecular electronic devices.

[Formula: see text]-symmetric interference transistor

We present a model of the molecular transistor, operation of which is based on the interplay between two physical mechanisms, peculiar to open quantum systems that act in concert: [Formula: see text] -symmetry breaking corresponding to coalescence of resonances at the exceptional point of the molecule, connected to the leads, and Fano-Feshbach antiresonance. This switching mechanism can be realised in particular in a special class of molecules with degenerate energy levels, e.g. diradicals, which possess mirror symmetry. At zero gate voltage infinitesimally small interaction of the molecule with the leads breaks the [Formula: see text] -symmetry of the system that, however, can be restored by application of the gate voltage preserving the mirror symmetry. [Formula: see text] -symmetry broken state at zero gate voltage with minimal transmission corresponds to the "off" state while the [Formula: see text] -symmetric state at non-zero gate voltage with maximum transmission - to the "on" state. At zero gate voltage energy of the antiresonance coincides with exceptional point. We construct a model of an all-electrical molecular switch based on such transistors acting as a conventional CMOS inverter and show that essentially lower power consumption and switching energy can be achieved, compared to the CMOS analogues.

Tunneling Probability Increases with Distance in Junctions Comprising Self-Assembled Monolayers of Oligothiophenes

Molecular tunneling junctions should enable the tailoring of charge-transport at the quantum level through synthetic chemistry but are hindered by the dominance of the electrodes. We show that the frontier orbitals of molecules can be decoupled from the electrodes, preserving their relative energies in self-assembled monolayers even when a top-contact is applied. This decoupling leads to the remarkable observation of tunneling probabilities that increase with distance in a series of oligothiophenes, which we explain using a two-barrier tunneling model. This model is generalizable to any conjugated oligomers for which the frontier orbital gap can be determined and predicts that the molecular orbitals that dominate tunneling charge-transport can be positioned via molecular design rather than by domination of Fermi-level pinning arising from strong hybridization. The ability to preserve the electronic structure of molecules in tunneling junctions facilitates the application of well-established synthetic design rules to tailor the properties of molecular-electronic devices.

Electric-field induced bistability in single-molecule conductance measurements for boron coordinated curcuminoid compounds

We have studied the single-molecule conductance of a family of curcuminoid molecules (CCMs) using the mechanically controlled break junction (MCBJ) technique. The CCMs under study contain methylthio (MeS-) as anchoring groups: MeS-CCM (1), the free-ligand organic molecule, and two coordination compounds, MeS-CCM-BF2 (2) and MeS-CCM-Cu (3), where ligand 1 coordinates to a boron center (BF2 group) and to a CuII moiety, respectively. We found that the three molecules present stable molecular junctions allowing detailed statistical analysis of their electronic properties. Compound 3 shows a slight increase in the conductance with respect to free ligand 1, whereas incorporation of BF2 (compound 2) promotes the presence of two conductance states in the measurements. Additional experiments with control molecules point out that this bistability is related to the combination of MeS- anchoring groups and the BF2 moiety within the structure of the molecules. Theoretical calculations show that this can be explained by the presence of two conformers once compound 2 is anchored between the gold electrodes. An energy minimum is found for a flat structure but there is a dramatic change in the magnitude and orientation of dipole moment (favouring a non-flat conformer in the presence of an external electric field) due to a conformational change of one of the terminal MeS- groups. The results thus point to an intricate interplay between the applied bias voltage and the molecule dipole moment which could be the basis for designing new molecules aiming at controlling their conformation in devices.

Remarkable Multichannel Conductance of Novel Single-Molecule Wires Built on Through-Space Conjugated Hexaphenylbenzene

Through-bond conjugated molecules are the major frameworks for traditional molecular wires, while through-space conjugated units are rarely utilized and studied although they have shown unique conducting potential. Herein, we present novel single-molecule wires built on through-space conjugated hexaphenylbenzene. Their conductance, measured by the scanning tunneling microscopy based break-junction technique, increases with the improvement of through-space conjugation and finally reaches a remarkable value (12.28 nS) which greatly exceeds that of conventional through-bond conjugated counterpart (2.45 nS). The multichannel conducting model by integrating through-space and through-bond conjugations could be a promising strategy for the further design of robust single-molecule wires with advanced conductance and stability.

A single-molecule porphyrin-based switch for graphene nano-gaps

Stable single-molecule switches with high on-off ratios are an essential component for future molecular-scale circuitry. Unfortunately, devices using gold electrodes are neither complementary metal-oxide-semiconductor (CMOS) compatible nor stable at room temperature. To overcome these limitations, several groups have been developing electroburnt graphene electrodes for single molecule electronics. Here, in anticipation of these developments, we examine how the electrical switching properties of a series of porphyrin molecules with pendant dipoles can be tuned by systematically increasing the number of spacer units between the porphyrin core and graphene electrodes. The porphyrin is sandwiched between a graphene source and drain and gated by a third electrode. It is found that the system has two stable states with high and low conductances, which can be controlled by coupling the dipole of the functionalised porphyrin to an external electric field. The associated rotation leads to the breaking of conjugation and a decrease in electrical conductances. As the number of spacers is increased, the conductance ratio can increase from 100 with one spacer to 200 with four spacers. This switching ratio is further enhanced by decreasing the temperature, reaching approximately 2200 at 100 K. This design for a molecular switch using graphene electrodes could be extended to other aromatic systems.

Spin-polarized transport properties in some transition metal dithiolene complexes

Spin filtering materials are of great current interest in part due to their applications in molecular electronics. In this study, we carried out a theoretical investigation on the charge transport properties of transition metal (TM) dithiolene complexes with TM = Ni, Fe and Mn by using non-equilibrium Green's function/density functional theory (NEGF-DFT) methods. The characteristics of current-voltage and spin-resolved transmission spectra pointed out that Ni complexes are non-polarized, while Fe and Mn complexes exhibit high polarization and can be regarded as excellent candidates for spin-filtering materials with high spin-filtering efficiency. These differences were rationalized on the basis of electron delocalization over the molecular junction of the partial distribution of α- and β-spin molecular projected self-consistent Hamiltonian (MPSH) orbitals, and also the first eigenchannels of molecular junctions.

Quantum interference in multi-branched molecules: The exact transfer matrix solutions

We present a transfer matrix formalism for studying quantum interference in a single molecule electronic system with internal branched structures. Based on the Schrödinger equation with the Bethe ansatz and employing Kirchhoff's rule for quantum wires, we derive a general closed-form expression for the transmission and reflection amplitudes of a two-port quantum network. We show that the transport through a molecule with complex internal structures can be reduced to that of a single two-port scattering unit, which contains all the information of the original composite molecule. Our method allows for the calculation of the transmission coefficient for various types of individual molecular modules giving rise to different resonant transport behaviors such as the Breit-Wigner, Fano, and Mach-Zehnder resonances. As an illustration, we first re-derive the transmittance of the Aharonov-Bohm ring, and then we apply our formulation to N identical parity-time (PT)-symmetric potentials, connected in series as well as in parallel. It is shown that the spectral singularities and PT-symmetric transitions of single scattering cells may be observed in coupled systems. Such transitions may occur at the same or distinct values of the critical parameters, depending on the connection modes under which the scattering objects are coupled.

Two-probe STM experiments at the atomic level

Direct characterization of planar atomic or molecular scale devices and circuits on a supporting surface by multi-probe measurements requires unprecedented stability of single atom contacts and manipulation of scanning probes over large, nanometer scale area with atomic precision. In this work, we describe the full methodology behind atomically defined two-probe scanning tunneling microscopy (STM) experiments performed on a model system: dangling bond dimer wire supported on a hydrogenated germanium (0 0 1) surface. We show that 70 nm long atomic wire can be simultaneously approached by two independent STM scanners with exact probe to probe distance reaching down to 30 nm. This allows direct wire characterization by two-probe I-V characteristics at distances below 50 nm. Our technical results presented in this work open a new area for multi-probe research, which can be now performed with precision so far accessible only by single-probe scanning probe microscopy (SPM) experiments.

Molecular attochemistry in non-polar liquid environments: ultrafast charge migration dynamics through gold-thiolate and gold-selenolate linkages

Molecular attosecond science has already started contributing to our fundamental understanding of ultrafast purely electron dynamics in isolated molecules under vacuum. Extending attosecond science to the liquid phase is expected to offer new insight into the influence of a surrounding solvent environment on the attosecond electron dynamics in solvated molecules. A systematic theoretical investigation of the attochemistry of solvated molecules would help one design attosecond experiments under ambient conditions to explore the attochemistry in a liquid environment. With this goal in mind, for the first time, we have explored the attochemistry of molecules surrounded by different non-polar solvent environments. For this work, we have focused on the attosecond charge conduction through gold-thiolate and gold-selenolate linkages following the vertical ionization of the S/Se(CH₃)-CH₂-phenyl-X unit anchored to a gold dimeric cluster (Au₂), where X represents either a strong electron donating N(CH₃)₂ group or a strong electron withdrawing NO₂ group. To model solvation effects on the attochemistry of molecules containing gold-chalcogen linkages, we have used an implicit solvent model (Polarizable Continuum Model) under the density functional theory (DFT) formalism for non-polar solvents. We have found that the charge migration time scale in molecules becomes faster in the presence of the solvent environment as compared to that under vacuum. Charge oscillation does not damp quickly in molecules surrounded by the solvent environment as compared to that under vacuum. Furthermore, the direction of the charge migration may change in molecules when they are surrounded by the solvent environment as compared to that under vacuum. Thus, the present work has laid the foundation, for the first time, for thinking of the attochemistry into the realm of liquids.

Apparent Reversal of Molecular Orbitals Reveals Entanglement

The frontier orbital sequence of individual dicyanovinyl-substituted oligothiophene molecules is studied by means of scanning tunneling microscopy. On NaCl/Cu(111), the molecules are neutral, and the two lowest unoccupied molecular states are observed in the expected order of increasing energy. On NaCl/Cu(311), where the molecules are negatively charged, the sequence of two observed molecular orbitals is reversed, such that the one with one more nodal plane appears lower in energy. These experimental results, in open contradiction with a single-particle interpretation, are explained by a many-body theory predicting a strongly entangled doubly charged ground state.

The Role of Through-Space Interactions in Modulating Constructive and Destructive Interference Effects in Benzene

Quantum interference effects, whether constructive or destructive, are key to predicting and understanding the electrical conductance of single molecules. Here, through theory and experiment, we investigate a family of benzene-like molecules that exhibit both constructive and destructive interference effects arising due to more than one contact between the molecule and each electrode. In particular, we demonstrate that the π-system of meta-coupled benzene can exhibit constructive interference and its para-coupled analog can exhibit destructive interference, and vice versa, depending on the specific through-space interactions. As a peculiarity, this allows a meta-coupled benzene molecule to exhibit higher conductance than a para-coupled benzene. Our results provide design principles for molecular electronic components with high sensitivity to through-space interactions and demonstrate that increasing the number of contacts between the molecule and electrodes can both increase and decrease the conductance.

Unexpected Interactions between Alkyl Straps and Pyridine Ligands in Sulfur-Strapped Porphyrin Nanorings

Strapped or “basket-handle” porphyrins have been investigated previously as hemoglobin mimics and catalysts. The facial selectivity of their interactions with axial ligands is a sensitive test for noncovalent bonding. Here the binding of pyridyl ligands to zinc porphyrins with thioester-linked alkyl straps is investigated in solution by NMR spectroscopy and UV–vis titration, and in the solid state by X-ray crystallography. We expected that coordination of the axial ligand would occur on the less hindered face of the porphyrin, away from the strap. Surprisingly, attractive interactions between the strap and the ligand direct axial coordination to the strapped face of the porphyrin, except when the strap is short and tight. The strapped porphyrins were incorporated into π-conjugated cyclic porphyrin hexamers using template-directed synthesis. The strap and the sulfur substituents are located either inside or outside the porphyrin nanoring, depending on the length of the strap. Six-porphyrin nanorings with outwardly pointing sulfur anchors were prepared for exploring quantum interference effects in single-molecule charge transport.

Thermally Activated Tunneling Transition in a Photoswitchable Single-Molecule Electrical Junction

Exploring the charge transport process in molecular junctions is essential to the development of molecular electronics. Here, we investigate the temperature-dependent charge transport mechanism of carbon electrode-diarylethene single-molecule junctions, which possess photocontrollable molecular orbital energy levels due to reversible photoisomerization of individual diarylethenes between open and closed conformations. Both the experimental results and theoretical calculations consistently demonstrate that the vibronic coupling (thermally activated at the proper temperature) drives the transition of charge transport in the junctions from coherent tunneling to incoherent transport. Due to the subtle electron-phonon coupling effect, incoherent transport in the junctions proves to have different activation energies, depending on the photoswitchable molecular energy levels of two different conformations. These results improve fundamental understanding of charge transport mechanisms in molecular junctions and should lead to the rapid development of functional molecular devices toward practical applications.

Kondo blockade due to quantum interference in single-molecule junctions

Molecular electronics offers unique scientific and technological possibilities, resulting from both the nanometre scale of the devices and their reproducible chemical complexity. Two fundamental yet different effects, with no classical analogue, have been demonstrated experimentally in single-molecule junctions: quantum interference due to competing electron transport pathways, and the Kondo effect due to entanglement from strong electronic interactions. Here we unify these phenomena, showing that transport through a spin-degenerate molecule can be either enhanced or blocked by Kondo correlations, depending on molecular structure, contacting geometry and applied gate voltages. An exact framework is developed, in terms of which the quantum interference properties of interacting molecular junctions can be systematically studied and understood. We prove that an exact Kondo-mediated conductance node results from destructive interference in exchange-cotunneling. Nonstandard temperature dependences and gate-tunable conductance peaks/nodes are demonstrated for prototypical molecular junctions, illustrating the intricate interplay of quantum effects beyond the single-orbital paradigm.

Constructive quantum interference in a bis-copper six-porphyrin nanoring

The exchange interaction, J, between two spin centres is a convenient measure of through bond electronic communication. Here, we investigate quantum interference phenomena in a bis-copper six-porphyrin nanoring by electron paramagnetic resonance spectroscopy via measurement of the exchange coupling between the copper centres. Using an analytical expression accounting for both dipolar and exchange coupling to simulate the time traces obtained in a double electron electron resonance experiment, we demonstrate that J can be quantified to high precision even in the presence of significant through-space coupling. We show that the exchange coupling between two spin centres is increased by a factor of 4.5 in the ring structure with two parallel coupling paths as compared to an otherwise identical system with just one coupling path, which is a clear signature of constructive quantum interference.

Quantum interference in charge transport is attracting interest with applications in nanoelectronics and quantum computing. Here, the authors present a method for quantifying electronic transmission through molecules, and demonstrate constructive quantum interference in a molecule with two identical, parallel coupling paths.

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

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

Molecular Orbital Rule for Quantum Interference in Weakly Coupled Dimers: Low-Energy Giant Conductivity Switching Induced by Orbital Level Crossing

Destructive quantum interference (QI) in molecular junctions has attracted much attention in recent years. It can tune the conductance of molecular devices dramatically, which implies numerous potential applications in thermoelectric and switching applications. There are several schemes that address and rationalize QI in single molecular devices. Dimers play a particular role in this respect because the QI signal may disappear, depending on the dislocation of monomers. We derive a simple rule that governs the occurrence of QI in weakly coupled dimer stacks of both alternant and nonalternant polyaromatic hydrocarbons (PAHs) and extends the Tada-Yoshizawa scheme. Starting from the Green's function formalism combined with the molecular orbital expansion approach, it is shown that QI-induced antiresonances and their energies can be predicted from the amplitudes of the respective monomer terminal molecular orbitals. The condition is illustrated for a toy model consisting of two hydrogen molecules and applied within density functional calculations to alternant dimers of oligo(phenylene-ethynylene) and nonalternant PAHs. Minimal dimer structure modifications that require only a few millielectronvolts and lead to an energy crossing of the essentially preserved monomer orbitals are shown to result in giant conductance switching ratios.

Discriminating single-molecule sensing by crown-ether-based molecular junctions

Crown-ether molecules are well known to selectively bind alkali atoms, so by incorporating these within wires, any change in electrical conductance of the wire upon binding leads to discriminating sensing. Using a density functional theory-based approach to quantum transport, we investigate the potential sensing capabilities of single-molecule junctions formed from crown ethers attached to anthraquinone units, which are in turn attached to gold electrodes via alkyl chains. We calculate the change in electrical conductance for binding of three different alkali ions (lithium, sodium, and potassium). Depending on the nature of the ionic analyte, the conductance is enhanced by different amounts. This change in electrical conductance is due to charge transfer from the ion to molecular wire causing the molecular resonances to shift closer to the electrode Fermi energy.

Conductance in a bis-terpyridine based single molecular breadboard circuit

Controlling charge flow in single molecule circuits with multiple electrical contacts and conductance pathways is a much sought after goal in molecular electronics. In this joint experimental and theoretical study, we advance the possibility of creating single molecule breadboard circuits through an analysis of the conductance of a bis-terpyridine based molecule (TP1). The TP1 molecule can adopt multiple conformations through relative rotations of 7 aromatic rings and can attach to electrodes in 61 possible single and multi-terminal configurations through 6 pyridyl groups. Despite this complexity, we show that it is possible to extract well defined conductance features for the TP1 breadboard and assign them rigorously to the underlying constituent circuits. Mechanically controllable break-junction (MCBJ) experiments on the TP1 molecular breadboard show an unprecedented 4 conductance states spanning a range 10 -2G0 to 10 -7G0. Quantitative theoretical examination of the conductance of TP1 reveals that combinations of 5 types of single terminal 2-5 ring subcircuits are accessed as a function of electrode separation to produce the distinct conductance steps observed in the MCBJ experiments. We estimate the absolute conductance for each single terminal subcircuit and its percentage contribution to the 4 experimentally observed conductance states. We also provide a detailed analysis of the role of quantum interference and thermal fluctuations in modulating conductance within the subcircuits of the TP1 molecular breadboard. Finally, we discuss the possible development of molecular circuit theory and experimental advances necessary for mapping conductance through complex single molecular breadboard circuits in terms of their constituent subcircuits.