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.

Porphyrin-fused graphene nanoribbons.

Graphene nanoribbons (GNRs), nanometre-wide strips of graphene, are promising materials for fabricating electronic devices. Many GNRs have been reported, yet no scalable strategies are known for synthesizing GNRs with metal atoms and heteroaromatic units at precisely defined positions in the conjugated backbone, which would be valuable for tuning their optical, electronic and magnetic properties. Here we report the solution-phase synthesis of a porphyrin-fused graphene nanoribbon (PGNR). This PGNR has metalloporphyrins fused into a twisted fjord-edged GNR backbone; it consists of long chains (>100 nm), with a narrow optical bandgap (~1.0 eV) and high local charge mobility (>400 cm2 V-1 s-1 by terahertz spectroscopy). We use this PGNR to fabricate ambipolar field-effect transistors with appealing switching behaviour, and single-electron transistors displaying multiple Coulomb diamonds. These results open an avenue to π-extended nanostructures with engineerable electrical and magnetic properties by transposing the coordination chemistry of porphyrins into graphene nanoribbons.

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.

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.

Observation and Manipulation of a Phase Separated State in a Charge Density Wave Material.

The 1T polytype of TaS2 has been studied extensively as a strongly correlated system. As 1T-TaS2 is thinned toward the 2D limit, its phase diagram shows significant deviations from that of the bulk material. Optoelectronic maps of ultrathin 1T-TaS2 have indicated the presence of nonequilibrium charge density wave phases within the hysteresis region of the nearly commensurate (NC) to commensurate (C) transition. We perform scanning tunneling microscopy on exfoliated ultrathin flakes of 1T-TaS2 within the NC-C hysteresis window, finding evidence that the observed nonequilibrium phases consist of intertwined, irregularly shaped NC-like and C-like domains. After applying lateral electrical signals to the sample, we image changes in the geometric arrangement of the different regions. We use a phase separation model to explore the relationship between electronic inhomogeneity present in ultrathin 1T-TaS2 and its bulk resistivity. These results demonstrate the role of phase competition morphologies in determining the properties of 2D materials.

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.

Role of dephasing on the conductance signatures of Majorana zero modes.

Conductance signatures that signal the presence of Majorana zero modes in a three terminal nanowire-topological superconductor hybrid system are analyzed in detail, in both the clean nanowire limit and in the presence of non-coherent dephasing interactions. In the coherent transport regime for a clean wire, we point out contributions of the local Andreev reflection and the non-local transmissions toward the total conductance lineshapes while clarifying the role of contact broadening on the Majorana conductance lineshapes at the magnetic field parity crossings. Interestingly, at largerB-field parity crossings, the contribution of the Andreev reflection process decreases which is compensated by the non-local processes in order to maintain the conductance quantum regardless of contact coupling strength. In the non-coherent transport regime, we include dephasing that is introduced by momentum randomization processes, that allows one to smoothly transition to the diffusive limit. Here, as expected, we note that while the Majorana character of the zero modes is unchanged, there is a reduction in the conductance peak magnitude that scales with the strength of the impurity scattering potentials. Dephasing due to fluctuating impurities is shown to affect the conductance lineshapes in ways that are distinguishable from the effects of contact-induced tunnel broadening. Most importantly our results reveal that the addition of dephasing in the set up does not lead to any notable length dependence to the conductance of the zero modes, contrary to what one would expect in a gradual transition to the diffusive limit. We believe this work paves a way for a systematic introduction of scattering processes into the realistic modeling of Majorana nanowire hybrid devices and assessing topological signatures in such systems in the presence of non-coherent scattering processes.

Graphene nanogaps for the directed assembly of single-nanoparticle devices.

Significant advances in the synthesis of low-dimensional materials with unique and tuneable electrical, optical and magnetic properties has led to an explosion of possibilities for realising hybrid nanomaterial devices with unconventional and desirable characteristics. However, the lack of ability to precisely integrate individual nanoparticles into devices at scale limits their technological application. Here, we report on a graphene nanogap based platform which employs the large electric fields generated around the point-like, atomically sharp nanogap electrodes to capture single nanoparticles from solution at predefined locations. We demonstrate how gold nanoparticles can be trapped and contacted to form single-electron transistors with a large coupling to a buried electrostatic gate. This platform offers a route to the creation of novel low-dimensional devices, nano- and optoelectronic applications, and the study of fundamental transport phenomena.

Roadmap on quantum nanotechnologies.

Quantum phenomena are typically observable at length and time scales smaller than those of our everyday experience, often involving individual particles or excitations. The past few decades have seen a revolution in the ability to structure matter at the nanoscale, and experiments at the single particle level have become commonplace. This has opened wide new avenues for exploring and harnessing quantum mechanical effects in condensed matter. These quantum phenomena, in turn, have the potential to revolutionize the way we communicate, compute and probe the nanoscale world. Here, we review developments in key areas of quantum research in light of the nanotechnologies that enable them, with a view to what the future holds. Materials and devices with nanoscale features are used for quantum metrology and sensing, as building blocks for quantum computing, and as sources and detectors for quantum communication. They enable explorations of quantum behaviour and unconventional states in nano- and opto-mechanical systems, low-dimensional systems, molecular devices, nano-plasmonics, quantum electrodynamics, scanning tunnelling microscopy, and more. This rapidly expanding intersection of nanotechnology and quantum science/technology is mutually beneficial to both fields, laying claim to some of the most exciting scientific leaps of the last decade, with more on the horizon.

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.

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

The electronic and magnetic properties of single-molecule transistors depend critically on the molecular charge state. Charge transport in single-molecule transistors is characterized by Coulomb-blocked regions in which the charge state of the molecule is fixed and current is suppressed, separated by high-conductance, sequential-tunneling regions. It is often difficult to assign the charge state of the molecular species in each Coulomb-blocked region due to variability in the work-function of the electrodes. In this work, we provide a simple and fast method to assign the charge state of the molecular species in the Coulomb-blocked regions based on signatures of electron-phonon coupling together with the Pauli-exclusion principle, simply by observing the asymmetry in the current in high-conductance regions of the stability diagram. We demonstrate that charge-state assignments determined in this way are consistent with those obtained from measurements of Zeeman splittings. Our method is applicable at 77 K, in contrast to magnetic-field-dependent measurements, which generally require low temperatures (below 4 K). Due to the ubiquity of electron-phonon coupling in molecular junctions, we expect this method to be widely applicable to single-electron transistors based on single molecules and graphene quantum dots. The correct assignment of charge states allows researchers to better understand the fundamental charge-transport properties of single-molecule transistors.

Nb/InAs nanowire proximity junctions from Josephson to quantum dot regimes.

The superconducting proximity effect is probed experimentally in Josephson junctions fabricated with InAs nanowires contacted by Nb leads. Contact transparencies [Formula: see text] are observed. The electronic phase coherence length at low temperatures exceeds the channel length. However, the elastic scattering length is a few times shorter than the channel length. Electrical measurements reveal two regimes of quantum transport: (i) the Josephson regime, characterised by a dissipationless current up to ∼100 nA, and (ii) the quantum dot (QD) regime, characterised by the formation of Andreev bound states (ABS) associated with spontaneous QDs inside the nanowire channel. In regime (i), the behaviour of the critical current I c versus an axial magnetic field [Formula: see text] shows an unexpected modulation and persistence to fields [Formula: see text] T. In the QD regime, the ABS are modelled as the current-biased solutions of an Anderson-type model. The applicability of devices in both transport regimes to Majorana fermion experiments is discussed.

Direct Evidence of Solution-Mediated Superoxide Transport and Organic Radical Formation in Sodium-Oxygen Batteries.

Advanced large-scale electrochemical energy storage requires cost-effective battery systems with high energy densities. Aprotic sodium-oxygen (Na-O2) batteries offer advantages, being comprised of low-cost elements and possessing much lower charge overpotential and higher reversibility compared to their lithium-oxygen battery cousins. Although such differences have been explained by solution-mediated superoxide transport, the underlying nature of this mechanism is not fully understood. Water has been suggested to solubilize superoxide via formation of hydroperoxyl (HO2), but direct evidence of these HO2 radical species in cells has proven elusive. Here, we use ESR spectroscopy at 210 K to identify and quantify soluble HO2 radicals in the electrolyte-cold-trapped in situ to prolong their lifetime-in a Na-O2 cell. These investigations are coupled to parallel SEM studies that image crystalline sodium superoxide (NaO2) on the carbon cathode. The superoxide radicals were spin-trapped via reaction with 5,5-dimethyl-pyrroline N-oxide at different electrochemical stages, allowing monitoring of their production and consumption during cycling. Our results conclusively demonstrate that transport of superoxide from cathode to electrolyte leads to the nucleation and growth of NaO2, which follows classical mechanisms based on the variation of superoxide content in the electrolyte and its correlation with the crystallization of cubic NaO2. The changes in superoxide content upon charge show that charge proceeds through the reverse solution process. Furthermore, we identify the carbon-centered/oxygen-centered alkyl radicals arising from attack of these solubilized HO2 species on the diglyme solvent. This is the first direct evidence of such species, which are likely responsible for electrolyte degradation.

Tomography is Necessary for Universal Entanglement Detection with Single-Copy Observables.

Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous tasks of quantum information science. A natural question of both theoretical and experimental importance is whether universal entanglement detection can be accomplished without full state tomography. In this Letter, we prove a no-go theorem that rules out this possibility for nonadaptive schemes that employ single-copy measurements only. We also examine a previously implemented experiment [H. Park et al., Phys. Rev. Lett. 105, 230404 (2010)], which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. In contrast, our simulation and experiment both support the opposite conclusion that the protocol, indeed, leads to full state tomography, which supplements our no-go theorem. These results reveal a fundamental limit of single-copy measurements in entanglement detection and provide a general framework of the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the k-symmetric extendibility.

Randomized benchmarking of quantum gates implemented by electron spin resonance.

Spin systems controlled and probed by magnetic resonance have been valuable for testing the ideas of quantum control and quantum error correction. This paper introduces an X-band pulsed electron spin resonance spectrometer designed for high-fidelity coherent control of electron spins, including a loop-gap resonator for sub-millimeter sized samples with a control bandwidth ∼40MHz. Universal control is achieved by a single-sideband upconversion technique with an I-Q modulator and a 1.2GS/s arbitrary waveform generator. A single qubit randomized benchmarking protocol quantifies the average errors of Clifford gates implemented by simple Gaussian pulses, using a sample of gamma-irradiated quartz. Improvements in unitary gate fidelity are achieved through phase transient correction and hardware optimization. A preparation pulse sequence that selects spin packets in a narrowed distribution of static fields confirms that inhomogeneous dephasing (1/T2(∗)) is the dominant source of gate error. The best average fidelity over the Clifford gates obtained here is 99.2%, which serves as a benchmark to compare with other technologies.

Estimating the Coherence of Noise in Quantum Control of a Solid-State Qubit.

To exploit a given physical system for quantum information processing, it is critical to understand the different types of noise affecting quantum control. Distinguishing coherent and incoherent errors is extremely useful as they can be reduced in different ways. Coherent errors are generally easier to reduce at the hardware level, e.g., by improving calibration, whereas some sources of incoherent errors, e.g., T_{2}^{*} processes, can be reduced by engineering robust pulses. In this work, we illustrate how purity benchmarking and randomized benchmarking can be used together to distinguish between coherent and incoherent errors and to quantify the reduction in both of them due to using optimal control pulses and accounting for the transfer function in an electron spin resonance system. We also prove that purity benchmarking provides bounds on the optimal fidelity and diamond norm that can be achieved by correcting the coherent errors through improving calibration.

Experimental estimation of average fidelity of a Clifford gate on a 7-qubit quantum processor.

One of the major experimental achievements in the past decades is the ability to control quantum systems to high levels of precision. To quantify the level of control we need to characterize the dynamical evolution. Full characterization via quantum process tomography is impractical and often unnecessary. For most practical purposes, it is enough to estimate more general quantities such as the average fidelity. Here we use a unitary 2-design and twirling protocol for efficiently estimating the average fidelity of Clifford gates, to certify a 7-qubit entangling gate in a nuclear magnetic resonance quantum processor. Compared with more than 10^{8} experiments required by full process tomography, we conducted 1656 experiments to satisfy a statistical confidence level of 99%. The average fidelity of this Clifford gate in experiment is 55.1%, and rises to at least 87.5% if the signal's decay due to decoherence is taken into account. The entire protocol of certifying Clifford gates is efficient and scalable, and can easily be extended to any general quantum information processor with minor modifications.

Temperature-dependent electron mobility in InAs nanowires.

Effective electron mobilities are obtained by transport measurements on InAs nanowire field-effect transistors at temperatures ranging from 10 to 200 K. The mobility increases with temperatures below ∼30-50 K, and then decreases with temperatures above 50 K, consistent with other reports. The magnitude and temperature dependence of the observed mobility can be explained by Coulomb scattering from ionized surface states at typical densities. The behaviour above 50 K is ascribed to the thermally activated increase in the number of scatterers, although nanoscale confinement also plays a role as higher radial subbands are populated, leading to interband scattering and a shift of the carrier distribution closer to the surface. Scattering rate calculations using finite-element simulations of the nanowire transistor confirm that these mechanisms are able to explain the data.