Search

While traditionally considered a deleterious effect in quantum dot spin qubits, the spin-orbit interaction is recently being revisited as it allows for rapid coherent control by on-chip AC electric fields. For electrons in bulk silicon, SOC is intrinsically weak, however, it can be enhanced at surfaces and interfaces, or through atomic placement. Here we show that the strength of the spin-orbit coupling can be locally enhanced by more than two orders of magnitude in the manybody wave functions of multi-donor quantum dots compared to a single donor, reaching strengths so far only reported for holes or two-donor system with certain symmetry. Our findings may provide a pathway towards all-electrical control of donor-bound spins in silicon using electric dipole spin resonance (EDSR).

Spin qubits in silicon are strong contenders for realizing a practical quantum computer. This technology has made remarkable progress with the demonstration of single and two-qubit gates above the fault-tolerant threshold and entanglement of up to three qubits. However, maintaining high fidelity operations while executing multi-qubit algorithms has remained elusive, only being achieved for two spin qubits to date due to the small qubit size, which makes it difficult to control qubits without creating crosstalk errors. Here, we use a four-qubit silicon processor with every operation above the fault tolerant limit and demonstrate Grover's algorithm with a ~95% probability of finding the marked state, one of the most successful implementations to date. Our four-qubit processor is made of three phosphorus atoms and one electron spin precision-patterned into 1.5 nm${}^2$ isotopically pure silicon. The strong resulting confinement potential, without additional confinement gates that can increase cross-talk, leverages the benefits of having both electron and phosphorus nuclear spins. Significantly, the all-to-all connectivity of the nuclear spins provided by the hyperfine interaction not only allows for efficient multi-qubit operations, but also provides individual qubit addressability. Together with the long coherence times of the nuclear and electron spins, this results in all four single qubit fidelities above 99.9% and controlled-Z gates between all pairs of nuclear spins above 99% fidelity. The high control fidelities, combined with >99% fidelity readout of all nuclear spins, allows for the creation of a three-qubit Greenberger-Horne-Zeilinger (GHZ) state with 96.2% fidelity, the highest reported for semiconductor spin qubits so far. Such nuclear spin registers can be coupled via electron exchange, establishing a path for larger scale fault-tolerant quantum processors., Comment: 16 pages, 9 figures, 3 tables

Atomic engineering in a solid-state material has the potential to functionalize the host with novel phenomena. STM-based lithographic techniques have enabled the placement of individual phosphorus atoms at selective lattice sites of silicon with atomic precision. Here, we show that by placing four phosphorus donors spaced 10-15 nm apart from their neighbours in a linear chain, it is possible to realize coherent spin coupling between the end dopants of the chain, analogous to the superexchange interaction in magnetic materials. Since phosphorus atoms are a promising building block of a silicon quantum computer, this enables spin coupling between their bound electrons beyond nearest neighbours, allowing the qubits to be spaced out by 30-45 nm. The added flexibility in architecture brought about by this long-range coupling not only reduces gate densities but can also reduce correlated noise between qubits from local noise sources that are detrimental to error correction codes. We base our calculations on a full configuration interaction technique in the atomistic tight-binding basis, solving the 4-electron problem exactly, over a domain of a million silicon atoms. Our calculations show that superexchange can be tuned electrically through gate voltages where it is less sensitive to charge noise and donor placement errors.

A requirement for quantum information processors is the in-situ tunability of the tunnel rates and the exchange interaction energy within the device. The large energy level separation for atom qubits in silicon is well suited for qubit operation but limits device tunability using in-plane gate architectures, requiring vertically separated top-gates to control tunnelling within the device. In this paper we address control of the simplest tunnelling device in Si:P, the tunnel junction. Here we demonstrate that we can tune its conductance by using a vertically separated top-gate aligned with +-5nm precision to the junction. We show that a monolithic 3D epitaxial top-gate increases the capacitive coupling by a factor of 3 compared to in-plane gates, resulting in a tunnel barrier height tunability of 0-186meV. By combining multiple gated junctions in series we extend our monolithic 3D gating technology to implement nanoscale logic circuits including AND and OR gates.

Multi-donor quantum dots have been at the forefront of recent progress in Si-based quantum computation. Among them, $2P:1P$ qubits have a built-in dipole moment, enabling all-electrical spin operation via hyperfine mediated electron dipole spin resonance (EDSR). The development of all-electrical multi-donor dot qubits requires a full understanding of their EDSR and coherence properties, incorporating multi-valley nature of their ground state. Here, by introducing a variational effective mass wave-function, we examine the impact of qubit geometry and nearby charge defects on the electrical operation and coherence of $2P:1P$ qubits. We report four outcomes: (i) The difference in the hyperfine interaction between the $2P$ and $1P$ sites enables fast EDSR, with $T_\pi \sim 10-50$ ns and a Rabi ratio $ (T_1/T_\pi) \sim 10^6$. We analyse qubits with the $2P:1P$ axis aligned along the [100], [110] and [111] crystal axes, finding that the fastest EDSR time $T_\pi$ occurs when the $2P:1P$ axis is $\parallel$[111], while the best Rabi ratio occurs when it is $\parallel$ [100]. This difference is attributed to the difference in the wave function overlap between $2P$ and $1P$ for different geometries. In contrast, the choice of $2P$ axis has no visible impact on qubit operation. (ii) Sensitivity to random telegraph noise due to nearby charge defects depends strongly on the location of the nearby defects with respect to the qubit. For certain orientations of defects random telegraph noise has an appreciable effect both on detuning and $2P-1P$ tunneling, with the latter inducing gate errors. (iii) The qubit is robust against $1/f$ noise provided it is operated away from the charge anticrossing. (iv) Entanglement via exchange is several orders of magnitude faster than dipole-dipole coupling. These findings pave the way towards fast, low-power, coherent and scalable donor dot-based quantum computing., Comment: 23 pages, 6 figures

Proposals for large-scale semiconductor spin-based quantum computers require high-fidelity single-shot qubit readout to perform error correction and read out qubit registers at the end of a computation. However, as devices scale to larger qubit numbers integrating readout sensors into densely packed qubit chips is a critical challenge. Two promising approaches are minimising the footprint of the sensors, and extending the range of each sensor to read more qubits. Here we show high-fidelity single-shot electron spin readout using a nanoscale single-lead quantum dot (SLQD) sensor that is both compact and capable of reading multiple qubits. Our gate-based SLQD sensor is deployed in an all-epitaxial silicon donor spin qubit device, and we demonstrate single-shot readout of three $^{31}$P donor quantum dot electron spins with a maximum fidelity of 95%. Importantly in our device the quantum dot confinement potentials are provided inherently by the donors, removing the need for additional metallic confinement gates and resulting in strong capacitive interactions between sensor and donor quantum dots. We observe a $1/d^{1.4}$ scaling of the capacitive coupling between sensor and $^{31}$P dots (where $d$ is the sensor-dot distance), compared to $1/d^{2.5-3.0}$ in gate-defined quantum dot devices. Due to the small qubit size and strong capacitive interactions in all-epitaxial donor devices, we estimate a single sensor can achieve single-shot readout of approximately 15 qubits in a linear array, compared to 3-4 qubits for a similar sensor in a gate-defined quantum dot device. Our results highlight the potential for spin qubit devices with significantly reduced sensor densities.

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 donor qubits with separations ~15nm is challenging. Here 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 which exhibits three peaks separated by 262(+/-10)MHz. Atomistic tight-binding simulations confirm the large hyperfine interaction strength in the 2P molecule with an inter-donor separation of ~0.7nm, consistent with lithographic STM 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., Comment: 8 pages, 4 figures - DEV053 - Team Viper

We investigate spin and charge dynamics of a quantum dot of phosphorus atoms coupled to a radio-frequency single-electron transistor (rf-SET) using full counting statistics. We show how the magnetic field plays a role in determining the bunching or anti-bunching tunnelling statistics of the donor dot and SET system. Using the counting statistics we show how to determine the lowest magnetic field where spin-readout is possible. We then show how such a measurement can be used to investigate and optimise single electron spin-readout fidelity., Comment: 11 pages, 6 figures

We propose a method to electrically control electron spins in donor-based qubits in silicon. By taking advantage of the hyperfine coupling difference between a single-donor and a two-donor quantum dot, spin rotation can be driven by inducing an electric dipole between them and applying an alternating electric field generated by in-plane gates. These qubits can be coupled with exchange interaction controlled by top detuning gates. The qubit device can be fabricated deep in the silicon lattice with atomic precision by scanning tunneling probe technique. We have combined a large-scale full band atomistic tight-binding modeling approach with a time-dependent effective Hamiltonian description, providing a design with quantitative guidelines.

Two-electron states bound to donors in silicon are important for both two qubit gates and spin readout. We present a full configuration interaction technique in the atomistic tight-binding basis to capture multi-electron exchange and correlation effects taking into account the full bandstructure of silicon and the atomic scale granularity of a nanoscale device. Excited $s$-like states of $A_1$-symmetry are found to strongly influence the charging energy of a negative donor centre. We apply the technique on sub-surface dopants subjected to gate electric fields, and show that bound triplet states appear in the spectrum as a result of decreased charging energy. The exchange energy, obtained for the two-electron states in various confinement regimes, may enable engineering electrical control of spins in donor-dot hybrid qubits., Comment: 7 pages, 4 figures

The ability to apply GHz frequencies to control the quantum state of a single $P$ atom is an essential requirement for the fast gate pulsing needed for qubit control in donor based silicon quantum computation. Here we demonstrate this with nanosecond accuracy in an all epitaxial single atom transistor by applying excitation signals at frequencies up to $\approx$ 13 GHz to heavily phosphorous doped silicon leads. These measurements allow the differentiation between the excited states of the single atom and the density of states in the one dimensional leads. Our pulse spectroscopy experiments confirm the presence of an excited state at an energy $\approx$ 9 meV consistent with the first excited state of a single $P$ donor in silicon. The relaxation rate of this first excited state to ground is estimated to be larger than 2.5 GHz, consistent with theoretical predictions. These results represent a systematic investigation of how an atomically precise single atom transistor device behaves under rf excitations., Comment: 21 pages and 6 figures including an addendum/corrigendum section DOI: 10.1021/acsnano.6b08154

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.

The long term scaling prospects for solid-state quantum computing architectures relies heavily on the ability to simply and reliably measure and control the coherent electron interaction strength, known as the tunnel coupling, $t_c$. Here, we describe a method to extract the $t_c$ between two quantum dots (QDs) utilising their different tunnel rates to a reservoir. We demonstrate the technique on a few donor triple QD tunnel coupled to a nearby single-electron transistor (SET) in silicon. The device was patterned using scanning tunneling microscopy-hydrogen lithography allowing for a direct measurement of the tunnel coupling for a given inter-dot distance. We extract ${t}_{{\rm{c}}}=5.5\pm 1.8\;{\rm{GHz}}$ and ${t}_{{\rm{c}}}=2.2\pm 1.3\;{\rm{GHz}}$ between each of the nearest-neighbour QDs which are separated by 14.5 nm and 14.0 nm, respectively. The technique allows for an accurate measurement of $t_c$ for nanoscale devices even when it is smaller than the electron temperature and is an ideal characterisation tool for multi-dot systems with a charge sensor., Comment: 6 pages, 4 figures

The aggressive scaling of silicon-based nanoelectronics has reached the regime where device function is affected not only by the presence of individual dopants, but more critically their position in the structure. The quantitative determination of the positions of subsurface dopant atoms is an important issue in a range of applications from channel doping in ultra-scaled transistors to quantum information processing, and hence poses a significant challenge. Here, we establish a metrology combining low-temperature scanning tunnelling microscopy (STM) imaging and a comprehensive quantum treatment of the dopant-STM system to pin-point the exact lattice-site location of sub-surface dopants in silicon. The technique is underpinned by the observation that STM images of sub surface dopants typically contain many atomic-sized features in ordered patterns, which are highly sensitive to the details of the STM tip orbital and the absolute lattice-site position of the dopant atom itself. We demonstrate the technique on two types of dopant samples in silicon -- the first where phosphorus dopants are placed with high precision, and a second containing randomly placed arsenic dopants. Based on the quantitative agreement between STM measurements and multi-million-atom calculations, the precise lattice site of these dopants is determined, demonstrating that the metrology works to depths of about 36 lattice planes. The ability to uniquely determine the exact positions of sub-surface dopants down to depths of 5 nm will provide critical knowledge in the design and optimisation of nanoscale devices for both classical and quantum computing applications.

We present an analysis of electron transport through two weakly coupled precision placed phosphorus donors in silicon. In particular, we examine the (1,1) to (0,2) charge transition where we predict a new type of current blockade driven entirely by the nuclear spin dynamics. Using this nuclear spin blockade mechanism we devise a protocol to readout the state of single nuclear spins using electron transport measurements only. We extend our model to include realistic effects such as Stark shifted hyperfine interactions and multi-donor clusters. In the case of multi-donor clusters we show how nuclear spin blockade can be alleviated allowing for low magnetic field electron spin measurements., Comment: 10 pages, 6 figures

We compare charge transitions on a deterministic single P donor in silicon using radio frequency reflectometry measurements with a tunnel coupled reservoir and DC charge sensing using a capacitively coupled single electron transistor (SET). By measuring the conductance through the SET and comparing this with the phase shift of the reflected RF excitation from the reservoir, we can discriminate between charge transfer within the SET channel and tunneling between the donor and reservoir. The RF measurement allows observation of donor electron transitions at every charge degeneracy point in contrast to the SET conductance signal where charge transitions are only observed at triple points. The tunnel coupled reservoir has the advantage of a large effective lever arm (~35%) allowing us to independently extract a neutral donor charging energy ~62 +/- 17meV. These results demonstrate that we can replace three terminal transistors by a single terminal dispersive reservoir, promising for high bandwidth scalable donor control and readout., Comment: 5 pages, 3 figures. Copyright (2015) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics

We investigate the electrical control of the exchange coupling (J) between donor bound electrons in silicon with a detuning gate bias, crucial for the implementation of the two-qubit gate in a silicon quantum computer. We find the asymmetric 2P-1P system provides a highly tunable exchange-curve with mitigated J-oscillation, in which 5 orders of magnitude change in the exchange energy can be achieved using a modest range of electric field for 15 nm qubit separation. Compared to the barrier gate control of exchange in the Kane qubit, the detuning gate design reduces the demanding constraints of precise donor separation, gate width, density and location, as a range of J spanning over a few orders of magnitude can be engineered for various donor separations. We have combined a large-scale full band atomistic tight-binding method with a full configuration interaction technique to capture the full two-electron spectrum of gated donors, providing state-of-the-art calculations of exchange energy in 1P-1P and 2P-1P qubits.

Control of hyperfine interactions is a fundamental requirement for quantum computing architecture schemes based on shallow donors in silicon. However, at present, there is lacking an atomistic approach including critical effects of central-cell corrections and non-static screening of the donor potential capable of describing the hyperfine interaction in the presence of both strain and electric fields in realistically sized devices. We establish and apply a theoretical framework, based on atomistic tight-binding theory, to quantitatively determine the strain and electric field dependent hyperfine couplings of donors. Our method is scalable to millions of atoms, and yet captures the strain effects with an accuracy level of DFT method. Excellent agreement with the available experimental data sets allow reliable investigation of the design space of multi-qubit architectures, based on both strain-only as well as hybrid (strain+field) control of qubits. The benefits of strain are uncovered by demonstrating that a hybrid control of qubits based on (001) compressive strain and in-plane (100 or 010) fields results in higher gate fidelities and/or faster gate operations, for all of the four donor species considered (P, As, Sb, and Bi). The comparison between different donor species in strained environments further highlights the trends of hyperfine shifts, providing predictions where no experimental data exists. Whilst faster gate operations are realisable with in-plane fields for P, As, and Sb donors, only for the Bi donor, our calculations predict faster gate response in the presence of both in-plane and out-of-plane fields, truly benefiting from the proposed planar field control mechanism of the hyperfine interactions., Comment: 14 pages, 4 figures

An atomistic method of calculating the spin-lattice relaxation times ($T_1$) is presented for donors in silicon nanostructures comprising of millions of atoms. The method takes into account the full band structure of silicon including the spin-orbit interaction. The electron-phonon Hamiltonian, and hence the deformation potential, is directly evaluated from the strain-dependent tight-binding Hamiltonian. The technique is applied to single donors and donor clusters in silicon, and explains the variation of $T_1$ with the number of donors and electrons, as well as donor locations. Without any adjustable parameters, the relaxation rates in a magnetic field for both systems are found to vary as $B^5$ in excellent quantitative agreement with experimental measurements. The results also show that by engineering electronic wavefunctions in nanostructures, $T_1$ times can be varied by orders of magnitude., Comment: 5 pages, 4 figures

Buried two dimensional electron gasses (2DEGs) have recently attracted considerable attention as a testing ground for both fundamental physics and quantum computation applications. Such 2DEGs can be created by phosphorus delta (\delta) doping of silicon, a technique in which a dense and narrow dopant profile is buried beneath the Si surface. Phosphorous \delta-doping is a particularly attractive platform for fabricating scalable spin quantum bit architectures, compatible with current semiconductor technology. The band structure of the \delta-layers that underpin these devices has been studied intensely using different theoretical methods, but it has hitherto not been possible to directly compare these predictions with experimental data. Here we report the first measurement of the electronic band structure of a \delta-doped layer below the Si(001) surface by angle resolved photoemission spectroscopy (ARPES). Our measurements confirm the layer to be metallic and give direct access to the Fermi level position. Surprisingly, the direct observation of the states is possible despite them being buried far below the surface. Using this experimental approach, buried states in a wide range of other material systems, including metallic oxide interfaces, could become accessible to direct spectroscopic investigations.

This review describes recent groundbreaking results in Si, Si/SiGe and dopant-based quantum dots, and it highlights the remarkable advances in Si-based quantum physics that have occurred in the past few years. This progress has been possible thanks to materials development for both Si quantum devices, and thanks to the physical understanding of quantum effects in silicon. Recent critical steps include the isolation of single electrons, the observation of spin blockade and single-shot read-out of individual electron spins in both dopants and gated quantum dots in Si. Each of these results has come with physics that was not anticipated from previous work in other material systems. These advances underline the significant progress towards the realization of spin quantum bits in a material with a long spin coherence time, crucial for quantum computation and spintronics., Comment: Accepted for publication in Reviews of Modern Physics. 64 pages, 62 figures

We report low-frequency 1/f noise measurements of degenerately doped Si:P \delta-layers at 4.2K. The noise was found to be over six orders of magnitude lower than that of bulk Si:P systems in the metallic regime and is one of the lowest values reported for doped semiconductors. The noise was found to be nearly independent of magnetic field at low fields, indicating negligible contribution from universal conductance fluctuations. Instead interaction of electrons with very few active structural two-level systems may explain the observed noise magnitude, Comment: 4 pages, 4 figures

Monolayer \delta-doped structures in silicon have attracted renewed interest with their recent incorporation into atomic-scale device fabrication strategies as source and drain electrodes and in-plane gates. Modeling the physics of \delta-doping at this scale proves challenging, however, due to the large computational overhead associated with ab initio and atomistic methods. Here, we develop an analytical theory based on an effective mass approximation. We specifically consider the Si:P materials system, and the limit of high donor density, which has been the subject of recent experiments. In this case, metallic behavior including screening tends to smooth out the local disorder potential associated with random dopant placement. While smooth potentials may be difficult to incorporate into microscopic, single-electron analyses, the problem is easily treated in the effective mass theory by means of a jellium approximation for the ionic charge. We then go beyond the analytic model, incorporating exchange and correlation effects within a simple numerical model. We argue that such an approach is appropriate for describing realistic, high-density, highly disordered devices, providing results comparable to density functional theory, but with greater intuitive appeal, and lower computational effort. We investigate valley coupling in these structures, finding that valley splitting in the low-lying \Gamma band grows much more quickly than the \Gamma-\Delta band splitting at high densities. We also find that many-body exchange and correlation corrections affect the valley splitting more strongly than they affect the band splitting.

In order to fabricate precise atomic-scale devices in silicon using a combination of scanning tunnelling microscopy (STM) and molecular beam epitaxy it is necessary to minimize the segregation/diffusion of dopant atoms during silicon encapsulation. We characterize the surface segregation/diffusion of phosphorus atoms from a $\delta$-doped layer in silicon after encapsulation at 250$^{\circ}$C and room temperature using secondary ion mass spectrometry (SIMS), Auger electron spectroscopy (AES), and STM. We show that the surface phosphorus density can be reduced to a few percent of the initial $\delta$-doped density if the phosphorus atoms are encapsulated with 5 or 10 monolayers of epitaxial silicon at room temperature. We highlight the limitations of SIMS and AES to determine phosphorus segregation at the atomic-scale and the advantage of using STM directly.