Charge-state assignment of nanoscale single-electron transistors from their current-voltage characteristics

Stable Unpaired Electron States in the Lu-Lu Bond Leading to the Absence of Odd-Even Parity in the Kondo Effect of Lu2@C82 Transistors

Spin qubits constructed in endohedral fullerenes benefit from the protective shielding of the carbon cage, which effectively mitigates external decoherence and enables ultralong coherence times. However, endohedral fullerene spin qubits face the challenge of charge transfer in complex electrical environments, such as during qubit readout or large-scale integration, which can induce spin state modifications. In this study, we developed transistors based on the endohedral fullerene Lu2@C82 and observed the absence of parity dependence in the Kondo effect; this result was contradictory to the typical behavior of the Kondo effect observed in C60. Density functional theory calculations revealed that upon electron loss, a spin-1/2 electron predominantly from the s-orbitals formed in the Lu-Lu bond and its orbital energy was significantly lower than that of the highest occupied molecular orbital. Based on these results, Lu2@C82 held stable unpaired electron states across multiple charge states and has potential applications in spin quantum devices.

Radical Anions of Porphyrin Molecular Wires: Delocalization and Dynamics

The delocalization length of charge carriers in organic semiconductors influences their mobility and is an important factor in the design of functional materials. Here, we have studied the radical anions of a series of linear and cyclic butadiyne-linked porphyrin oligomers using CW-EPR, 1H Mims ENDOR and NIR/MIR spectroelectrochemistry together with DFT calculations and multiscale molecular modeling. Low-temperature hyperfine EPR spectroscopy and optical data show that polarons are delocalized nonuniformly over about four porphyrins with most of the spin density on just two units even in the cyclic structures, in which all porphyrin sites are identical. Room temperature CW-EPR spectra indicate a larger spatial distribution of spin density on the EPR time scale. We introduce a combined molecular dynamics simulations and DFT approach to demonstrate that dynamic migration of delocalized polarons can occur in porphyrin oligomers and that this fully accounts for the apparent spin density distribution at room temperature. This method is a powerful tool in both the study and development of molecular wires and molecular electronics.

Quantum interference enhances the performance of single-molecule transistors

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

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

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

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

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

Hydrogen-bond-induced quantum interference in single-molecule junctions of regioisomers

Solvents can play a significant role in tuning the electrical conductance of single-molecule junctions. In this respect, protic solvents offer the potential to form hydrogen bonds with molecular backbones and induce electrostatic gating via their dipole moments. Here we demonstrate that the effect of hydrogen bond formation on conductance depends on whether transport through the junction is controlled by destructive quantum interference (DQI) or constructive quantum interference (CQI). Furthermore, we show that a protic solvent can be used to switch the conductance of single-molecule junctions between the two forms of quantum interference. To explore this possibility, two regioisomers (BIT-Zwitterion and BIT-Neutral) were synthesized and their single-molecule conductances in aprotic and protic solvents were investigated using a scanning-tunneling-microscope-based break junction technique, combined with density functional theory and quantum transport theory. We find that the protic solvent twists the geometry of BIT-Zwitterion by introducing intermolecular hydrogen bonds between the solvent and target molecule. Moreover, it increases the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the molecule by imposing different electrostatic gating on the delocalized HOMO and localized LUMO, leading to a lower conductance compared to that in aprotic solvent. In contrast, the conductance of BIT-Neutral increases due to a transformation from DQI to CQI originating from a change from a planar to a folded conformation in the protic solvent. In addition, the stacking between the two folded moieties produces an extra through-space transport path, which further contributes to conductance. This study demonstrates that combinations of protic solvents and regioisomers present a versatile route to controlling quantum interference and therefore single-molecule conductance, by enabling control of hydrogen bond formation, electrostatic gating and through-space transport.

Exchange-induced spin polarization in a single magnetic molecule junction

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

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

Porphyrins as building blocks for single-molecule devices

Direct measurement of single-molecule electrical transparency by break junction experiments has become a major field of research over the two last decades. This review specifically and comprehensively highlights the use of porphyrins as molecular components and discusses their potential use for the construction of future devices. Throughout the review, the features provided by porphyrins, such as low level misalignments and very low attenuation factors, are shown with numerous examples, illustrating the potential and limitations of these molecular junctions, as well as differences emerging from applied integration/investigation techniques.

Charge transport through extended molecular wires with strongly correlated electrons

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

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

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

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

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

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

Beyond Marcus theory and the Landauer-Büttiker approach in molecular junctions. II. A self-consistent Born approach

Marcus and Landauer-Büttiker approaches to charge transport through molecular junctions describe two contrasting mechanisms of electronic conduction. In previous work, we have shown how these charge transport theories can be unified in the single-level case by incorporating lifetime broadening into the second-order quantum master equation. Here, we extend our previous treatment by incorporating lifetime broadening in the spirit of the self-consistent Born approximation. By comparing both theories to numerically converged hierarchical-equations-of-motion results, we demonstrate that our novel self-consistent approach rectifies shortcomings of our earlier framework, which are present especially in the case of relatively strong electron-vibrational coupling. We also discuss circumstances under which the theory developed here simplifies to the generalized theory developed in our earlier work. Finally, by considering the high-temperature limit of our new self-consistent treatment, we show how lifetime broadening can also be self-consistently incorporated into Marcus theory. Overall, we demonstrate that the self-consistent approach constitutes a more accurate description of molecular conduction while retaining most of the conceptual simplicity of our earlier framework.

Understanding resonant charge transport through weakly coupled single-molecule junctions

Off-resonant charge transport through molecular junctions has been extensively studied since the advent of single-molecule electronics and is now well understood within the framework of the non-interacting Landauer approach. Conversely, gaining a qualitative and quantitative understanding of the resonant transport regime has proven more elusive. Here, we study resonant charge transport through graphene-based zinc-porphyrin junctions. We experimentally demonstrate an inadequacy of non-interacting Landauer theory as well as the conventional single-mode Franck–Condon model. Instead, we model overall charge transport as a sequence of non-adiabatic electron transfers, with rates depending on both outer and inner-sphere vibrational interactions. We show that the transport properties of our molecular junctions are determined by a combination of electron–electron and electron-vibrational coupling, and are sensitive to interactions with the wider local environment. Furthermore, we assess the importance of nuclear tunnelling and examine the suitability of semi-classical Marcus theory as a description of charge transport in molecular devices.

The mechanism of nonadiabatic electron transfer in molecular systems is an important research topic for understanding various chemical reactions. Thomas et al. quantify resonant charge transport through single-molecule junctions as a model system for examining quantum and Marcus theories.