Engineering topological states in atom-based semiconductor quantum dots.

The realization of controllable fermionic quantum systems via quantum simulation is instrumental for exploring many of the most intriguing effects in condensed-matter physics1-3. Semiconductor quantum dots are particularly promising for quantum simulation as they can be engineered to achieve strong quantum correlations. However, although simulation of the Fermi-Hubbard model4 and Nagaoka ferromagnetism5 have been reported before, the simplest one-dimensional model of strongly correlated topological matter, the many-body Su-Schrieffer-Heeger (SSH) model6-11, has so far remained elusive-mostly owing to the challenge of precisely engineering long-range interactions between electrons to reproduce the chosen Hamiltonian. Here we show that for precision-placed atoms in silicon with strong Coulomb confinement, we can engineer a minimum of six all-epitaxial in-plane gates to tune the energy levels across a linear array of ten quantum dots to realize both the trivial and the topological phases of the many-body SSH model. The strong on-site energies (about 25 millielectronvolts) and the ability to engineer gates with subnanometre precision in a unique staggered design allow us to tune the ratio between intercell and intracell electron transport to observe clear signatures of a topological phase with two conductance peaks at quarter-filling, compared with the ten conductance peaks of the trivial phase. The demonstration of the SSH model in a fermionic system isomorphic to qubits showcases our highly controllable quantum system and its usefulness for future simulations of strongly interacting electrons.

A two-qubit gate between phosphorus donor electrons in silicon.

Electron spin qubits formed by atoms in silicon have large (tens of millielectronvolts) orbital energies and weak spin-orbit coupling, giving rise to isolated electron spin ground states with coherence times of seconds1,2. High-fidelity (more than 99.9 per cent) coherent control of such qubits has been demonstrated3, promising an attractive platform for quantum computing. However, inter-qubit coupling-which is essential for realizing large-scale circuits in atom-based qubits-has not yet been achieved. Exchange interactions between electron spins4,5 promise fast (gigahertz) gate operations with two-qubit gates, as recently demonstrated in gate-defined silicon quantum dots6-10. However, creating a tunable exchange interaction between two electrons bound to phosphorus atom qubits has not been possible until now. This is because it is difficult to determine the atomic distance required to turn the exchange interaction on and off while aligning the atomic circuitry for high-fidelity, independent spin readout. Here we report a fast (about 800 picoseconds) [Formula: see text] two-qubit exchange gate between phosphorus donor electron spin qubits in silicon using independent single-shot spin readout with a readout fidelity of about 94 per cent on a complete set of basis states. By engineering qubit placement on the atomic scale, we provide a route to the realization and efficient characterization of multi-qubit quantum circuits based on donor qubits in silicon.

High-Fidelity Single-Shot Singlet-Triplet Readout of Precision-Placed Donors in Silicon.

In this work we perform direct single-shot readout of the singlet-triplet states in exchange coupled electrons confined to precision-placed donor atoms in silicon. Our method takes advantage of the large energy splitting given by the Pauli-spin blockaded (2,0) triplet states, from which we can achieve a single-shot readout fidelity of 98.4±0.2%. We measure the triplet-minus relaxation time to be of the order 3 s at 2.5 T and observe its predicted decrease as a function of magnetic field, reaching 0.5 s at 1 T.

Reaction paths of phosphine dissociation on silicon (001).

Using density functional theory and guided by extensive scanning tunneling microscopy (STM) image data, we formulate a detailed mechanism for the dissociation of phosphine (PH3) molecules on the Si(001) surface at room temperature. We distinguish between a main sequence of dissociation that involves PH2+H, PH+2H, and P+3H as observable intermediates, and a secondary sequence that gives rise to PH+H, P+2H, and isolated phosphorus adatoms. The latter sequence arises because PH2 fragments are surprisingly mobile on Si(001) and can diffuse away from the third hydrogen atom that makes up the PH3 stoichiometry. Our calculated activation energies describe the competition between diffusion and dissociation pathways and hence provide a comprehensive model for the numerous adsorbate species observed in STM experiments.

Spatially resolving valley quantum interference of a donor in silicon.

Electron and nuclear spins of donor ensembles in isotopically pure silicon experience a vacuum-like environment, giving them extraordinary coherence. However, in contrast to a real vacuum, electrons in silicon occupy quantum superpositions of valleys in momentum space. Addressable single-qubit and two-qubit operations in silicon require that qubits are placed near interfaces, modifying the valley degrees of freedom associated with these quantum superpositions and strongly influencing qubit relaxation and exchange processes. Yet to date, spectroscopic measurements have only probed wavefunctions indirectly, preventing direct experimental access to valley population, donor position and environment. Here we directly probe the probability density of single quantum states of individual subsurface donors, in real space and reciprocal space, using scanning tunnelling spectroscopy. We directly observe quantum mechanical valley interference patterns associated with linear superpositions of valleys in the donor ground state. The valley population is found to be within 5% of a bulk donor when 2.85 ± 0.45 nm from the interface, indicating that valley-perturbation-induced enhancement of spin relaxation will be negligible for depths greater than 3 nm. The observed valley interference will render two-qubit exchange gates sensitive to atomic-scale variations in positions of subsurface donors. Moreover, these results will also be of interest for emerging schemes proposing to encode information directly in valley polarization.

High-Fidelity Rapid Initialization and Read-Out of an Electron Spin via the Single Donor D(-) Charge State.

We demonstrate high-fidelity electron spin read-out of a precision placed single donor in silicon via spin selective tunneling to either the D(+) or D(-) charge state of the donor. By performing read-out at the stable two electron D(0)↔D(-) charge transition we can increase the tunnel rates to a nearby single electron transistor charge sensor by nearly 2 orders of magnitude, allowing faster qubit read-out (1 ms) with minimum loss in read-out fidelity (98.4%) compared to read-out at the D(+)↔D(0) transition (99.6%). Furthermore, we show that read-out via the D(-) charge state can be used to rapidly initialize the electron spin qubit in its ground state with a fidelity of F(I)=99.8%.

Spontaneous breaking of time-reversal symmetry in strongly interacting two-dimensional electron layers in silicon and germanium.

We report experimental evidence of a remarkable spontaneous time-reversal symmetry breaking in two-dimensional electron systems formed by atomically confined doping of phosphorus (P) atoms inside bulk crystalline silicon (Si) and germanium (Ge). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si:P and Ge:P delta layers, suggesting an effect driven by Coulomb interactions. In-plane magnetotransport measurements indicate the presence of intrinsic local spin fluctuations at low doping, providing a microscopic mechanism for spontaneous lifting of the time-reversal symmetry. Our experiments suggest the emergence of a new many-body quantum state when two-dimensional electrons are confined to narrow half-filled impurity bands.

Noncollinear paramagnetism of a GaAs two-dimensional hole system.

We have performed transport measurements in tilted magnetic fields in a two-dimensional hole system grown on the surface of a (311)A GaAs crystal. A striking asymmetry of Shubnikov-de Haas oscillations occurs upon reversing the in-plane component of the magnetic field along the low-symmetry [2[over ¯]33] axis. As usual, the magnetoconductance oscillations are symmetric with respect to reversal of the in-plane field component aligned with the high-symmetry [011[over ¯]] axis. Our observations demonstrate that an in-plane magnetic field can generate an out-of-plane component of magnetization in a low-symmetry hole system, creating new possibilities for spin manipulation.

Lithography and doping in strained Si towards atomically precise device fabrication.

We investigate the ability to introduce strain into atomic-scale silicon device fabrication by performing hydrogen lithography and creating electrically active phosphorus δ-doped silicon on strained silicon-on-insulator (sSOI) substrates. Lithographic patterns were obtained by selectively desorbing hydrogen atoms from a H resist layer adsorbed on a clean, atomically flat sSOI(001) surface with a scanning tunnelling microscope tip operating in ultra-high vacuum. The influence of the tip-to-sample bias on the lithographic process was investigated allowing us to pattern feature-sizes from several microns down to 1.3 nm. In parallel we have investigated the impact of strain on the electrical properties of P:Si δ-doped layers. Despite the presence of strain inducing surface variations in the silicon substrate we still achieve high carrier densities (>1.0 × 10(14) cm(-2)) with mobilities of ∼100 cm(2) V(-1) s(-1). These results open up the possibility of a scanning-probe lithography approach to the fabrication of strained atomic-scale devices in silicon.

High-fidelity initialization and control of electron and nuclear spins in a four-qubit register.

Single electron spins bound to multi-phosphorus nuclear spin registers in silicon have demonstrated fast (0.8 ns) two-qubit SWAP gates and long spin relaxation times (~30 s). In these spin registers, when the donors are ionized, the nuclear spins remain weakly coupled to their environment, allowing exceptionally long coherence times. When the electron is present, the hyperfine interaction allows coupling of the spin and charge degrees of freedom for fast qubit operation and control. Here we demonstrate the use of the hyperfine interaction to enact electric dipole spin resonance to realize high-fidelity ( F = 10 0 - 6 + 0 %) initialization of all the nuclear spins within a four-qubit nuclear spin register. By controllably initializing the nuclear spins to ⇓ ⇓ ⇓ , we achieve single-electron qubit gate fidelities of F = 99.78 ± 0.07% (Clifford gate fidelities of 99.58 ± 0.14%), above the fault-tolerant threshold for the surface code with a coherence time of T 2 * = 12 µ s .

Epitaxial top-gated atomic-scale silicon wire in a three-dimensional architecture.

Three-dimensional (3D) control of dopant profiles in silicon is a critical requirement for fabricating atomically precise transistors. We demonstrate conductance modulation through an atomic scale 3 nm wide δ-doped silicon-phosphorus wire using a vertically separated epitaxial doped Si:P top-gate. We show that intrinsic crystalline silicon grown at low temperatures (∼250 °C) serves as an effective gate dielectric permitting us to achieve large gate ranges (∼2.6 V) with leakage currents below 1 pA. Combining scanning tunneling lithography for precise lateral confinement, with monolayer doping and low temperature epitaxial overgrowth for precise vertical confinement, we can realize multiple layers of nano-patterned dopants in a single crystal material. These results demonstrate the viability of highly doped, vertically separated epitaxial gates in an all-crystalline architecture with long-term implications for monolithic 3D silicon circuits and for the realization of atomically precise donor architectures for quantum computing.

Stacking of 2D electron gases in Ge probed at the atomic level and its correlation to low-temperature magnetotransport.

Stacking of two-dimensional electron gases (2DEGs) obtained by δ-doping of Ge and patterned by scanning probe lithography is a promising approach to realize ultrascaled 3D epitaxial circuits, where multiple layers of active electronic components are integrated both vertically and horizontally. We use atom probe tomography and magnetotransport to correlate the real space 3D atomic distribution of dopants in the crystal with the quantum correction to the conductivity observed at low temperatures, probing if closely stacked δ-layers in Ge behave as independent 2DEGs. We find that at a separation of 9 nm the stacked-2DEGs, while interacting, still maintain their individuality in terms of electron transport and show long phase coherence lengths (∼220 nm). Strong vertical electron confinement is crucial to this finding, resulting in an interlayer scattering time much longer (∼1000 × ) than the scattering time within the dopant plane.

n-type doping of germanium from phosphine: early stages resolved at the atomic level.

To understand the atomistic doping process of phosphorus in germanium, we present a combined scanning tunneling microscopy, temperature programed desorption, and density functional theory study of the reactions of phosphine with the Ge(001) surface. Combining experimental and theoretical results, we demonstrate that PH(2) + H with a footprint of one Ge dimer is the only product of room temperature chemisorption. Further dissociation requires thermal activation. At saturation coverage, PH(2) + H species self-assemble into ordered patterns leading to phosphorus coverages of up to 0.5 monolayers.

A complete fabrication route for atomic-scale, donor-based devices in single-crystal germanium.

Despite the rapidly growing interest in Ge for ultrascaled classical transistors and innovative quantum devices, the field of Ge nanoelectronics is still in its infancy. One major hurdle has been electron confinement since fast dopant diffusion occurs when traditional Si CMOS fabrication processes are applied to Ge. We demonstrate a complete fabrication route for atomic-scale, donor-based devices in single-crystal Ge using a combination of scanning tunneling microscope lithography and high-quality crystal growth. The cornerstone of this fabrication process is an innovative lithographic procedure based on direct laser patterning of the semiconductor surface, allowing the gap between atomic-scale STM-patterned structures and the outside world to be bridged. Using this fabrication process, we show electron confinement in a 5 nm wide phosphorus-doped nanowire in single-crystal Ge. At cryogenic temperatures, Ohmic behavior is observed and a low planar resistivity of 8.3 kΩ/□ is measured.

Preparation of the Ge(001) surface towards fabrication of atomic-scale germanium devices.

We demonstrate the preparation of a clean Ge(001) surface with minimal roughness (RMS ~0.6 Å), low defect densities (~0.2% ML) and wide mono-atomic terraces (~80-100 nm). We use an ex situ wet chemical process combined with an in situ anneal treatment followed by a homoepitaxial buffer layer grown by molecular beam epitaxy and a subsequent final thermal anneal. Using scanning tunneling microscopy, we investigate the effect on the surface morphology of using different chemical reagents, concentrations as well as substrate temperature during growth. Such a high quality Ge(001) surface enables the formation of defect-free H-terminated Ge surfaces for subsequent patterning of atomic-scale devices by scanning tunneling lithography. We have achieved atomic-scale dangling bond wire structures 1.6 nm wide and 40 nm long as well as large, micron-size patterns with clear contrast of lithography in STM images.

Phosphorus atomic layer doping of germanium by the stacking of multiple δ layers.

In this paper we demonstrate the fabrication of multiple, narrow, and closely spaced δ-doped P layers in Ge. The P profiles are obtained by repeated phosphine adsorption onto atomically flat Ge(001) surfaces and subsequent thermal incorporation of P into the lattice. A dual-temperature epitaxial Ge overgrowth separates the layers, minimizing dopant redistribution and guaranteeing an atomically flat starting surface for each doping cycle. This technique allows P atomic layer doping in Ge and can be scaled up to an arbitrary number of doped layers maintaining atomic level control of the interface. Low sheet resistivities (280 Ω/ [symbol see text ) and high carrier densities (2 × 10(14) cm( - 2), corresponding to 7.4 × 10(19) cm( - 3)) are demonstrated at 4.2 K.

Valley interference and spin exchange at the atomic scale in silicon.

Tunneling is a fundamental quantum process with no classical equivalent, which can compete with Coulomb interactions to give rise to complex phenomena. Phosphorus dopants in silicon can be placed with atomic precision to address the different regimes arising from this competition. However, they exploit wavefunctions relying on crystal band symmetries, which tunneling interactions are inherently sensitive to. Here we directly image lattice-aperiodic valley interference between coupled atoms in silicon using scanning tunneling microscopy. Our atomistic analysis unveils the role of envelope anisotropy, valley interference and dopant placement on the Heisenberg spin exchange interaction. We find that the exchange can become immune to valley interference by engineering in-plane dopant placement along specific crystallographic directions. A vacuum-like behaviour is recovered, where the exchange is maximised to the overlap between the donor orbitals, and pair-to-pair variations limited to a factor of less than 10 considering the accuracy in dopant positioning. This robustness remains over a large range of distances, from the strongly Coulomb interacting regime relevant for high-fidelity quantum computation to strongly coupled donor arrays of interest for quantum simulation in silicon.

Observation of charge transport by negatively charged excitons.

We report transport of electron-hole complexes in semiconductor quantum wells under applied electric fields. Negatively charged excitons (X-), created by laser excitation of a high electron mobility transistor, are observed to drift upon applying a voltage between the source and drain. In contrast, neutral excitons do not drift under similar conditions. The X- mobility is found to be as high as 6.5 x 10(4) cm2 V-1 s-1. The results demonstrate that X- exists as a free particle in the best-quality samples and suggest that light emission from opto-electronic devices can be manipulated through exciton drift under applied electric fields.

Atomic-scale patterning of hydrogen terminated Ge(001) by scanning tunneling microscopy.

In this paper we demonstrate atomic-scale lithography on hydrogen terminated Ge(001). The lithographic patterns were obtained by selectively desorbing hydrogen atoms from a H resist layer adsorbed on a clean, atomically flat Ge(001) surface with a scanning tunneling microscope tip operating in ultra-high vacuum. The influence of the tip-to-sample bias on the lithographic process have been investigated. Lithographic patterns with feature-sizes from 200 to 1.8 nm have been achieved by varying the tip-to-sample bias. These results open up the possibility of a scanning-probe lithography approach to the fabrication of future atomic-scale devices in germanium.

Two-electron spin correlations in precision placed donors in silicon.

Substitutional donor atoms in silicon are promising qubits for quantum computation with extremely long relaxation and dephasing times demonstrated. One of the critical challenges of scaling these systems is determining inter-donor distances to achieve controllable wavefunction overlap while at the same time performing high fidelity spin readout on each qubit. Here we achieve such a device by means of scanning tunnelling microscopy lithography. We measure anti-correlated spin states between two donor-based spin qubits in silicon separated by 16 ± 1 nm. By utilising an asymmetric system with two phosphorus donors at one qubit site and one on the other (2P-1P), we demonstrate that the exchange interaction can be turned on and off via electrical control of two in-plane phosphorus doped detuning gates. We determine the tunnel coupling between the 2P-1P system to be 200 MHz and provide a roadmap for the observation of two-electron coherent exchange oscillations.