Statistical signature of electrobreakdown in graphene nanojunctions.

Controlled electrobreakdown of graphene is important for the fabrication of stable nanometer-size tunnel gaps, large-scale graphene quantum dots, and nanoscale resistive switches, etc. However, owing to the complex thermal, electronic, and electrochemical processes at the nanoscale that dictate the rupture of graphene, it is difficult to generate conclusions from individual devices. We describe here a way to explore the statistical signature of the graphene electrobreakdown process. Such analysis tells us that feedback-controlled electrobreakdown of graphene in the air first shows signs of joule heating-induced cleaning followed by rupturing of the graphene lattice that is manifested by the lowering of its conductance. We show that when the conductance of the graphene becomes smaller than around 0.1 G0, the effective graphene notch width starts to decrease exponentially slower with time. Further, we show how this signature gets modified as we change the environment and or the substrate. Using statistical analysis, we show that the electrobreakdown under a high vacuum could lead to substrate modification and resistive-switching behavior, without the application of any electroforming voltage. This is attributed to the formation of a semiconducting filament that makes a Schottky barrier with the graphene. We also provide here the statistically extracted Schottky barrier threshold voltages for various substrate studies. Such analysis not only gives a better understanding of the electrobreakdown of graphene but also can serve as a tool in the future for single-molecule diagnostics.

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.

Phase-Coherent Charge Transport through a Porphyrin Nanoribbon.

Since the early days of quantum mechanics, it has been known that electrons behave simultaneously as particles and waves, and now quantum electronic devices can harness this duality. When devices are shrunk to the molecular scale, it is unclear under what conditions does electron transmission remain phase-coherent, as molecules are usually treated as either scattering or redox centers, without considering the wave-particle duality of the charge carrier. Here, we demonstrate that electron transmission remains phase-coherent in molecular porphyrin nanoribbons connected to graphene electrodes. The devices act as graphene Fabry-Pérot interferometers and allow for direct probing of the transport mechanisms throughout several regimes. Through electrostatic gating, we observe electronic interference fringes in transmission that are strongly correlated to molecular conductance across multiple oxidation states. These results demonstrate a platform for the use of interferometric effects in single-molecule junctions, opening up new avenues for studying quantum coherence in molecular electronic and spintronic devices.

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.

Implementation of Quantum Level Addressability and Geometric Phase Manipulation in Aligned Endohedral Fullerene Qudits.

Endohedral nitrogen fullerenes have been proposed as building blocks for quantum information processing due to their long spin coherence time. However, addressability of the individual electron spin levels in such a multiplet system of 4 S3/2 has never been achieved because of the molecular isotropy and transition degeneracy among the Zeeman levels. Herein, by molecular engineering, we lifted the degeneracy by zero-field splitting effects and made the multiple transitions addressable by a liquid-crystal-assisted method. The endohedral nitrogen fullerene derivatives with rigid addends of spiro structure and large aspect ratios of regioselective bis-addition improve the ordering of the spin ensemble. These samples empower endohedral-fullerene-based qudits, in which the transitions between the 4 electron spin levels were respectively addressed and coherently manipulated. The quantum geometric phase manipulation, which has long been proposed for the advantages in error tolerance and gating speed, was implemented in a pure electron spin system using molecules for the first time.

Geometrically Enhanced Thermoelectric Effects in Graphene Nanoconstrictions.

The influence of nanostructuring and quantum confinement on the thermoelectric properties of materials has been extensively studied. While this has made possible multiple breakthroughs in the achievable figure of merit, classical confinement, and its effect on the local Seebeck coefficient has mostly been neglected, as has the Peltier effect in general due to the complexity of measuring small temperature gradients locally. Here we report that reducing the width of a graphene channel to 100 nm changes the Seebeck coefficient by orders of magnitude. Using a scanning thermal microscope allows us to probe the local temperature of electrically contacted graphene two-terminal devices or to locally heat the sample. We show that constrictions in mono- and bilayer graphene facilitate a spatially correlated gradient in the Seebeck and Peltier coefficient, as evidenced by the pronounced thermovoltage Vth and heating/cooling response Δ TPeltier, respectively. This geometry dependent effect, which has not been reported previously in 2D materials, has important implications for measurements of patterned nanostructures in graphene and points to novel solutions for effective thermal management in electronic graphene devices or concepts for single material thermocouples.

Distance Measurement of a Noncovalently Bound Y@C82 Pair with Double Electron Electron Resonance Spectroscopy.

Paramagnetic endohedral fullerenes with long spin coherence times, such as N@C60 and Y@C82, are being explored as potential spin quantum bits (qubits). Their use for quantum information processing requires a way to hold them in fixed spatial arrangements. Here we report the synthesis of a porphyrin-based two-site receptor 1, offering a rigid structure that binds spin-active fullerenes (Y@C82) at a center-to-center distance of 5.0 nm, predicted from molecular simulations. The spin-spin dipolar coupling was measured with the pulsed EPR spectroscopy technique of double electron electron resonance and analyzed to give a distance of 4.87 nm with a small distribution of distances.

Beyond Marcus theory and the Landauer-Büttiker approach in molecular junctions: A unified framework.

Charge transport through molecular junctions is often described either as a purely coherent or a purely classical phenomenon, and described using the Landauer-Büttiker formalism or Marcus theory (MT), respectively. Using a generalised quantum master equation, we here derive an expression for current through a molecular junction modelled as a single electronic level coupled with a collection of thermalised vibrational modes. We demonstrate that the aforementioned theoretical approaches can be viewed as two limiting cases of this more general expression and present a series of approximations of this result valid at higher temperatures. We find that MT is often insufficient in describing the molecular charge transport characteristics and gives rise to a number of artefacts, especially at lower temperatures. Alternative expressions, retaining its mathematical simplicity, but rectifying those shortcomings, are suggested. In particular, we show how lifetime broadening can be consistently incorporated into MT, and we derive a low-temperature correction to the semi-classical Marcus hopping rates. Our results are applied to examples building on phenomenological as well as microscopically motivated electron-vibrational coupling. We expect them to be particularly useful in experimental studies of charge transport through single-molecule junctions as well as self-assembled monolayers.

Conductance enlargement in picoscale electroburnt graphene nanojunctions.

Provided the electrical properties of electroburnt graphene junctions can be understood and controlled, they have the potential to underpin the development of a wide range of future sub-10-nm electrical devices. We examine both theoretically and experimentally the electrical conductance of electroburnt graphene junctions at the last stages of nanogap formation. We account for the appearance of a counterintuitive increase in electrical conductance just before the gap forms. This is a manifestation of room-temperature quantum interference and arises from a combination of the semimetallic band structure of graphene and a cross-over from electrodes with multiple-path connectivity to single-path connectivity just before breaking. Therefore, our results suggest that conductance enlargement before junction rupture is a signal of the formation of electroburnt junctions, with a picoscale current path formed from a single sp(2) bond.

Scaling Limits of Graphene Nanoelectrodes.

Graphene nanogap electrodes have been of recent interest in a variety of fields, ranging from molecular electronics to phase change memories. Several recent reports have highlighted that scaling graphene nanogaps to even smaller sizes is a promising route to more efficient and robust molecular and memory devices. Despite the significant interest, the operating and scaling limits of these electrodes are completely unknown. In this paper, we report on our observations of consistent voltage driven resistance switching in sub-5 nm graphene nanogaps. We find that such electrical switching from an insulating state to a conductive state occurs at very low currents and voltages (0.06 µA and 140 mV), independent of the conditions (room ambient, low temperatures, as well as in vacuum), thus portending potential limits to scaling of functional devices with carbon electrodes. We then associate this phenomenon to the formation and rupture of carbon chains. Using a phase change material in the nanogap as a demonstrator device, fabricated using a self-alignment technique, we show that for gap sizes approaching 1 nm the switching is dominated by such carbon chain formation, creating a fundamental scaling limit for potential devices. These findings have important implications, not only for fundamental science, but also in terms of potential applications.

Field-Effect Control of Graphene-Fullerene Thermoelectric Nanodevices.

Although it was demonstrated that discrete molecular levels determine the sign and magnitude of the thermoelectric effect in single-molecule junctions, full electrostatic control of these levels has not been achieved to date. Here, we show that graphene nanogaps combined with gold microheaters serve as a testbed for studying single-molecule thermoelectricity. Reduced screening of the gate electric field compared to conventional metal electrodes allows control of the position of the dominant transport orbital by hundreds of meV. We find that the power factor of graphene-fullerene junctions can be tuned over several orders of magnitude to a value close to the theoretical limit of an isolated Breit-Wigner resonance. Furthermore, our data suggest that the power factor of an isolated level is only given by the tunnel coupling to the leads and temperature. These results open up new avenues for exploring thermoelectricity and charge transport in individual molecules and highlight the importance of level alignment and coupling to the electrodes for optimum energy conversion in organic thermoelectric materials.

Strong Coupling of Microwave Photons to Antiferromagnetic Fluctuations in an Organic Magnet.

Coupling between a crystal of di(phenyl)-(2,4,6-trinitrophenyl)iminoazanium radicals and a superconducting microwave resonator is investigated in a circuit quantum electrodynamics (circuit QED) architecture. The crystal exhibits paramagnetic behavior above 4 K, with antiferromagnetic correlations appearing below this temperature, and we demonstrate strong coupling at base temperature. The magnetic resonance acquires a field angle dependence as the crystal is cooled down, indicating anisotropy of the exchange interactions. These results show that multispin modes in organic crystals are suitable for circuit QED, offering a platform for their coherent manipulation. They also utilize the circuit QED architecture as a way to probe spin correlations at low temperature.

CF2 -Bridged C60 Fullerene Dimers and their Optical Transitions.

Fullerene dyads bridged with perfluorinated linking groups have been synthesized through a modified arc-discharge procedure. The addition of Teflon inside an arc-discharge reactor leads to the formation of dyads, consisting of two C60 fullerenes bridged by CF2 groups. The incorporation of bridging groups containing electronegative atoms lead to different energy levels and to new features in the photoluminescence spectrum. A suppression of the singlet oxygen photosensitization indicated that the radiative decay from singlet-to-singlet state is favoured against the intersystem crossing singlet-to-triplet transition.

Environment-assisted quantum transport through single-molecule junctions.

Single-molecule electronics has been envisioned as the ultimate goal in the miniaturisation of electronic circuits. While the aim of incorporating single-molecule junctions into modern technology still proves elusive, recent developments in this field have begun to enable experimental investigation of fundamental concepts within the area of chemical physics. One such phenomenon is the concept of environment-assisted quantum transport which has emerged from the investigation of exciton transport in photosynthetic complexes. Here, we study charge transport through a two-site molecular junction coupled to a vibrational environment. We demonstrate that vibrational interactions can significantly enhance the current through specific molecular orbitals. Our study offers a clear pathway towards finding and identifying environment-assisted transport phenomena in charge transport settings.

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.

Quantum Interference in Graphene Nanoconstrictions.

We report quantum interference effects in the electrical conductance of chemical vapor deposited graphene nanoconstrictions fabricated using feedback controlled electroburning. The observed multimode Fabry-Pérot interferences can be attributed to reflections at potential steps inside the channel. Sharp antiresonance features with a Fano line shape are observed. Theoretical modeling reveals that these Fano resonances are due to localized states inside the constriction, which couple to the delocalized states that also give rise to the Fabry-Pérot interference patterns. This study provides new insight into the interplay between two fundamental forms of quantum interference in graphene nanoconstrictions.

Probing the Dipolar Coupling in a Heterospin Endohedral Fullerene-Phthalocyanine Dyad.

Paramagnetic endohedral fullerenes and phthalocyanine (Pc) complexes are promising building blocks for molecular quantum information processing, for which tunable dipolar coupling is required. We have linked these two spin qubit candidates together and characterized the resulting electron paramagnetic resonance properties, including the spin dipolar coupling between the fullerene spin and the copper spin. Having interpreted the distance-dependent coupling strength quantitatively and further discussed the antiferromagnetic aggregation effect of the CuPc moieties, we demonstrate two ways of tuning the dipolar coupling in such dyad systems: changing the spacer group and adjusting the solution concentration.

Opening up three quantum boxes causes classically undetectable wavefunction collapse.

One of the most striking features of quantum mechanics is the profound effect exerted by measurements alone. Sophisticated quantum control is now available in several experimental systems, exposing discrepancies between quantum and classical mechanics whenever measurement induces disturbance of the interrogated system. In practice, such discrepancies may frequently be explained as the back-action required by quantum mechanics adding quantum noise to a classical signal. Here, we implement the "three-box" quantum game [Aharonov Y, et al. (1991) J Phys A Math Gen 24(10):2315-2328] by using state-of-the-art control and measurement of the nitrogen vacancy center in diamond. In this protocol, the back-action of quantum measurements adds no detectable disturbance to the classical description of the game. Quantum and classical mechanics then make contradictory predictions for the same experimental procedure; however, classical observers are unable to invoke measurement-induced disturbance to explain the discrepancy. We quantify the residual disturbance of our measurements and obtain data that rule out any classical model by ≳7.8 standard deviations, allowing us to exclude the property of macroscopic state definiteness from our system. Our experiment is then equivalent to the test of quantum noncontextuality [Kochen S, Specker E (1967) J Math Mech 17(1):59-87] that successfully addresses the measurement detectability loophole.

Thermoelectric Limitations of Graphene Nanodevices at Ultrahigh Current Densities.

Graphene is atomically thin, possesses excellent thermal conductivity, and is able to withstand high current densities, making it attractive for many nanoscale applications such as field-effect transistors, interconnects, and thermal management layers. Enabling integration of graphene into such devices requires nanostructuring, which can have a drastic impact on the self-heating properties, in particular at high current densities. Here, we use a combination of scanning thermal microscopy, finite element thermal analysis, and operando scanning transmission electron microscopy techniques to observe prototype graphene devices in operation and gain a deeper understanding of the role of geometry and interfaces during high current density operation. We find that Peltier effects significantly influence the operational limit due to local electrical and thermal interfacial effects, causing asymmetric temperature distribution in the device. Thus, our results indicate that a proper understanding and design of graphene devices must include consideration of the surrounding materials, interfaces, and geometry. Leveraging these aspects provides opportunities for engineered extreme operation devices.