Bounds to electron spin qubit variability for scalable CMOS architectures.

Spins of electrons in silicon MOS quantum dots combine exquisite quantum properties and scalable fabrication. In the age of quantum technology, however, the metrics that crowned Si/SiO2 as the microelectronics standard need to be reassessed with respect to their impact upon qubit performance. We chart spin qubit variability due to the unavoidable atomic-scale roughness of the Si/SiO2 interface, compiling experiments across 12 devices, and develop theoretical tools to analyse these results. Atomistic tight binding and path integral Monte Carlo methods are adapted to describe fluctuations in devices with millions of atoms by directly analysing their wavefunctions and electron paths instead of their energy spectra. We correlate the effect of roughness with the variability in qubit position, deformation, valley splitting, valley phase, spin-orbit coupling and exchange coupling. These variabilities are found to be bounded, and they lie within the tolerances for scalable architectures for quantum computing as long as robust control methods are incorporated.

Engineering Spin-Orbit Interactions in Silicon Qubits at the Atomic-Scale.

Spin-orbit interactions arise whenever the bulk inversion symmetry and/or structural inversion symmetry of a crystal is broken providing a bridge between a qubit's spin and orbital degree of freedom. While strong interactions can facilitate fast qubit operations by all-electrical control, they also provide a mechanism to couple charge noise thereby limiting qubit lifetimes. Previously believed to be negligible in bulk silicon, recent silicon nano-electronic devices have shown larger than bulk spin-orbit coupling strengths from Dresselhaus and Rashba couplings. Here, it is shown that with precision placement of phosphorus atoms in silicon along the [110] direction (without inversion symmetry) or [111] direction (with inversion symmetry), a wide range of Dresselhaus and Rashba coupling strength can be achieved from zero to 1113 × 10-13eV-cm. It is shown that with precision placement of phosphorus atoms, the local symmetry (C2v, D2d, and D3d) can be changed to engineer spin-orbit interactions. Since spin-orbit interactions affect both qubit operation and lifetimes, understanding their impact is essential for quantum processor design.

Symmetry Breaking and Spin-Orbit Coupling for Individual Vacancy-Induced In-Gap States in MoS2 Monolayers.

Spins confined to point defects in atomically thin semiconductors constitute well-defined atomic-scale quantum systems that are being explored as single-photon emitters and spin qubits. Here, we investigate the in-gap electronic structure of individual sulfur vacancies in molybdenum disulfide (MoS2) monolayers using resonant tunneling scanning probe spectroscopy in the Coulomb blockade regime. Spectroscopic mapping of defect wave functions reveals an interplay of local symmetry breaking by a charge-state-dependent Jahn-Teller lattice distortion that, when combined with strong (≃100 meV) spin-orbit coupling, leads to a locking of an unpaired spin-1/2 magnetic moment to the lattice at low temperature, susceptible to lattice strain. Our results provide new insights into the spin and electronic structure of vacancy-induced in-gap states toward their application as electrically and optically addressable quantum systems.

Colour, nutritional composition and antioxidant properties of dehydrated carrot (Daucus carota var. sativus) using solar drying techniques and pretreatments.

Carrot is a seasonal perishable tuberous root vegetable which presents a preservation challenge owing to its elevated moisture content. Recently, carrot processing has received more attention because of its many health-promoting qualities and the reduction of postharvest losses in a cost-effective safe way. This study was designed to sort out the effective solar drying technique including pre-treatment that would retain the color and quality characteristics of dehydrated carrot. Carrot slices were subjected to dry using open sun drying (D1), solar drying long chimney (D2), solar drying short chimney (D3) and box solar drying (D4) techniques with the pretreatments of ascorbic acid 1 % (C3), citric acid 5 % (C4), potassium metabisulfite 1 % (C5) and potassium sodium tartrate 0.3 % (C6) before drying. Drying characteristics, nutritional attributes, phytochemicals and antioxidant of the dehydrated carrot samples were compared with the fresh sample and untreated (control) sample. Results showed that D4 was a good drying method to preserve nutritional quality with good appearance. Among the pretreatments, C5 and C4 resulted improved nutritional quality retention, enhanced visual acceptability and enriched antioxidant activities. PCA (Principal Component Analysis) and correlation matrix revealed that D4 with C5 retained the maximum amount of vitamin, minerals, total phenolic content, antioxidant and admirable dehydrated carrot color by inactivating enzymatic reaction. Therefore, box solar drying with potassium metabisulfite pretreatment would be very promising for functional carrot drying retaining acceptable color and nutrition composition.

Atomic Engineering of Molecular Qubits for High-Speed, High-Fidelity Single Qubit Gates.

Universal quantum computing requires fast single- and two-qubit gates with individual qubit addressability to minimize decoherence errors during processor operation. Electron spin qubits using individual phosphorus donor atoms in silicon have demonstrated long coherence times with high fidelities, providing an attractive platform for scalable quantum computing. While individual qubit addressability has been demonstrated by controlling the hyperfine interaction between the electron and nuclear wave function in a global magnetic field, the small hyperfine Stark coefficient of 0.34 MHz/MV m-1 achieved to date has limited the speed of single quantum gates to ∼42 µs to avoid rotating neighboring qubits due to power broadening from the antenna. The use of molecular 2P qubits with more than one donor atom has not only demonstrated fast (0.8 ns) two-qubit SWAP gates and long spin relaxation times of ∼30 s but provides an alternate way to achieve high selectivity of the qubit resonance frequency. Here, we show in two different devices that by placing the donors with comparable interatomic spacings (∼0.8 nm) but along different crystallographic axes, either the [110] or [310] orientations using STM lithography, we can engineer the hyperfine Stark shift from 1 MHz/MV m-1 to 11.2 MHz/MV m-1, respectively, a factor of 10 difference. NEMO atomistic calculations show that larger hyperfine Stark coefficients of up to ∼70 MHz/MV m-1 can be achieved within 2P molecules by placing the donors ≥5 nm apart. When combined with Gaussian pulse shaping, we show that fast single qubit gates with 2π rotation times of 10 ns and ∼99% fidelity single qubit operations are feasible without affecting neighboring qubits. By increasing the single qubit gate time to ∼550 ns, two orders of magnitude faster than previously measured, our simulations confirm that >99.99% single qubit control fidelities are achievable.

Spin-Valley Locking for In-Gap Quantum Dots in a MoS2 Transistor.

Spins confined to atomically thin semiconductors are being actively explored as quantum information carriers. In transition metal dichalcogenides (TMDCs), the hexagonal crystal lattice gives rise to an additional valley degree of freedom with spin-valley locking and potentially enhanced spin life and coherence times. However, realizing well-separated single-particle levels and achieving transparent electrical contact to address them has remained challenging. Here, we report well-defined spin states in a few-layer MoS2 transistor, characterized with a spectral resolution of ∼50 µeV at Tel = 150 mK. Ground state magnetospectroscopy confirms a finite Berry-curvature induced coupling of spin and valley, reflected in a pronounced Zeeman anisotropy, with a large out-of-plane g-factor of g⊥ ≃ 8. A finite in-plane g-factor (g∥ ≃ 0.55-0.8) allows us to quantify spin-valley locking and estimate the spin-orbit splitting 2ΔSO ∼ 100 µeV. The demonstration of spin-valley locking is an important milestone toward realizing spin-valley quantum bits.

The Use of Exchange Coupled Atom Qubits as Atomic-Scale Magnetic Field Sensors.

Phosphorus atoms in silicon offer a rich quantum computing platform where both nuclear and electron spins can be used to store and process quantum information. While individual control of electron and nuclear spins has been demonstrated, the interplay between them during qubit operations has been largely unexplored. This study investigates the use of exchange-based operation between donor bound electron spins to probe the local magnetic fields experienced by the qubits with exquisite precision at the atomic scale. To achieve this, coherent exchange oscillations are performed between two electron spin qubits, where the left and right qubits are hosted by three and two phosphorus donors, respectively. The frequency spectrum of exchange oscillations shows quantized changes in the local magnetic fields at the qubit sites, corresponding to the different hyperfine coupling between the electron and each of the qubit-hosting nuclear spins. This ability to sense the hyperfine fields of individual nuclear spins using the exchange interaction constitutes a unique metrology technique, which reveals the exact crystallographic arrangements of the phosphorus atoms in the silicon crystal for each qubit. The detailed knowledge obtained of the local magnetic environment can then be used to engineer hyperfine fields in multi-donor qubits for high-fidelity two-qubit gates.

SiGe quantum wells with oscillating Ge concentrations for quantum dot qubits.

Large-scale arrays of quantum-dot spin qubits in Si/SiGe quantum wells require large or tunable energy splittings of the valley states associated with degenerate conduction band minima. Existing proposals to deterministically enhance the valley splitting rely on sharp interfaces or modifications in the quantum well barriers that can be difficult to grow. Here, we propose and demonstrate a new heterostructure, the "Wiggle Well", whose key feature is Ge concentration oscillations inside the quantum well. Experimentally, we show that placing Ge in the quantum well does not significantly impact our ability to form and manipulate single-electron quantum dots. We further observe large and widely tunable valley splittings, from 54 to 239 µeV. Tight-binding calculations, and the tunability of the valley splitting, indicate that these results can mainly be attributed to random concentration fluctuations that are amplified by the presence of Ge alloy in the heterostructure, as opposed to a deterministic enhancement due to the concentration oscillations. Quantitative predictions for several other heterostructures point to the Wiggle Well as a robust method for reliably enhancing the valley splitting in future qubit devices.

Atomic fluctuations lifting the energy degeneracy in Si/SiGe quantum dots.

Electron spins in Si/SiGe quantum wells suffer from nearly degenerate conduction band valleys, which compete with the spin degree of freedom in the formation of qubits. Despite attempts to enhance the valley energy splitting deterministically, by engineering a sharp interface, valley splitting fluctuations remain a serious problem for qubit uniformity, needed to scale up to large quantum processors. Here, we elucidate and statistically predict the valley splitting by the holistic integration of 3D atomic-level properties, theory and transport. We find that the concentration fluctuations of Si and Ge atoms within the 3D landscape of Si/SiGe interfaces can explain the observed large spread of valley splitting from measurements on many quantum dot devices. Against the prevailing belief, we propose to boost these random alloy composition fluctuations by incorporating Ge atoms in the Si quantum well to statistically enhance valley splitting.

Deep ultra-violet plasmonics: exploiting momentum-resolved electron energy loss spectroscopy to probe germanium.

Germanium is typically used for solid-state electronics, fiber-optics, and infrared applications, due to its semiconducting behavior at optical and infrared wavelengths. In contrast, here we show that the germanium displays metallic nature and supports propagating surface plasmons in the deep ultraviolet (DUV) wavelengths, that is typically not possible to achieve with conventional plasmonic metals such as gold, silver, and aluminum. We measure the photonic band spectrum and distinguish the plasmonic excitation modes: bulk plasmons, surface plasmons, and Cherenkov radiation using a momentum-resolved electron energy loss spectroscopy. The observed spectrum is validated through the macroscopic electrodynamic electron energy loss theory and first-principles density functional theory calculations. In the DUV regime, intraband transitions of valence electrons dominate over the interband transitions, resulting in the observed highly dispersive surface plasmons. We further employ these surface plasmons in germanium to design a DUV radiation source based on the Smith-Purcell effect. Our work opens a new frontier of DUV plasmonics to enable the development of DUV devices such as metasurfaces, detectors, and light sources based on plasmonic germanium thin films.

Exchange Coupling in a Linear Chain of Three Quantum-Dot Spin Qubits in Silicon.

Quantum gates between spin qubits can be implemented leveraging the natural Heisenberg exchange interaction between two electrons in contact with each other. This interaction is controllable by electrically tailoring the overlap between electronic wave functions in quantum dot systems, as long as they occupy neighboring dots. An alternative route is the exploration of superexchange-the coupling between remote spins mediated by a third idle electron that bridges the distance between quantum dots. We experimentally demonstrate direct exchange coupling and provide evidence for second neighbor mediated superexchange in a linear array of three single-electron spin qubits in silicon, inferred from the electron spin resonance frequency spectra. We confirm theoretically, through atomistic modeling, that the device geometry only allows for sizable direct exchange coupling for neighboring dots, while next-nearest neighbor coupling cannot stem from the vanishingly small tail of the electronic wave function of the remote dots, and is only possible if mediated.

WSe2 Homojunction Devices: Electrostatically Configurable as Diodes, MOSFETs, and Tunnel FETs for Reconfigurable Computing.

In this paper, electrostatically configurable 2D tungsten diselenide (WSe2 ) electronic devices are demonstrated. Utilizing a novel triple-gate design, a WSe2 device is able to operate as a tunneling field-effect transistor (TFET), a metal-oxide-semiconductor field-effect transistor (MOSFET) as well as a diode, by electrostatically tuning the channel doping to the desired profile. The implementation of scaled gate dielectric and gate electrode spacing enables higher band-to-band tunneling transmission with the best observed subthreshold swing (SS) among all reported homojunction TFETs on 2D materials. Self-consistent full-band atomistic quantum transport simulations quantitatively agree with electrical measurements of both the MOSFET and TFET and suggest that scaling gate oxide below 3 nm is necessary to achieve sub-60 mV dec-1 SS, while further improvement can be obtained by optimizing the spacers. Diode operation is also demonstrated with the best ideality factor of 1.5, owing to the enhanced electrostatic control compared to previous reports. This research sheds light on the potential of utilizing electrostatic doping scheme for low-power electronics and opens a path toward novel designs of field programmable mixed analog/digital circuitry for reconfigurable computing.

Complementary Black Phosphorus Tunneling Field-Effect Transistors.

Band-to-band tunneling field-effect transistors (TFETs) have emerged as promising candidates for low-power integration circuits beyond conventional metal-oxide-semiconductor field-effect transistors (MOSFETs) and have been demonstrated to overcome the thermionic limit, which results intrinsically in sub-threshold swings of at least 60 mV/dec at room temperature. Here, we demonstrate complementary TFETs based on few-layer black phosphorus, in which multiple top gates create electrostatic doping in the source and drain regions. By electrically tuning the doping types and levels in the source and drain regions, the device can be reconfigured to allow for TFET or MOSFET operation and can be tuned to be n-type or p-type. Owing to the proper choice of materials and careful engineering of device structures, record-high current densities have been achieved in 2D TFETs. Full-band atomistic quantum transport simulations of the fabricated devices agree quantitatively with the current-voltage measurements, which gives credibility to the promising simulation results of ultrascaled phosphorene TFETs. Using atomistic simulations, we project substantial improvements in the performance of the fabricated TFETs when channel thicknesses and oxide thicknesses are scaled down.

Addressable electron spin resonance using donors and donor molecules in silicon.

Phosphorus donor impurities in silicon are a promising candidate for solid-state quantum computing due to their exceptionally long coherence times and high fidelities. However, individual addressability of exchange coupled donors with separations ~15 nm is challenging. We show that by using atomic precision lithography, we can place a single P donor next to a 2P molecule 16 ± 1 nm apart and use their distinctive hyperfine coupling strengths to address qubits at vastly different resonance frequencies. In particular, the single donor yields two hyperfine peaks separated by 97 ± 2.5 MHz, in contrast to the donor molecule that exhibits three peaks separated by 262 ± 10 MHz. Atomistic tight-binding simulations confirm the large hyperfine interaction strength in the 2P molecule with an interdonor separation of ~0.7 nm, consistent with lithographic scanning tunneling microscopy images of the 2P site during device fabrication. We discuss the viability of using donor molecules for built-in addressability of electron spin qubits in silicon.

Theoretical study of strain-dependent optical absorption in a doped self-assembled InAs/InGaAs/GaAs/AlGaAs quantum dot.

A detailed theoretical study of the optical absorption in doped self-assembled quantum dots is presented. A rigorous atomistic strain model as well as a sophisticated 20-band tight-binding model are used to ensure accurate prediction of the single particle states in these devices. We also show that for doped quantum dots, many-particle configuration interaction is also critical to accurately capture the optical transitions of the system. The sophisticated models presented in this work reproduce the experimental results for both undoped and doped quantum dot systems. The effects of alloy mole fraction of the strain controlling layer and quantum dot dimensions are discussed. Increasing the mole fraction of the strain controlling layer leads to a lower energy gap and a larger absorption wavelength. Surprisingly, the absorption wavelength is highly sensitive to the changes in the diameter, but almost insensitive to the changes in dot height. This behavior is explained by a detailed sensitivity analysis of different factors affecting the optical transition energy.

Atomically engineered electron spin lifetimes of 30 s in silicon.

Scaling up to large arrays of donor-based spin qubits for quantum computation will require the ability to perform high-fidelity readout of multiple individual spin qubits. Recent experiments have shown that the limiting factor for high-fidelity readout of many qubits is the lifetime of the electron spin. We demonstrate the longest reported lifetimes (up to 30 s) of any electron spin qubit in a nanoelectronic device. By atomic-level engineering of the electron wave function within phosphorus atom quantum dots, we can minimize spin relaxation in agreement with recent theoretical predictions. These lifetimes allow us to demonstrate the sequential readout of two electron spin qubits with fidelities as high as 99.8%, which is above the surface code fault-tolerant threshold. This work paves the way for future experiments on multiqubit systems using donors in silicon.

Silicon quantum processor with robust long-distance qubit couplings.

Practical quantum computers require a large network of highly coherent qubits, interconnected in a design robust against errors. Donor spins in silicon provide state-of-the-art coherence and quantum gate fidelities, in a platform adapted from industrial semiconductor processing. Here we present a scalable design for a silicon quantum processor that does not require precise donor placement and leaves ample space for the routing of interconnects and readout devices. We introduce the flip-flop qubit, a combination of the electron-nuclear spin states of a phosphorus donor that can be controlled by microwave electric fields. Two-qubit gates exploit a second-order electric dipole-dipole interaction, allowing selective coupling beyond the nearest-neighbor, at separations of hundreds of nanometers, while microwave resonators can extend the entanglement to macroscopic distances. We predict gate fidelities within fault-tolerance thresholds using realistic noise models. This design provides a realizable blueprint for scalable spin-based quantum computers in silicon.Quantum computers will require a large network of coherent qubits, connected in a noise-resilient way. Tosi et al. present a design for a quantum processor based on electron-nuclear spins in silicon, with electrical control and coupling schemes that simplify qubit fabrication and operation.

Direct Observation of 2D Electrostatics and Ohmic Contacts in Template-Grown Graphene/WS2 Heterostructures.

Large-area two-dimensional (2D) heterojunctions are promising building blocks of 2D circuits. Understanding their intriguing electrostatics is pivotal but largely hindered by the lack of direct observations. Here graphene-WS2 heterojunctions are prepared over large areas using a seedless ambient-pressure chemical vapor deposition technique. Kelvin probe force microscopy, photoluminescence spectroscopy, and scanning tunneling microscopy characterize the doping in graphene-WS2 heterojunctions as-grown on sapphire and transferred to SiO2 with and without thermal annealing. Both p-n and n-n junctions are observed, and a flat-band condition (zero Schottky barrier height) is found for lightly n-doped WS2, promising low-resistance ohmic contacts. This indicates a more favorable band alignment for graphene-WS2 than has been predicted, likely explaining the low barriers observed in transport experiments on similar heterojunctions. Electrostatic modeling demonstrates that the large depletion width of the graphene-WS2 junction reflects the electrostatics of the one-dimensional junction between two-dimensional materials.

Characterizing Si:P quantum dot qubits with spin resonance techniques.

Quantum dots patterned by atomically precise placement of phosphorus donors in single crystal silicon have long spin lifetimes, advantages in addressability, large exchange tunability, and are readily available few-electron systems. To be utilized as quantum bits, it is important to non-invasively characterise these donor quantum dots post fabrication and extract the number of bound electron and nuclear spins as well as their locations. Here, we propose a metrology technique based on electron spin resonance (ESR) measurements with the on-chip circuitry already needed for qubit manipulation to obtain atomic scale information about donor quantum dots and their spin configurations. Using atomistic tight-binding technique and Hartree self-consistent field approximation, we show that the ESR transition frequencies are directly related to the number of donors, electrons, and their locations through the electron-nuclear hyperfine interaction.