Oligoyne Molecular Junctions for Efficient Room Temperature Thermoelectric Power Generation

Thermoelectric Properties of Porphyrin Nano Rings: A Theoretical and Modelling Investigation

Propagation of De Broglie waves through nanomolecular junctions is greatly affected by molecular topology changes, which in turn plays a key role in determining the electronic and thermoelectric properties of source|molecule|drain junctions. The probing and realization of the constructive quantum interference (CQI) and a destructive quantum interference (DQI) are well established in this work. The critical role of quantum interference (QI) in governing and enhancing the transmission coefficient T(E), thermopower (S), power factor (P) and electronic figure of merit (ZelT) of porphyrin nanorings has been investigated using a combination of density functional theory (DFT) methods, a tight binding (Hückel) modelling (TBHM) and quantum transport theory (QTT). Remarkably, DQI not only dominates the asymmetric molecular pathways and lowering T(E), but also improves the thermoelectric properties.

Large Mechanosensitive Thermoelectric Enhancement in Metallo-Organic Magnetic Molecules

Organic materials are promising candidates for thermoelectric cooling and energy harvesting at room temperature. However, their electrical conductance (G) and Seebeck coefficient (S) need to be improved to make them technologically competitive. Therefore, radically new strategies need to be developed to tune their thermoelectric properties. Here, we demonstrate that G and S can be tuned mechanically in paramagnetic metallocenes, and their thermoelectric properties can be significantly enhanced by the application of mechanical forces. With a 2% junction compression, the full thermoelectric figure of merit is enhanced by more than 200 times. We demonstrate that this is because spin transport resonances in paramagnetic metallocenes are strongly sensitive to the interaction between organic ligands and the metal center, which is not the case in their diamagnetic analogue. These results open a new avenue for the development of organic thermoelectric materials for cooling future quantum computers and generating electricity from low-grade energy sources.

Quantum bath augmented stochastic nonequilibrium atomistic simulations for molecular heat conduction

Classical molecular dynamics (MD) has been shown to be effective in simulating heat conduction in certain molecular junctions since it inherently takes into account some essential methodological components which are lacking in the quantum Landauer-type transport model, such as many-body full force-field interactions, anharmonicity effects and nonlinear responses for large temperature biases. However, the classical MD reaches its limit in the environments where the quantum effects are significant (e.g. with low-temperatures substrates, presence of extremely high frequency molecular modes). Here, we present an atomistic simulation methodology for molecular heat conduction that incorporates the quantum Bose-Einstein statistics into an "effective temperature" in the form of a modified Langevin equation. We show that the results from such a quasi-classical effective temperature MD method deviates drastically when the baths temperature approaches zero from classical MD simulations and the results converge to the classical ones when the bath approaches the high-temperature limit, which makes the method suitable for full temperature range. In addition, we show that our quasi-classical thermal transport method can be used to model the conducting substrate layout and molecular composition (e.g. anharmonicities, high-frequency modes). Anharmonic models are explicitly simulated via the Morse potential and compared to pure harmonic interactions to show the effects of anharmonicities under quantum colored bath setups. Finally, the chain length dependence of heat conduction is examined for one-dimensional polymer chains placed in between quantum augmented baths.

Exploring relationships between chemical structure and molecular conductance: from α,ω-functionalised oligoynes to molecular circuits

The quantum circuit rule (QCR) allows estimation of the conductance of molecular junctions, electrode|X-bridge-Y|electrode, by considering the molecule as a series of independent scattering regions associated with the anchor groups (X, Y) and bridge, provided the numerical parameters that characterise the anchor groups (a_X, a_Y) and molecular backbones (b_B) are known. Single-molecule conductance measurements made with a series of α,ω-substituted oligoynes (X-{(CC)_N}-X, N = 1, 2, 3, 4), functionalised by terminal groups, X (4-thioanisole (C₆H₄SMe), 5-(3,3-dimethyl-2,3-dihydrobenzo[b]thiophene) (DMBT), 4-aniline (C₆H₄NH₂), 4-pyridine (Py), capable of serving as 'anchor groups' to contact the oligoyne fragment within a molecular junction, have shown the expected exponential dependence of molecular conductance, G, with the number of alkyne repeating units. In turn, this allows estimation of the anchor (a_i) and backbone (b_i) parameters. Using these values, together with previously determined parameters for other molecular fragments, the QCR is found to accurately estimate the junction conductance of more complex molecular circuits formed from smaller components assembled in series.

Enhanced Thermoelectricity in Metal-[60]Fullerene-Graphene Molecular Junctions

The thermoelectric properties of molecular junctions consisting of a metal Pt electrode contacting [60]fullerene derivatives covalently bound to a graphene electrode have been studied by using a conducting-probe atomic force microscope (c-AFM). The [60]fullerene derivatives are covalently linked to the graphene via two meta-connected phenyl rings, two para-connected phenyl rings, or a single phenyl ring. We find that the magnitude of the Seebeck coefficient is up to nine times larger than that of Au-C₆₀-Pt molecular junctions. Moreover, the sign of the thermopower can be either positive or negative depending on the details of the binding geometry and on the local value of the Fermi energy. Our results demonstrate the potential of using graphene electrodes for controlling and enhancing the thermoelectric properties of molecular junctions and confirm the outstanding performance of [60]fullerene derivatives.

Exploring seebeck-coefficient fluctuations in endohedral-fullerene, single-molecule junctions

For the purpose of creating single-molecule junctions, which can convert a temperature difference ΔT into a voltage ΔV via the Seebeck effect, it is of interest to screen molecules for their potential to deliver high values of the Seebeck coefficient S = -ΔV/ΔT. Here we demonstrate that insight into molecular-scale thermoelectricity can be obtained by examining the widths and extreme values of Seebeck histograms. Using a combination of experimental scanning-tunnelling-microscopy-based transport measurements and density-functional-theory-based transport calculations, we study the electrical conductance and Seebeck coefficient of three endohedral metallofullerenes (EMFs) Sc₃N@C₈₀, Sc₃C₂@C₈₀, and Er₃N@C₈₀, which based on their structures, are selected to exhibit different degrees of charge inhomogeneity and geometrical disorder within a junction. We demonstrate that standard deviations in the Seebeck coefficient σ_S of EMF-based junctions are correlated with the geometric standard deviation σ and the charge inhomogeneity σ_q. We benchmark these molecules against C₆₀ and demonstrate that both σ_q, σ_S are the largest for Sc₃C₂@C₈₀, both are the smallest for C₆₀ and for the other EMFs, they follow the order Sc₃C₂@C₈₀ > Sc₃N@C₈₀ > Er₃N@C₈₀ > C₆₀. A large value of σ_S is a sign that a molecule can exhibit a wide range of Seebeck coefficients, which means that if orientations corresponding to high values can be selected and controlled, then the molecule has the potential to exhibit high-performance thermoelectricity. For the EMFs studied here, large values of σ_S are associated with distributions of Seebeck coefficients containing both positive and negative signs, which reveals that all these EMFs are bi-thermoelectric materials.

Thermoelectric Enhancement in Single Organic Radical Molecules

Organic thermoelectric materials have potential for wearable heating, cooling, and energy generation devices at room temperature. For this to be technologically viable, high-conductance (G) and high-Seebeck-coefficient (S) materials are needed. For most semiconductors, the increase in S is accompanied by a decrease in G. Here, using a combined experimental and theoretical investigation, we demonstrate that a simultaneous enhancement of S and G can be achieved in single organic radical molecules, thanks to their intrinsic spin state. A counterintuitive quantum interference (QI) effect is also observed in stable Blatter radical molecules, where constructive QI occurs for a meta-connected radical, leading to further enhancement of thermoelectric properties. Compared to an analogous closed-shell molecule, the power factor is enhanced by more than 1 order of magnitude in radicals. These results open a new avenue for the development of organic thermoelectric materials operating at room temperature.

Electronic and transport property of two-dimensional boron phosphide sheet

Using density functional theory (DFT) approach, we have investigated the effect of strain on the electronic properties of two-dimensional (2D) boron phosphide (BP) sheet. With the increase in uniaxial and biaxial tensile strain band gap increases while band gap decreases and becomes metallic with the increase in uniaxial and biaxial compressive strain. Electrical and thermal transport properties of zigzag and armchair 2D BP sheets have been explored using nonequilibrium Green's function formalism (NEGF) and the changes in the nature of I-V characteristics with the application of strain have been reported. The magnitude of the current decreases with the increase of strain value along transport direction for both zigzag and armchair 2D BP sheets. For unstrained systems, the magnitude of current is nearly same for both zigzag and armchair 2D BP sheets. However, for a particular strain value, magnitude of current is more for zigzag sheet compared to armchair sheet. Though both zigzag and armchair 2D BP sheets have reasonably high ZT_e which confirms its potentiality for designing efficient thermoelectric material but zigzag sheet is more preferable for thermoelectric application compared to armchair sheet due to its higher ZT_e in comparison to armchair sheet_.

Thermoelectric Properties of Pristine Graphyne and the BN-Doped Graphyne Family

In this paper, we have investigated the thermoelectric properties of BN-doped graphynes and compared them with respect to their pristine counterpart using first-principles calculations. The effect of temperature on the thermoelectric properties has also been explored. Pristine γ-graphyne is an intrinsic band gap semiconductor and the band gap significantly increases due to the incorporation of boron and nitrogen atoms into the system, which simultaneously results in high electrical conductivity, a large Seebeck coefficient, and low thermal conductivity. The Seebeck coefficient for all these systems is significantly higher than that of conventional thermoelectric materials, suggesting their potential in thermoelectric applications. Among all the considered systems, the "graphyne-like BN sheet" has the highest electrical conductance and lowest thermal conductance, ensuring its superiority in thermoelectric properties over the other studied systems. We find that a maximum full ZT of ∼6 at room temperature is accessible in the "graphyne-like BN sheet".

Molecular Structure-(Thermo)electric Property Relationships in Single-Molecule Junctions and Comparisons with Single- and Multiple-Parameter Models

The most probable single-molecule conductance of each member of a series of 12 conjugated molecular wires, 6 of which contain either a ruthenium or platinum center centrally placed within the backbone, has been determined. The measurement of a small, positive Seebeck coefficient has established that transmission through these molecules takes place by tunneling through the tail of the HOMO resonance near the middle of the HOMO-LUMO gap in each case. Despite the general similarities in the molecular lengths and frontier-orbital compositions, experimental and computationally determined trends in molecular conductance values across this series cannot be satisfactorily explained in terms of commonly discussed "single-parameter" models of junction conductance. Rather, the trends in molecular conductance are better rationalized from consideration of the complete molecular junction, with conductance values well described by transport calculations carried out at the DFT level of theory, on the basis of the Landauer-Büttiker model.

The Effect of Anchor Group on the Phonon Thermal Conductance of Single Molecule Junctions

There is a worldwide race to convert waste heat to useful energy using thermoelectric materials. Molecules are attractive candidates for thermoelectricity because they can be synthesised with the atomic precision, and intriguing properties due to quantum effects such as quantum interference can be induced at room temperature. Molecules are also expected to show a low thermal conductance that is needed to enhance the performance of thermoelectric materials. Recently, the technological challenge of measuring the thermal conductance of single molecules was overcome. Therefore, it is timely to develop strategies to reduce their thermal conductance for high performance thermoelectricity. In this paper and for the first time, we exploit systematically the effect of anchor groups on the phonon thermal conductance of oligo (phenylene ethynylene) (OPE3) molecules connected to gold electrodes via pyridyl, thiol, methyl sulphide and carbodithioate anchor groups. We show that thermal conductance is affected significantly by the choice of anchor group. The lowest and highest thermal conductances were obtained in the OPE3 with methyl sulphide and carbodithioate anchor groups, respectively. The thermal conductance of OPE3 with thiol anchor was higher than that with methyl sulphide but lower than the OPE3 with pyridyl anchor group.

Thermoelectric properties of a double-dot system in serial configuration within the Coulomb blockade regime

In the present work, we theoretically study thermoelectric transport and heat transfer in a junction including a double quantum dot in a serial configuration coupled to nonferromagnetic electrodes. We focus on the electron transport within the Coulomb blockade regime in the limit of strong intradot interactions between electrons. It is shown that under these conditions, characteristics of thermoelectric transport in such systems strongly depend on electron occupation on the dots and on interdot Coulomb interactions. We demonstrate that these factors may lead to a heat current rectification and analyze potentialities of a double-dot in a serial configuration as a heat diod.

Charge and heat current rectification by a double-dot system within the Coulomb blockade regime

Nanoscale rectifiers are known to have significant nanoelectronic and nanoheatronic applications. In the present work we theoretically analyze rectifying properties of a junction including a couple of quantum dots asymmetrically coupled to the electrodes. The charge and heat current rectification in the system is controlled by the dots occupation numbers and interdot Coulomb interactions. We examine the dependencies of the rectification ratio on the electron energy levels on the dots, on the intensity of electron-electron interactions, on the gate and bias voltages and on the thermal gradients applied across the system. It is shown that the considered double-dot system possesses significant potentialities as a common as well as a heat diode.

Constructive Quantum Interference in Single-Molecule Benzodichalcogenophene Junctions

Heteroatom substitution into the cores of alternant, aromatic hydrocarbons containing only even-membered rings is attracting increasing interest as a method of tuning their electrical conductance. Here, the effect of heteroatom substitution into molecular cores of non-alternant hydrocarbons, containing odd-membered rings, is examined. Benzodichalcogenophene (BDC) compounds are rigid, planar π-conjugated structures, with molecular cores containing five-membered rings fused to a six-membered aryl ring. To probe the sensitivity or resilience of constructive quantum interference (CQI) in these non-bipartite molecular cores, two C₂ -symmetric molecules (I and II) and one asymmetric molecule (III) were investigated. I (II) contains S (O) heteroatoms in each of the five-membered rings, while III contains an S in one five-membered ring and an O in the other. Differences in their conductances arise primarily from the longer S-C and shorter O-C bond lengths compared with the C-C bond and the associated changes in their resonance integrals. Although the conductance of III is significantly lower than the conductances of the others, CQI was found to be resilient and persist in all molecules.

Radical enhancement of molecular thermoelectric efficiency

There is a worldwide race to find materials with high thermoelectric efficiency to convert waste heat to useful energy in consumer electronics and server farms. Here, we propose a radically new method to enhance simultaneously the electrical conductance and thermopower and suppress heat transport through ultra-thin materials formed by single radical molecules. This leads to a significant enhancement of room temperature thermoelectric efficiency. The proposed strategy utilises the formation of transport resonances due to singly occupied spin orbitals in radical molecules. This enhances the electrical conductance by a couple of orders of magnitude in molecular junctions formed by nitroxide radicals compared to the non-radical counterpart. It also increases the Seebeck coefficient to high values of 200 μV K^-1. Consequently, the power factor increases by more than two orders of magnitude. In addition, the asymmetry and destructive phonon interference that was induced by the stable organic radical side group significantly decreases the phonon thermal conductance. The enhanced power factor and suppressed thermal conductance in the nitroxide radical lead to the significant enhancement of room temperature ZT to values ca. 0.8. Our result confirms the great potential of stable organic radicals to form ultra-thin film thermoelectric materials with unprecedented thermoelectric efficiency.

Enhanced thermopower in covalent graphite-molecule contacts

The Seebeck effect is very attractive for technological applications as it leads to the direct conversion of heat into electricity. One of the key quantities determining the efficiency of such conversion is the thermopower S. In this paper we explore theoretically what electronic properties are responsible for the Seebeck effect in molecular junctions with graphite or graphene electrodes. We propose that S can be enhanced because of the combined effect of the dip in the density of states at the Fermi energy of these materials and the molecular resonance. Then to understand the impact of the covalent vs. non-covalent molecule-carbon bonding we calculate from first principles the electronic and transport properties of graphite/molecule/Au junctions, where both types of bonding have been reported experimentally. We ultimately predict that S is about 120 μV K^-1 at room temperature for a 3,5-dimethyl-4-aminobenzene (DMAB) molecule covalently attached to the graphite electrode. This value is one order of magnitude larger than the typical values measured to date for molecular junctions and it is a signature of the direct C-C molecule-graphite bond. Finally we also demonstrate how one can control not just the absolute magnitude of S, but also its sign by designing the graphite-molecule contact. Our results lead the way towards the use of junctions with molecules covalently attached to a C-based substrate as possible new improved platforms for molecular thermoelectric devices.

Thermal Transport through Single-Molecule Junctions

Molecular junctions exhibit a rich and tunable set of thermal transport phenomena. However, the predicted high thermoelectric efficiencies, phonon quantum interference effects, rectification, and nonlinear heat transport properties of organic molecules are yet to be verified because suitable experimental techniques have been missing. Here, by combining the break junction technique with suspended heat-flux sensors with picowatt per Kelvin sensitivity, we measured the thermal and electrical conductance of single organic molecules at room temperature simultaneously. We used this method to study the thermal transport properties of two model systems, namely, dithiol-oligo(phenylene ethynylene) and octane dithiol junctions with gold electrodes. In agreement with our density functional theory and phase-coherent transport calculations, we show that heat transport across these systems is governed by the phonon mismatch between the molecules and the metallic electrodes. This work represents the first measurement of thermal transport through single molecules and opens new opportunities for studying heat management at the nanoscale level.

Quantum and Phonon Interference-Enhanced Molecular-Scale Thermoelectricity

Simultaneous engineering of electron and phonon transport through nanoscale molecular junctions is fundamental to the development of high-performance thermoelectric materials for the conversion of waste heat into electricity and cooling. Here, we demonstrate a systematic improvement of the room-temperature thermoelectric figure of merit (ZT) of molecular junctions. This is achieved by phonon interference (PI)-suppressed thermal conductance and quantum interference-enhanced electrical conductance and Seebeck coefficient. This strategy leads to a significant enhancement of ZT from low values ca. 10^-6 in oligo(phenylene-ethynylene) (OPE2) to the record values of 2.4 in dinitro-functionalized OPE2 (DOPE2). The dinitro functionalization also considerably enhances ZT of biphenyl-dithiol (BDT) and bipyridyl molecular junctions. Remarkably, the energy levels of electron-withdrawing nitro groups are hardly changed from one molecule to the other. Because of this generic feature, a resonance transport in the vicinity of Fermi energy of electrodes is formed leading to a significant improvement of Seebeck coefficient and ZT of all derivatives. For example, the Seebeck coefficient enhances from 10.8 μV/K in BDT to -470 μV/K in dinitro-BDT (DBDT). In addition, destructive PI due to the nitro groups suppresses phonon thermal conductance, for example, from 20 pW/K in BDT to 11 pW/K in DBDT at room temperature. We also demonstrate that quantum and PI-enhanced single-molecule thermoelectric efficiency is conserved when parallel molecules are placed between gold electrodes. These results promise to remove the key roadblocks and open new avenues to exploit functionalized organic molecules for thermoelectric energy harvesting and cooling.

Ballistic and diffusive vibrational energy transport in molecules

Energy transport in molecules is essential for many areas of science and technology. Strong covalent bonds of a molecular backbone can facilitate the involvement of the molecule's high-frequency modes in energy transport, which, under certain conditions, makes the transport fast and efficient. We discuss such conditions and describe various transport regimes in molecules, including ballistic, diffusive, directed diffusion, and intermediate regime cases, in light of recently developed experimental and theoretical approaches.

Cross-plane conductance through a graphene/molecular monolayer/Au sandwich

The functionalities offered by single-molecule electrical junctions are yet to be translated into monolayer or few-layer molecular films, where making effective and reproducible electrical contact is one of the challenging bottlenecks. Here we take a significant step in this direction by demonstrating that excellent electrical contact can be made with a monolayer biphenyl-4,4'-dithiol (BPDT) molecular film, sandwiched between gold and graphene electrodes. This sandwich device structure is advantageous, because the current flows through the molecules to the gold substrate in a 'cross-plane' manner, perpendicular to the plane of graphene, yielding high-conductance devices. We elucidate the nature of the cross-plane graphene/molecule/Au transport using quantum transport calculations and introduce a simple analytical model, which captures generic features of the current-voltage characteristic. Asymmetry in junction properties results from the disparity in electrode electrical properties, the alignment of the BPDT HOMO-LUMO energy levels and the specific characteristics of the graphene electrode. The experimental observation of scalability of junction properties within the junction area, in combination with a theoretical description of the transmission probability of the thiol-graphene contact, demonstrates that between 10% and 100% of the molecules make contact with the electrodes, which is several orders of magnitude greater than that achieved to date in the literature.

Stable-radicals increase the conductance and Seebeck coefficient of graphene nanoconstrictions

Nanoscale thermoelectricity is an attractive target technology, because it can convert ambient heat into electricity for powering embedded devices in the internet of things. We demonstrate that the thermoelectric performance of graphene nanoconstrictions can be significantly enhanced by the presence of stable radical adsorbates, because radical molecules adsorbed on the graphene nanoconstrictions create singly-occupied orbitals in the vicinity of Fermi energy. This in turn leads to sharp features in their transmission functions close to Fermi energy, which increases the electrical conductance and Seebeck coefficient of the nanoconstrictions. This is a generic feature of radical adsorbates and can be employed in the design of new thermoelectric devices and materials.

Probing Lewis acid-base interactions in single-molecule junctions

A novel strategy to regulate the tunneling mechanism for charge transport through an organoborane wire via Lewis acid-base interactions has been developed. A change from LUMO- to HOMO-dominated charge transport upon the addition of the fluoride is verified both experimentally and theoretically.

Theory of electron, phonon and spin transport in nanoscale quantum devices

At the level of fundamental science, it was recently demonstrated that molecular wires can mediate long-range phase-coherent tunnelling with remarkably low attenuation over a few nanometre even at room temperature. Furthermore, a large mean free path has been observed in graphene and other graphene-like two-dimensional materials. These create the possibility of using quantum and phonon interference to engineer electron and phonon transport through nanoscale junctions for a wide range of applications such as molecular switches, sensors, piezoelectricity, thermoelectricity and thermal management. To understand transport properties of such devices, it is crucial to calculate their electronic and phononic transmission coefficients. The aim of this tutorial article is to outline the basic theoretical concepts and review the state-of-the-art theoretical and mathematical techniques needed to treat electron, phonon and spin transport in nanoscale molecular junctions. This helps not only to explain new phenomenon observed experimentally but also provides a vital design tool to develop novel nanoscale quantum devices.

Rise of Conjugated Poly-ynes and Poly(Metalla-ynes): From Design Through Synthesis to Structure-Property Relationships and Applications

Conjugated poly-ynes and poly(metalla-ynes) constitute an important class of new materials with potential application in various domains of science. The key factors responsible for the diverse usage of these materials is their intriguing and tunable chemical and photophysical properties. This review highlights fascinating advances made in the field of conjugated organic poly-ynes and poly(metalla-ynes) incorporating group 4-11 metals. This includes several important aspects of conjugated poly-ynes viz. synthetic protocols, bonding, electronic structure, nature of luminescence, structure-property relationships, diverse applications, and concluding remarks. Furthermore, we delineated the future directions and challenges in this particular area of research.

Towards molecular electronic devices based on 'all-carbon' wires

Nascent molecular electronic devices based on linear 'all-carbon' wires attached to gold electrodes through robust and reliable C-Au contacts are prepared via efficient in situ sequential cleavage of trimethylsilyl end groups from an oligoyne, Me₃Si-(C[triple bond, length as m-dash]C)₄-SiMe₃ (1). In the first stage of the fabrication process, removal of one trimethylsilyl (TMS) group in the presence of a gold substrate, which ultimately serves as the bottom electrode, using a stoichiometric fluoride-driven process gives a highly-ordered monolayer, Au|C[triple bond, length as m-dash]CC[triple bond, length as m-dash]CC[triple bond, length as m-dash]CC[triple bond, length as m-dash]CSiMe₃ (Au|C₈SiMe₃). In the second stage, treatment of Au|C₈SiMe₃ with excess fluoride results in removal of the remaining TMS protecting group to give a modified monolayer Au|C[triple bond, length as m-dash]CC[triple bond, length as m-dash]CC[triple bond, length as m-dash]CC[triple bond, length as m-dash]CH (Au|C₈H). The reactive terminal C[triple bond, length as m-dash]C-H moiety in Au|C₈H can be modified by 'click' reactions with (azidomethyl)ferrocene (N₃CH₂Fc) to introduce a redox probe, to give Au|C₆C₂N₃HCH₂Fc. Alternatively, incubation of the modified gold substrate supported monolayer Au|C₈H in a solution of gold nanoparticles (GNPs), results in covalent attachment of GNPs on top of the film via a second alkynyl carbon-Au σ-bond, to give structures Au|C₈|GNP in which the monolayer of linear, 'all-carbon' C₈ chains is sandwiched between two macroscopic gold contacts. The covalent carbon-surface bond as well as the covalent attachment of the metal particles to the monolayer by cleavage of the alkyne C-H bond is confirmed by surface-enhanced Raman scattering (SERS). The integrity of the carbon chain in both Au|C₆C₂N₃HCH₂Fc systems and after formation of the gold top-contact electrode in Au|C₈|GNP is demonstrated through electrochemical methods. The electrical properties of these nascent metal-monolayer-metal devices Au|C₈|GNP featuring 'all-carbon' molecular wires were characterised by sigmoidal I-V curves, indicative of well-behaved junctions free of short circuits.

The Conductance of Porphyrin-Based Molecular Nanowires Increases with Length

High electrical conductance molecular nanowires are highly desirable components for future molecular-scale circuitry, but typically molecular wires act as tunnel barriers and their conductance decays exponentially with length. Here, we demonstrate that the conductance of fused-oligo-porphyrin nanowires can be either length independent or increase with length at room temperature. We show that this negative attenuation is an intrinsic property of fused-oligo-porphyrin nanowires, but its manifestation depends on the electrode material or anchor groups. This highly desirable, nonclassical behavior signals the quantum nature of transport through such wires. It arises because with increasing length the tendency for electrical conductance to decay is compensated by a decrease in their highest occupied molecular orbital-lowest unoccupied molecular orbital gap. Our study reveals the potential of these molecular wires as interconnects in future molecular-scale circuitry.

MoS2 nano flakes with self-adaptive contacts for efficient thermoelectric energy harvesting

We examine the potential of the low-dimensional material MoS2 for the efficient conversion of waste heat to electricity via the Seebeck effect. Recently monolayer MoS2 nano flakes with self-adaptive Mo6S6 contacts were formed, which take advantage of mechanical stability and chemical covalent bonding to the MoS2. Here, we study the thermoelectric properties of these junctions by calculating their conductance, thermopower and thermal conductance due to both electrons and phonons. We show that thermoelectric figures of merit ZT as high as ∼2.8 are accessible in these junctions, independent of the flake size and shape, provided the Fermi energy is close to a band edge. We show that Nb dopants as substituents for Mo atoms can be used to tune the Fermi energy, and despite the associated inhomogeneous broadening, room temperature values as high as ZT ∼ 0.6 are accessible, increasing to 0.8 at 500 K.

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.

Strain-induced bi-thermoelectricity in tapered carbon nanotubes

We show that carbon-based nanostructured materials are a novel testbed for controlling thermoelectricity and have the potential to underpin the development of new cost-effective environmentally-friendly thermoelectric materials. In single-molecule junctions, it is known that transport resonances associated with the discrete molecular levels play a key role in the thermoelectric performance, but such resonances have not been exploited in carbon nanotubes (CNTs). Here we study junctions formed from tapered CNTs and demonstrate that such structures possess transport resonances near the Fermi level, whose energetic location can be varied by applying strain, resulting in an ability to tune the sign of their Seebeck coefficient. These results reveal that tapered CNTs form a new class of bi-thermoelectric materials, exhibiting both positive and negative thermopower. This ability to change the sign of the Seebeck coefficient allows the thermovoltage in carbon-based thermoelectric devices to be boosted by placing CNTs with alternating-sign Seebeck coefficients in tandem.

High cross-plane thermoelectric performance of metallo-porphyrin molecular junctions

We investigated the thermoelectric properties of flat-stacked 5,15-diphenylporphyrins containing divalent metal ions Ni, Co, Cu or Zn, which are strongly coordinated with the nitrogens of pyridyl coated gold electrodes. Changing metal atom has little effect on the thermal conductance due to the phonons. The room-temperature Seebeck coefficients of these junctions are rather high, ranging from 90 μV K^-1 for Cu, Ni and Zn-porphyrins to -16 μV K^-1 for Co-porphyrin. These values could be further increased by lowering molecular energy levels relative to the DFT-predicted Fermi energy. In contrast, the phonon contribution to the thermal conductance of these junctions is rather insensitive to the choice of metal atom. The thermopower, thermal conductance and electrical conductance combined to yield the room-temperature values for the thermoelectric figure of merit ZT ranging from 1.6 for Cu porphyrin to ∼0.02 for Ni-porphyrin.

Peltier cooling in molecular junctions

The study of thermoelectricity in molecular junctions is of fundamental interest for the development of various technologies including cooling (refrigeration) and heat-to-electricity conversion ^1-4 . Recent experimental progress in probing the thermopower (Seebeck effect) of molecular junctions ^5-9 has enabled studies of the relationship between thermoelectricity and molecular structure ^10,11 . However, observations of Peltier cooling in molecular junctions-a critical step for establishing molecular-based refrigeration-have remained inaccessible. Here, we report direct experimental observations of Peltier cooling in molecular junctions. By integrating conducting-probe atomic force microscopy ^12,13 with custom-fabricated picowatt-resolution calorimetric microdevices, we created an experimental platform that enables the unified characterization of electrical, thermoelectric and energy dissipation characteristics of molecular junctions. Using this platform, we studied gold junctions with prototypical molecules (Au-biphenyl-4,4'-dithiol-Au, Au-terphenyl-4,4''-dithiol-Au and Au-4,4'-bipyridine-Au) and revealed the relationship between heating or cooling and charge transmission characteristics. Our experimental conclusions are supported by self-energy-corrected density functional theory calculations. We expect these advances to stimulate studies of both thermal and thermoelectric transport in molecular junctions where the possibility of extraordinarily efficient energy conversion has been theoretically predicted ^2-4,14 .

Connectivity-driven bi-thermoelectricity in heteroatom-substituted molecular junctions

To improve the thermoelectric performance of molecular junctions formed by polyaromatic hydrocarbon (PAH) cores, we present a new strategy for enhancing their Seebeck coefficient by utilizing connectivities with destructive quantum interference combined with heteroatom substitution.

Thermoelectricity in vertical graphene-C60-graphene architectures

Recent studies of single-molecule thermoelectricity have identified families of high-performance molecules. However, in order to translate this discovery into practical thin-film energy-harvesting devices, there is a need for an understanding of the fundamental issues arising when such junctions are placed in parallel. This is relevant because controlled scalability might be used to boost electrical and thermoelectric performance over the current single-junction paradigm. As a first step in this direction, we investigate here the properties of two C₆₀ molecules placed in parallel and sandwiched between top and bottom graphene electrodes. In contrast with classical conductors, we find that increasing the number of parallel junctions from one to two can cause the electrical conductance to increase by more than a factor of 2. Furthermore, we show that the Seebeck coefficient is sensitive to the number of parallel molecules sandwiched between the electrodes, whereas classically it should be unchanged. This non-classical behaviour of the electrical conductance and Seebeck coefficient are due to inter-junction quantum interference, mediated by the electrodes, which leads to an enhanced response in these vertical molecular devices.

Robust Molecular Anchoring to Graphene Electrodes

Recent advances in the engineering of picoscale gaps between electroburnt graphene electrodes provide new opportunities for studying electron transport through electrostatically gated single molecules. But first we need to understand and develop strategies for anchoring single molecules to such electrodes. Here, for the first time we present a systematic theoretical study of transport properties using four different modes of anchoring zinc-porphyrin monomer, dimer, and trimer molecular wires to graphene electrodes. These involve either amine anchor groups, covalent C-C bonds to the edges of the graphene, or coupling via π-π stacking of planar polyaromatic hydrocarbons formed from pyrene or tetrabenzofluorene (TBF). π-π stacked pyrene anchors are particularly stable, which may be advantageous for forming robust single-molecule transistors. Despite their planar, multiatom coupling to the electrodes, pyrene anchors can exhibit both destructive interference and different degrees of constructive interference, depending on their connectivity to the porphyrin wire, which makes them attractive also for thermoelectricity. TBF anchors are more weakly coupled to both the graphene and the porphyrin wires and induce negative differential conductance at finite source-drain voltages. Furthermore, although direct C-C covalent bonding to the edges of graphene electrodes yields the highest electrical conductance, electron transport is significantly affected by the shape and size of the graphene electrodes because the local density of states at the carbon atoms connecting the electrode edges to the molecule is sensitive to the electrode surface shape. This sensitivity suggests that direct C-C bonding may be the most desirable for sensing applications. The ordering of the low-bias electrical conductances with different anchors is as follows: direct C-C coupling > π-π stacking with the pyrene anchors > direct coupling via amine anchors > π-π stacking with TBF anchors. Despite this dependency of conductances on the mode of anchoring, the decay of conductance with the length of the zinc-porphyrin wires is relatively insensitive with the associated attenuation factor β lying between 0.9 and 0.11 Å^-1.

High-performance thermoelectricity in edge-over-edge zinc-porphyrin molecular wires

If high efficiency organic thermoelectric materials could be identified, then these would open the way to a range of energy harvesting technologies and Peltier coolers using flexible and transparent thin-film materials. We have compared the thermoelectric properties of three zinc porphyrin (ZnP) dimers and a ZnP monomer and found that the "edge-over-edge" dimer formed from stacked ZnP rings possesses a high electrical conductance, negligible phonon thermal conductance and a high Seebeck coefficient of the order of 300 μV K^-1. These combine to yield a predicted room-temperature figure of merit of ZT ≈ 4, which is the highest room-temperature ZT ever reported for a single organic molecule. This high value of ZT is a consequence of the low phonon thermal conductance arising from the stacked nature of the porphyrin rings, which hinders phonon transport through the edge-over-edge molecule and enhances the Seebeck coefficient.

Tuning the Seebeck coefficient of naphthalenediimide by electrochemical gating and doping

We investigate the sign and magnitude of the single-molecule Seebeck coefficient of naphthalenediimide (NDI) under the influence of electrochemical gating and doping. The molecule consists of a NDI core with two alkyl chains in the bay-area position, connected to gold electrodes via benzothiophene (DBT) anchor groups. By switching between the neutral, radical and di-anion charge states, we are able to tune the molecular energy levels relative to the Fermi energy of the electrodes. The resulting single-molecule room-temperature Seebeck coefficents of the three charge states are -294.5 μV K^-1, 122 μV K^-1 and 144 μV K^-1 respectively and the room-temperature power factors are 4.4 × 10^-5 W m^-1 K^-2, 3 × 10^-5 W m^-1 K^-2 and 8.2 × 10^-4 W m^-1 K^-2. As a further strategy for optimising thermoelectric properties, we also investigate the effect on both phonon and electron transport of doping the NDI with either an electron donor (TTF) or an electron acceptor (TCNE). We find that doping by TTF increases the room-temperature Seebeck coefficient and power factor from -73.7 μV K^-1 and 2.6 × 10^-7 W m^-1 K^-2 for bare NDI to -105 μV K^-1 and 3.6 × 10^-4 W m^-1 K^-2 in presence of TTF. The low thermal conductance of NDI-TTF, combined with the higher Seebeck coefficient and higher electrical conductance lead to a maximum thermoelectric figure of merit of ZT = 1.2, which is higher than that of bare NDI in several orders of magnitude. This demonstrates that both the sign and magnitude of NDI Seebeck coefficient can be tuned reversibly by electrochemical gating and doping, suggesting that such redox active molecules are attractive materials for ultra-thin-film thermoelectric devices.

Thermoelectric efficiency of molecular junctions

Focus of the review is on experimental set-ups and theoretical proposals aimed to enhance thermoelectric performances of molecular junctions. In addition to charge conductance, the thermoelectric parameter commonly measured in these systems is the thermopower, which is typically rather low. We review recent experimental outcomes relative to several junction configurations used to optimize the thermopower. On the other hand, theoretical calculations provide estimations of all the thermoelectric parameters in the linear and non-linear regime, in particular of the thermoelectric figure of merit and efficiency, completing our knowledge of molecular thermoelectricity. For this reason, the review will mainly focus on theoretical studies analyzing the role of not only electronic, but also of the vibrational degrees of freedom. Theoretical results about thermoelectric phenomena in the coherent regime are reviewed focusing on interference effects which play a significant role in enhancing the figure of merit. Moreover, we review theoretical studies including the effects of molecular many-body interactions, such as electron-vibration couplings, which typically tend to reduce the efficiency. Since a fine tuning of many parameters and coupling strengths is required to optimize the thermoelectric conversion in molecular junctions, new theoretically proposed set-ups are discussed in the conclusions.

Exploring quantum interference in heteroatom-substituted graphene-like molecules

If design principles for controlling quantum interference in single molecules could be elucidated and verified, then this will lay the foundations for exploiting such effects in nanoscale devices and thin-film materials. When the core of a graphene-like polyaromatic hydrocarbon (PAH) is weakly coupled to external electrodes by atoms i and j, the single-molecule electrical conductance σij depends on the choice of connecting atoms i,j. Furthermore, provided the Fermi energy is located between the HOMO and LUMO, conductance ratios σij/σlm corresponding to different connectivities i,j and l,m are determined by quantum interference within the PAH core. In this paper, we examine how such conductance ratios change when one of the carbon atoms within the 'parent' PAH core is replaced by a heteroatom to yield a 'daughter' molecule. For bipartite parental cores, in which odd-numbered sites are connected to even-numbered sites only, the effect of heteroatom substitution onto an odd-numbered site is summarized by the following qualitative rules: (a) when i and j are odd, both parent and daughter have low conductances, (b) when i is odd and j is even, or vice versa both parent and daughter have high conductances and (c) when i,j are both even, the parent has a low conductance and the daughter a high conductance. These rules are verified by comparison with density-functional calculations on naphthalene, anthracene, pyrene and anthanthrene cores connected via two different anchor groups to gold electrodes.

Identification of a positive-Seebeck-coefficient exohedral fullerene

If fullerene-based thermoelectricity is to become a viable technology, then fullerenes exhibiting both positive and negative Seebeck coefficients are needed. C60 is known to have a negative Seebeck coefficient and therefore in this paper we address the challenge of identifying a positive-Seebeck-coefficient fullerene. We investigated the thermoelectric properties of single-molecule junctions of the exohedral fullerene C50Cl10 connected to gold electrodes and found that it indeed possesses a positive Seebeck coefficient. Furthermore, in common with C60, the Seebeck coefficient can be increased by placing more than one C50Cl10 in series. For a single C50Cl10, we find S = +8 μV K(-1) and for two C50Cl10's in series we find S = +30 μV K(-1). We also find that the C50Cl10 monomer and dimer have power factors of 0.5 × 10(-5) W m(-1) K(-2) and 6.0 × 10(-5) W m(-1) K(-2) respectively. These results demonstrate that exohedral fullerenes provide a new class of thermoelectric materials with desirable properties, which complement those of all-carbon fullerenes, thereby enabling the boosting of the thermovoltage in all-fullerene tandem structures.

Tuning the thermoelectric properties of metallo-porphyrins

We investigated the thermoelectric properties of metalloporphyrins connected by thiol anchor groups to gold electrodes. By varying the transition metal-centre over the family Mn, Co, Ni, Cu, Fe, and Zn we are able to tune the molecular energy levels relative to the Fermi energy of the electrodes. The resulting single-molecule room-temperature thermopowers range from almost zero for Co and Cu centres, to +80 μV K(-1) and +230 μV K(-1) for Ni and Zn respectively. In contrast, the thermopowers with Mn(II) or Fe(II) metal centres are negative and lie in the range -280 to -260 μV K(-1). Complexing these with a counter anion to form Fe(III) and Mn(III) changes both the sign and magnitude of their thermopowers to +218 and +95 respectively. The room-temperature power factors of Mn(II), Mn(III), Fe(III), Zn and Fe(II) porphyrins are predicted to be 5.9 × 10(-5) W m(-1) K(-2), 5.4 × 10(-4) W m(-1) K(-2), 9.5 × 10(-4) W m(-1) K(-2), 1.6 × 10(-4) W m(-1) K(-2) and 2.3 × 10(-4) W m(-1) K(-2) respectively, which makes these attractive materials for molecular-scale thermoelectric devices.

Redox-Dependent Franck-Condon Blockade and Avalanche Transport in a Graphene-Fullerene Single-Molecule Transistor

We report transport measurements on a graphene-fullerene single-molecule transistor. The device architecture where a functionalized C60 binds to graphene nanoelectrodes results in strong electron-vibron coupling and weak vibron relaxation. Using a combined approach of transport spectroscopy, Raman spectroscopy, and DFT calculations, we demonstrate center-of-mass oscillations, redox-dependent Franck-Condon blockade, and a transport regime characterized by avalanche tunnelling in a single-molecule transistor.