Thermal conductance of single-molecule junctions.

Single-molecule junctions have been extensively used to probe properties as diverse as electrical conduction1-3, light emission4, thermoelectric energy conversion5,6, quantum interference7,8, heat dissipation9,10 and electronic noise11 at atomic and molecular scales. However, a key quantity of current interest-the thermal conductance of single-molecule junctions-has not yet been directly experimentally determined, owing to the challenge of detecting minute heat currents at the picowatt level. Here we show that picowatt-resolution scanning probes previously developed to study the thermal conductance of single-metal-atom junctions12, when used in conjunction with a time-averaging measurement scheme to increase the signal-to-noise ratio, also allow quantification of the much lower thermal conductance of single-molecule junctions. Our experiments on prototypical Au-alkanedithiol-Au junctions containing two to ten carbon atoms confirm that thermal conductance is to a first approximation independent of molecular length, consistent with detailed ab initio simulations. We anticipate that our approach will enable systematic exploration of thermal transport in many other one-dimensional systems, such as short molecules and polymer chains, for which computational predictions of thermal conductance13-16 have remained experimentally inaccessible.

Electrical Conductance and Thermopower of ß-Substituted Porphyrin Molecular Junctions─Synthesis and Transport.

Molecular junctions offer significant potential for enhancing thermoelectric power generation. Quantum interference effects and associated sharp features in electron transmission are expected to enable the tuning and enhancement of thermoelectric properties in molecular junctions. To systematically explore the effect of quantum interferences, we designed and synthesized two new classes of porphyrins, P1 and P2, with two methylthio anchoring groups in the 2,13- and 2,12-positions, respectively, and their Zn complexes, Zn-P1 and Zn-P2. Past theory suggests that P1 and Zn-P1 feature destructive quantum interference in single-molecule junctions with gold electrodes and may thus show high thermopower, while P2 and Zn-P2 do not. Our detailed experimental single-molecule break-junction studies of conductance and thermopower, the latter being the first ever performed on porphyrin molecular junctions, revealed that the electrical conductance of the P1 and Zn-P1 junctions is relatively close, and the same holds for P2 and Zn-P2, while there is a 6 times reduction in the electrical conductance between P1 and P2 type junctions. Further, we observed that the thermopower of P1 junctions is slightly larger than for P2 junctions, while Zn-P1 junctions show the largest thermopower and Zn-P2 junctions show the lowest. We relate the experimental results to quantum transport theory using first-principles approaches. While the conductance of P1 and Zn-P1 junctions is robustly predicted to be larger than those of P2 and Zn-P2, computed thermopowers depend sensitively on the level of theory and the single-molecule junction geometry. However, the predicted large difference in conductance and thermopower values between Zn-P1 and Zn-P2 derivatives, suggested in previous model calculations, is not supported by our experimental and theoretical findings.

Designing mechanosensitive molecules from molecular building blocks: A genetic algorithm-based approach.

Single molecules can be used as miniaturized functional electronic components, when contacted by macroscopic electrodes. Mechanosensitivity describes a change in conductance for a certain change in electrode separation and is a desirable feature for applications such as ultrasensitive stress sensors. We combine methods of artificial intelligence with high-level simulations based on electronic structure theory to construct optimized mechanosensitive molecules from predefined, modular molecular building blocks. In this way, we overcome time-consuming, inefficient trial-and-error cycles in molecular design. We unveil the black box machinery usually connected to methods of artificial intelligence by presenting all-important evolutionary processes. We identify the general features that characterize well-performing molecules and point out the crucial role of spacer groups for increased mechanosensitivity. Our genetic algorithm provides a powerful way to search chemical space and to identify the most promising molecular candidates.

Substitution Pattern Controlled Quantum Interference in [2.2]Paracyclophane-Based Single-Molecule Junctions.

Quantum interference (QI) of electron waves passing through a single-molecule junction provides a powerful means to influence its electrical properties. Here, we investigate the correlation between substitution pattern, conductance, and mechanosensitivity in [2.2]paracyclophane (PCP)-based molecular wires in a mechanically controlled break junction experiment. The effect of the meta versus para connectivity in both the central PCP core and the phenyl ring connecting the terminal anchoring group is studied. We find that the meta-phenyl-anchored PCP yields such low conductance levels that molecular features cannot be resolved; in the case of para-phenyl-coupled anchoring, however, large variations in conductance values for modulations of the electrode separation occur for the pseudo-para-coupled PCP core, while this mechanosensitivity is absent for the pseudo-meta-PCP core. The experimental findings are interpreted in terms of QI effects between molecular frontier orbitals by theoretical calculations based on density functional theory and the Landauer formalism.

Voltage-Induced Rearrangements in Atomic-Size Contacts.

We study voltage-induced conductance changes of Pb, Au, Al, and Cu atomic contacts. The experiments are performed in vacuum at low temperature using mechanically controllable break junctions. We determine switching histograms, i.e., distribution functions of switching voltages and switching currents, as a function of the conductance. We observe a clear material dependence: Au reveals the highest and almost conductance-independent switching voltage, while Al has the lowest with a pronounced dependence on the conductance. The theoretical study uses density functional theory and a generalized Langevin equation considering the pumping of particular phonon modes. We identify a runaway voltage as the threshold at which the pumping destabilizes the atomic arrangement. We find qualitative agreement between the average switching voltage and the runaway voltage regarding the material and conductance dependence and contact-to-contact variation of the average characteristic voltages, suggesting that the phonon pumping is a relevant mechanism driving the rearrangements in the experimental contacts.

Harnessing Exciton-Exciton Annihilation in Two-Dimensional Semiconductors.

Strong many-body interactions in two-dimensional (2D) semiconductors give rise to efficient exciton-exciton annihilation (EEA). This process is expected to result in the generation of unbound high energy carriers. Here, we report an unconventional photoresponse of van der Waals heterostructure devices resulting from efficient EEA. Our heterostructures, which consist of monolayer transition metal dichalcogenide (TMD), hexagonal boron nitride (hBN), and few-layer graphene, exhibit photocurrent when photoexcited carriers possess sufficient energy to overcome the high energy barrier of hBN. Interestingly, we find that the device exhibits moderate photocurrent quantum efficiency even when the semiconducting TMD layer is excited at its ground exciton resonance despite the high exciton binding energy and large transport barrier. Using ab initio calculations, we show that EEA yields highly energetic electrons and holes with unevenly distributed energies depending on the scattering condition. Our findings highlight the dominant role of EEA in determining the photoresponse of 2D semiconductor optoelectronic devices.

Dynamical Coulomb Blockade as a Local Probe for Quantum Transport.

Quantum fluctuations are imprinted with valuable information about transport processes. Experimental access to this information is possible, but challenging. We introduce the dynamical Coulomb blockade (DCB) as a local probe for fluctuations in a scanning tunneling microscope (STM) and show that it provides information about the conduction channels. In agreement with theoretical predictions, we find that the DCB disappears in a single-channel junction with increasing transmission following the Fano factor, analogous to what happens with shot noise. Furthermore we demonstrate local differences in the DCB expected from changes in the conduction channel configuration. Our experimental results are complemented by ab initio transport calculations that elucidate the microscopic nature of the conduction channels in our atomic-scale contacts. We conclude that probing the DCB by STM provides a technique complementary to shot noise measurements for locally resolving quantum transport characteristics.

Electric-field control of single-molecule tautomerization.

The electric field is an important parameter to vary in a single-molecule experiment, because it can directly affect the charge distribution around the molecule. Yet, performing such an experiment with a well-defined electric field for a model chemical reaction at an interface has proven to be extremely difficult. Here, by combining a graphene field-effect transistor and a gate-tunable scanning tunneling microscope (STM), we reveal how this strategy enables the intramolecular H atom transfer of a metal-free macrocycle to be controlled with an external field. Experiments and theory both elucidate how the energetic barrier to tautomerization decreases with increasing electric field. The consistency between the two results demonstrates the potential in using electric fields to engineer molecular switching mechanisms that are ubiquitous in nanoscale electronic devices.

Heat dissipation in atomic-scale junctions.

Atomic and single-molecule junctions represent the ultimate limit to the miniaturization of electrical circuits. They are also ideal platforms for testing quantum transport theories that are required to describe charge and energy transfer in novel functional nanometre-scale devices. Recent work has successfully probed electric and thermoelectric phenomena in atomic-scale junctions. However, heat dissipation and transport in atomic-scale devices remain poorly characterized owing to experimental challenges. Here we use custom-fabricated scanning probes with integrated nanoscale thermocouples to investigate heat dissipation in the electrodes of single-molecule ('molecular') junctions. We find that if the junctions have transmission characteristics that are strongly energy dependent, this heat dissipation is asymmetric--that is, unequal between the electrodes--and also dependent on both the bias polarity and the identity of the majority charge carriers (electrons versus holes). In contrast, junctions consisting of only a few gold atoms ('atomic junctions') whose transmission characteristics show weak energy dependence do not exhibit appreciable asymmetry. Our results unambiguously relate the electronic transmission characteristics of atomic-scale junctions to their heat dissipation properties, establishing a framework for understanding heat dissipation in a range of mesoscopic systems where transport is elastic--that is, without exchange of energy in the contact region. We anticipate that the techniques established here will enable the study of Peltier effects at the atomic scale, a field that has been barely explored experimentally despite interesting theoretical predictions. Furthermore, the experimental advances described here are also expected to enable the study of heat transport in atomic and molecular junctions--an important and challenging scientific and technological goal that has remained elusive.

Multipole-based distance-dependent screening of Coulomb integrals.

We derive a new estimate for two-electron repulsion integrals (ERIs), when evaluated within a local atomic basis set. It is based on the multipole expansion and provides a rigorous upper bound of an ERI for well-separated charge distributions. The scheme is generally applicable in any formalism that uses ERIs. We employ it here to screen for potentially negligible contributions in the calculation of the Fock exchange matrix. Using Gaussian basis functions, we show that the estimate allows us to accelerate the construction of the exchange matrix by up to a factor of two without introducing further approximations.

Doping hepta-alanine with tryptophan: A theoretical study of its effect on the electrical conductance of peptide-based single-molecule junctions.

Motivated by a recent experiment [C. Guo et al., Proc. Natl. Acad. Sci. U. S. A. 113, 10785 (2016)], we carry out a theoretical study of electron transport through peptide-based single-molecule junctions. We analyze the pristine hepta-alanine and its functionalizations with a single tryptophan unit, which is placed in three different locations along the backbone. Contrary to expectations from the experiment on self-assembled monolayers, we find that insertion of tryptophan does not raise the electrical conductance and that the resulting peptides instead remain insulating in the framework of a coherent transport picture. The poor performance of these molecules as conductors can be ascribed to the strongly off-resonant transport and low electrode-molecule coupling of the frontier orbitals. Although the introduction of tryptophan increases the energy of the highest occupied molecular orbital (HOMO) of the peptides in the gas phase, the new HOMO states are localized on the tryptophan unit and therefore essentially do not contribute to coherent charge transport.

Influence of Quantum Interference on the Thermoelectric Properties of Molecular Junctions.

Molecular junctions offer unique opportunities for controlling charge transport on the atomic scale and for studying energy conversion. For example, quantum interference effects in molecular junctions have been proposed as an avenue for highly efficient thermoelectric power conversion at room temperature. Toward this goal, we investigated the effect of quantum interference on the thermoelectric properties of molecular junctions. Specifically, we employed oligo(phenylene ethynylene) (OPE) derivatives with a para-connected central phenyl ring ( para-OPE3) and meta-connected central ring ( meta-OPE3), which both covalently bind to gold via sulfur anchoring atoms located at their ends. In agreement with predictions from ab initio modeling, our experiments on both single molecules and monolayers show that meta-OPE3 junctions, which are expected to exhibit destructive interference effects, yield a higher thermopower (with ∼20 µV/K) compared with para-OPE3 (with ∼10 µV/K). Our results show that quantum interference effects can indeed be employed to enhance the thermoelectric properties of molecular junctions.

Large Conductance Variations in a Mechanosensitive Single-Molecule Junction.

An appealing feature of molecular electronics is the possibility of inducing changes in the orbital structure through external stimuli. This can provide functionality on the single-molecule level that can be employed for sensing or switching purposes if the associated conductance changes are sizable upon application of the stimuli. Here, we show that the room-temperature conductance of a spring-like molecule can be mechanically controlled up to an order of magnitude by compressing or elongating it. Quantum-chemistry calculations indicate that the large conductance variations are the result of destructive quantum interference effects between the frontier orbitals that can be lifted by applying either compressive or tensile strain to the molecule. When periodically modulating the electrode separation, a conductance modulation at double the driving frequency is observed, providing a direct proof for the presence of quantum interference. Furthermore, oscillations in the conductance occur when the stress built up in the molecule is high enough to allow the anchoring groups to move along the surface in a stick-slip-like fashion. The mechanical control of quantum interference effects results in the largest-gauge factor reported for single-molecule devices up to now, which may open the door for applications in, e.g., a nanoscale mechanosensitive sensing device that is functional at room temperature.

Charge Transport through Ferrocene 1,1'-Diamine Single-Molecule Junctions.

The charge transport through ferrocene 1,1'-diamine (FDA) molecules between gold electrodes is investigated using the mechanically controllable break junction technique combined with a theoretical framework of density functional theory simulations to understand the physics of these molecular junctions. The characteristic conductances of the molecule are measured at low bias as well as current-voltage (IV) characteristics. By fitting the IV characteristics to the single-level model, the values for the position of the molecular level, mainly responsible for the transport, and its coupling to the leads, are obtained. The influence of the binding sites, molecular conformation, and electrode distance are systematically studied from a theoretical perspective. While a strong dependence of conductance on the adsorption geometry is found, the decrease of conductance as a function of electrode distance arises mainly from a decrease of coupling strength of the molecular electronic orbitals through a reduced overlap and, to a lesser extent, from a shift of their alignment with respect to the Fermi energy.

Redox-Active Tetraruthenium Macrocycles Built from 1,4-Divinylphenylene-Bridged Diruthenium Complexes.

Metallamacrocylic tetraruthenium complexes were generated by treatment of 1,4-divinylphenylene-bridged diruthenium complexes with functionalized 1,3-benzene dicarboxylic acids and characterized by HR ESI-MS and multinuclear NMR spectroscopy. Every divinylphenylene diruthenium subunit is oxidized in two consecutive one-electron steps with half-wave potential splittings in the range of 250 to 330 mV. Additional, smaller redox-splittings between the +/2+ and 0/+ and the 3+/4+ and 2+/3+ redox processes, corresponding to the first and the second oxidations of every divinylphenylene diruthenium entity, are due to electrostatic effects. The lack of electronic coupling through bond or through space is explained by the nodal properties of the relevant molecular orbitals and the lateral side-by-side arrangement of the divinylphenylene linkers. The polyelectrochromic behavior of the divinylphenylene diruthenium precursors is retained and even amplified in these metallamacrocyclic structures. EPR studies down to T=4 K indicate that the dications 1-H(2+) and 1-OBu(2+) are paramagnetic. The dications and the tetracation of macrocycle 3-H display intense (dications) or weak (3-H(4+) ) EPR signals. Quantum chemical calculations indicate that the four most stable conformers of the macrocycles are largely devoid of strain. Bond parameters, energies as well as charge and spin density distributions of model macrocycle 5-H(Me) were calculated for the different charge and spin states.

Highly Ordered Surface Self-Assembly of Fe4 Single Molecule Magnets.

Single molecule magnets (SMMs) have attracted considerable attention due to low-temperature magnetic hysteresis and fascinating quantum effects. The investigation of these properties requires the possibility to deposit well-defined monolayers or spatially isolated molecules within a well-controlled adsorption geometry. Here we present a successful fabrication of self-organized arrays of Fe4 SMMs on hexagonal boron nitride (h-BN) on Rh(111) as template. Using a rational design of the ligand shell optimized for surface assembly and electrospray as a gentle deposition method, we demonstrate how to obtain ordered arrays of molecules forming perfect hexagonal superlattices of tunable size, from small islands to an almost perfect monolayer. High-resolution low temperature scanning tunneling microscopy (STM) reveals that the Fe4 molecule adsorbs on the substrate in a flat geometry, meaning that its magnetic easy axis is perpendicular to the surface. By scanning tunneling spectroscopy (STS) and density functional theory (DFT) calculations, we infer that the majority- and minority-spin components of the spin-split lowest unoccupied molecular orbital (LUMO) can be addressed separately on a submolecular level.

Quantum thermopower of metallic atomic-size contacts at room temperature.

We report conductance and thermopower measurements of metallic atomic-size contacts, namely gold and platinum, using a scanning tunneling microscope (STM) at room temperature. We find that few-atom gold contacts have an average negative thermopower, whereas platinum contacts present a positive thermopower, showing that for both metals, the sign of the thermopower in the nanoscale differs from that of bulk wires. We also find that the magnitude of the thermopower exhibits minima at the maxima of the conductance histogram in the case of gold nanocontacts while for platinum it presents large fluctuations. Tight-binding calculations and Green's function techniques, together with molecular dynamics simulations, show that these observations can be understood in the context of the Landauer-Büttiker picture of coherent transport in atomic-scale wires. In particular, we show that the differences in the thermopower between these two metals are due to the fact that the elastic transport is dominated by the 6s orbitals in the case of gold and by the 5d orbitals in the case of platinum.

Single-molecule conductance of a chemically modified, π-extended tetrathiafulvalene and its charge-transfer complex with F4TCNQ.

We describe the synthesis and single-molecule electrical transport properties of a molecular wire containing a π-extended tetrathiafulvalene (exTTF) group and its charge-transfer complex with F4TCNQ. We form single-molecule junctions using the in situ break junction technique using a homebuilt scanning tunneling microscope with a range of conductance between 10 G0 down to 10(-7) G0. Within this range we do not observe a clear conductance signature of the neutral parent molecule, suggesting either that its conductance is too low or that it does not form a stable junction. Conversely, we do find a clear conductance signature in the experiments carried out on the charge-transfer complex. Due to the fact we expected this species to have a higher conductance than the neutral molecule, we believe this supports the idea that the conductance of the neutral molecule is very low, below our measurement sensitivity. This idea is further supported by theoretical calculations. To the best of our knowledge, these are the first reported single-molecule conductance measurements on a molecular charge-transfer species.

How substituents tune quantum interference in meta-OPE3 molecular junctions to control thermoelectric transport.

Quantum interference (QI) can strongly affect electric and thermoelectric properties of molecular junctions (MJs). So far, however, a limited number of experimental studies have explored the influence of QI on thermoelectric transport in MJs. To address this open point, we synthesized derivatives of meta-OPE3 with an electron-withdrawing nitro (-NO2) substituent or an electron-donating N,N-dimethyl amine (-NMe2) substituent, attached at two different positions of the central phenylene ring, and systematically studied the electrical conductance and thermopower of the corresponding gold-molecule-gold junctions. We show that (i) the electrical conductance of MJs depends weakly on the polarity of the substituents but strongly on the substitution position and (ii) MJs with the N,N-dimethyl amine group feature a higher thermopower than MJs with the nitro group. We also present calculations based on first principles, which explain these trends and show that the transport properties are highly sensitive to microscopic details in junctions, exhibiting destructive QI features.

Benchmarking break-junction techniques: electric and thermoelectric characterization of naphthalenophanes.

Break-junction techniques provide the possibility to study electric and thermoelectric properties of single-molecule junctions in great detail. These techniques rely on the same principle of controllably breaking metallic contacts in order to create single-molecule junctions, whilst keeping track of the junction's conductance. Here, we compare results from mechanically controllable break junction (MCBJ) and scanning tunneling microscope (STM) methods, while characterizing conductance properties of the same novel mechanosensitive para- and meta-connected naphtalenophane compounds. In addition, thermopower measurements are carried out for both compounds using the STM break junction (STM-BJ) technique. For the conductance experiments, the same data processing using a clustering analysis is performed. We obtain to a large extent similar results for both methods, although values of conductance and stretching lengths for the STM-BJ technique are slightly larger in comparison with the MCBJ. STM-BJ thermopower experiments show similar Seebeck coefficients for both compounds. An increase in the Seebeck coefficient is revealed, whilst the conductance decreases, after which it saturates at around 10 µV K-1. This phenomenon is studied theoretically using a tight binding model. It shows that changes of molecule-electrode electronic couplings combined with shifts of the resonance energies explain the correlated behavior of conductance and Seebeck coefficient.