Universal intrinsic spin Hall effect

We describe a new effect in semiconductor spintronics that leads to dissipationless spin currents in paramagnetic spin-orbit coupled systems. We argue that in a high-mobility two-dimensional electron system with substantial Rashba spin-orbit coupling, a spin current that flows perpendicular to the charge current is intrinsic. In the usual case where both spin-orbit split bands are occupied, the intrinsic spin-Hall conductivity has a universal value for zero quasiparticle spectral broadening.

Antisymmetric magnetoresistance in van der Waals Fe3GeTe2/graphite/Fe3GeTe2 trilayer heterostructures

With no requirements for lattice matching, van der Waals (vdW) ferromagnetic materials are rapidly establishing themselves as effective building blocks for next-generation spintronic devices. We report a hitherto rarely seen antisymmetric magnetoresistance (MR) effect in vdW heterostructured Fe₃GeTe₂ (FGT)/graphite/FGT devices. Unlike conventional giant MR (GMR), which is characterized by two resistance states, the MR in these vdW heterostructures features distinct high-, intermediate-, and low-resistance states. This unique characteristic is suggestive of underlying physical mechanisms that differ from those observed before. After theoretical calculations, the three-resistance behavior was attributed to a spin momentum locking induced spin-polarized current at the graphite/FGT interface. Our work reveals that ferromagnetic heterostructures assembled from vdW materials can exhibit substantially different properties to those exhibited by similar heterostructures grown in vacuum. Hence, it highlights the potential for new physics and new spintronic applications to be discovered using vdW heterostructures.

Semiclassical spin transport in spin-orbit-coupled bands

Motivated by recent interest in novel spintronics effects, we develop a semiclassical theory of spin transport that is valid for spin-orbit coupled bands. Aside from the obvious convective term in which the average spin is transported at the wave packet group velocity, the spin current has additional contributions from the wave packet's spin and torque dipole moments. Electric field corrections to the group velocity and carrier spin contribute to the convective term. Summing all terms we obtain an expression for the intrinsic spin-Hall conductivity of a hole-doped semiconductor, which agrees with the Kubo formula prediction for the same quantity. We discuss the calculation of spin accumulation, which illustrates the importance of the torque dipole near the boundary of the system.

Weak Localization and Antilocalization in Topological Materials with Impurity Spin-Orbit Interactions

Topological materials have attracted considerable experimental and theoretical attention. They exhibit strong spin-orbit coupling both in the band structure (intrinsic) and in the impurity potentials (extrinsic), although the latter is often neglected. In this work, we discuss weak localization and antilocalization of massless Dirac fermions in topological insulators and massive Dirac fermions in Weyl semimetal thin films, taking into account both intrinsic and extrinsic spin-orbit interactions. The physics is governed by the complex interplay of the chiral spin texture, quasiparticle mass, and scalar and spin-orbit scattering. We demonstrate that terms linear in the extrinsic spin-orbit scattering are generally present in the Bloch and momentum relaxation times in all topological materials, and the correction to the diffusion constant is linear in the strength of the extrinsic spin-orbit. In topological insulators, which have zero quasiparticle mass, the terms linear in the impurity spin-orbit coupling lead to an observable density dependence in the weak antilocalization correction. They produce substantial qualitative modifications to the magnetoconductivity, differing greatly from the conventional Hikami-Larkin-Nagaoka formula traditionally used in experimental fits, which predicts a crossover from weak localization to antilocalization as a function of the extrinsic spin-orbit strength. In contrast, our analysis reveals that topological insulators always exhibit weak antilocalization. In Weyl semimetal thin films having intermediate to large values of the quasiparticle mass, we show that extrinsic spin-orbit scattering strongly affects the boundary of the weak localization to antilocalization transition. We produce a complete phase diagram for this transition as a function of the mass and spin-orbit scattering strength. Throughout the paper, we discuss implications for experimental work, and, at the end, we provide a brief comparison with transition metal dichalcogenides.

Gate-Controlled Magnetic Phase Transition in a van der Waals Magnet Fe5GeTe2

Magnetic van der Waals (vdW) materials are poised to enable all-electrical control of magnetism in the two-dimensional limit. However, tuning the magnetic ground state in vdW itinerant ferromagnets by voltage-induced charge doping remains a significant challenge, due to the extremely large carrier densities in these materials. Here, by cleaving the vdW itinerant ferromagnet Fe₅GeTe₂ (F5GT) into 5.4 nm (around two unit cells), we find that the ferromagnetism (FM) in F5GT can be substantially tuned by the thickness. Moreover, by utilizing a solid protonic gate, an electron doping concentration of above 10²¹ cm^-3 has been exhibited in F5GT nanosheets. Such a high carrier accumulation exceeds that possible in widely used electric double-layer transistors (EDLTs) and surpasses the intrinsic carrier density of F5GT. Importantly, it is accompanied by a magnetic phase transition from FM to antiferromagnetism (AFM). The realization of an antiferromagnetic phase in nanosheet F5GT suggests the promise of applications in high-temperature antiferromagnetic vdW devices and heterostructures.

Anisotropic Pauli Spin Blockade of Holes in a GaAs Double Quantum Dot

Electrically defined semiconductor quantum dots are attractive systems for spin manipulation and quantum information processing. Heavy-holes in both Si and GaAs are promising candidates for all-electrical spin manipulation, owing to the weak hyperfine interaction and strong spin-orbit interaction. However, it has only recently become possible to make stable quantum dots in these systems, mainly due to difficulties in device fabrication and stability. Here, we present electrical transport measurements on holes in a gate-defined double quantum dot in a GaAs/Al_xGa_1-xAs heterostructure. We observe clear Pauli spin blockade and demonstrate that the lifting of this spin blockade by an external magnetic field is highly anisotropic. Numerical calculations of heavy-hole transport through a double quantum dot in the presence of strong spin-orbit coupling show quantitative agreement with experimental results and suggest that the observed anisotropy can be explained by both the anisotropic effective hole g-factor and the surface Dresselhaus spin-orbit interaction.

Resonant Second-Harmonic Generation as a Probe of Quantum Geometry

Nonlinear responses are actively studied as probes of topology and band geometric properties of solids. Here, we show that second harmonic generation serves as a probe of the Berry curvature, quantum metric, and quantum geometric connection. We generalize the theory of second harmonic generation to include Fermi surface effects in metallic systems, and finite scattering timescale. In doped materials the Fermi surface and Fermi sea cause all second harmonic terms to exhibit resonances, and we identify two novel contributions to the second harmonic signal: a double resonance due to the Fermi surface and a higher-order pole due to the Fermi sea. We discuss experimental observation in the monolayer of time reversal symmetric Weyl semimetal WTe_{2} and the parity-time reversal symmetric topological antiferromagnet CuMnAs.

Valley-based noise-resistant quantum computation using Si quantum dots

We devise a platform for noise-resistant quantum computing using the valley degree of freedom of Si quantum dots. The qubit is encoded in two polarized (1,1) spin-triplet states with different valley compositions in a double quantum dot, with a Zeeman field enabling unambiguous initialization. A top gate gives a difference in the valley splitting between the dots, allowing controllable interdot tunneling between opposite valley eigenstates, which enables one-qubit rotations. Two-qubit operations rely on a stripline resonator, and readout on charge sensing. Sensitivity to charge and spin fluctuations is determined by intervalley processes and is greatly reduced as compared to conventional spin and charge qubits. We describe a valley echo for further noise suppression.

Generation of spin currents and spin densities in systems with reduced symmetry

We show that the spin-current response of a semiconductor crystal to an external electric field is considerably more complex than previously assumed. While in systems of high symmetry only the spin-Hall components are allowed, in systems of lower symmetry other non-spin-Hall components may be present. We argue that, when spin-orbit interactions are present only in the band structure, the distinction between intrinsic and extrinsic contributions to the spin current is not useful. We show that the generation of spin currents and that of spin densities in an electric field are closely related, and that our general theory provides a systematic way to distinguish between them in experiment. We discuss also the meaning of vertex corrections in systems with spin-orbit interactions.

Generating a Topological Anomalous Hall Effect in a Nonmagnetic Conductor: An In-Plane Magnetic Field as a Direct Probe of the Berry Curvature

We demonstrate that the Berry curvature monopole of nonmagnetic two-dimensional spin-3/2 holes leads to a novel Hall effect linear in an applied in-plane magnetic field B_{∥}. Remarkably, all scalar and spin-dependent disorder contributions vanish to leading order in B_{∥}, while there is no Lorentz force and hence no ordinary Hall effect. This purely intrinsic phenomenon, which we term the anomalous planar Hall effect (APHE), provides a direct transport probe of the Berry curvature accessible in all p-type semiconductors. We discuss experimental setups for its measurement.

Charge-Insensitive Single-Atom Spin-Orbit Qubit in Silicon

High fidelity entanglement of an on-chip array of spin qubits poses many challenges. Spin-orbit coupling (SOC) can ease some of these challenges by enabling long-ranged entanglement via electric dipole-dipole interactions, microwave photons, or phonons. However, SOC exposes conventional spin qubits to decoherence from electrical noise. Here, we propose an acceptor-based spin-orbit qubit in silicon offering long-range entanglement at a sweet spot where the qubit is protected from electrical noise. The qubit relies on quadrupolar SOC with the interface and gate potentials. As required for surface codes, 10^{5} electrically mediated single-qubit and 10^{4} dipole-dipole mediated two-qubit gates are possible in the predicted spin lifetime. Moreover, circuit quantum electrodynamics with single spins is feasible, including dispersive readout, cavity-mediated entanglement, and spin-photon entanglement. An industrially relevant silicon-based platform is employed.

Quantum computing with acceptor spins in silicon

The states of a boron acceptor near a Si/SiO2 interface, which bind two low-energy Kramers pairs, have exceptional properties for encoding quantum information and, with the aid of strain, both heavy hole and light hole-based spin qubits can be designed. Whereas a light-hole spin qubit was introduced recently (arXiv:1508.04259), here we present analytical and numerical results proving that a heavy-hole spin qubit can be reliably initialised, rotated and entangled by electrical means alone. This is due to strong Rashba-like spin-orbit interaction terms enabled by the interface inversion asymmetry. Single qubit rotations rely on electric-dipole spin resonance (EDSR), which is strongly enhanced by interface-induced spin-orbit terms. Entanglement can be accomplished by Coulomb exchange, coupling to a resonator, or spin-orbit induced dipole-dipole interactions. By analysing the qubit sensitivity to charge noise, we demonstrate that interface-induced spin-orbit terms are responsible for sweet spots in the dephasing time [Formula: see text] as a function of the top gate electric field, which are close to maxima in the EDSR strength, where the EDSR gate has high fidelity. We show that both qubits can be described using the same starting Hamiltonian, and by comparing their properties we show that the complex interplay of bulk and interface-induced spin-orbit terms allows a high degree of electrical control and makes acceptors potential candidates for scalable quantum computation in Si.

Overcoming Boltzmann's Tyranny in a Transistor via the Topological Quantum Field Effect

The subthreshold swing is the critical parameter determining the operation of a transistor in low-power applications such as switches. It determines the fraction of dissipation due to the gate capacitance used for turning the device on and off, and in a conventional transistor it is limited by Boltzmann's tyranny to k_BT ln(10)/q. Here, we demonstrate that the subthreshold swing of a topological transistor in which conduction is enabled by a topological phase transition via electric field switching, can be sizably reduced in a noninteracting system by modulating the Rashba spin-orbit interaction. By developing a theoretical framework for quantum spin Hall materials with honeycomb lattices, we show that the Rashba interaction can reduce the subthreshold swing by more than 25% compared to Boltzmann's limit in currently available materials but without any fundamental lower bound, a discovery that can guide future material design and steer the engineering of topological quantum devices.

Resonant Photovoltaic Effect in Doped Magnetic Semiconductors

The rectified nonlinear response of a clean, time-reversal symmetric, undoped semiconductor to an ac electric field includes a well known intrinsic shift current. We show that when Kramers degeneracy is broken, a distinct second order rectified response appears due to Bloch state anomalous velocities in a system with an oscillating Fermi surface. This effect, which we refer to as the resonant photovoltaic effect, produces a resonant galvanic current peak at the interband absorption threshold in doped semiconductors or semimetals with approximate particle-hole symmetry. We evaluate the resonant photovoltaic effect for a model of the surface states of a magnetized topological insulator.

Engineering long spin coherence times of spin-orbit qubits in silicon

Electron-spin qubits have long coherence times suitable for quantum technologies. Spin-orbit coupling promises to greatly improve spin qubit scalability and functionality, allowing qubit coupling via photons, phonons or mutual capacitances, and enabling the realization of engineered hybrid and topological quantum systems. However, despite much recent interest, results to date have yielded short coherence times (from 0.1 to 1 μs). Here we demonstrate ultra-long coherence times of 10 ms for holes where spin-orbit coupling yields quantized total angular momentum. We focus on holes bound to boron acceptors in bulk silicon 28, whose wavefunction symmetry can be controlled through crystal strain, allowing direct control over the longitudinal electric dipole that causes decoherence. The results rival the best electron-spin qubits and are 10⁴ to 10⁵ longer than previous spin-orbit qubits. These results open a pathway to develop new artificial quantum systems and to improve the functionality and scalability of spin-based quantum technologies.

Helical Edge Transport in Millimeter-Scale Thin Films of Na3Bi

A two-dimensional topological insulator (2DTI) has an insulating bulk and helical edges robust to nonmagnetic backscattering. While ballistic transport has been demonstrated in micron-scale 2DTIs, larger samples show significant backscattering and a nearly temperature-independent resistance of unclear origin. Spin polarization has been measured, however the degree of helicity is difficult to quantify. Here, we study 2DTI few-layer Na₃Bi on insulating Al₂O₃. A nonlocal conductance measurement demonstrates edge conductance in the topological regime with an edge mean free path ∼100 nm. A perpendicular magnetic field suppresses spin-flip scattering in the helical edges, resulting in a giant negative magnetoresistance (GNMR) up to 80% at 0.9 T. Comparison to theory indicates >96% of scattering is helical spin scattering significantly exceeding the maximum (67%) expected for a nonhelical metal. GNMR, coupled with nonlocal measurements, thus provides an unambiguous experimental signature of helical edges that we expect to be generically useful in understanding 2DTIs.

Quantum phase transitions and topological proximity effects in graphene nanoribbon heterostructures

Topological insulators are bulk insulators that possess robust chiral conducting states along their interfaces with normal insulators. A tremendous research effort has recently been devoted to topological insulator-based heterostructures, in which conventional proximity effects give rise to a series of exotic physical phenomena. Here we establish the potential existence of topological proximity effects at the interface between a topological insulator and a normal insulator, using graphene-based heterostructures as prototypical systems. Unlike conventional proximity effects in topological insulator based heterostructures, which refer to various phase transitions associated with the symmetry breaking of specific local order parameters, topological proximity effects describe the rich variety of quantum phase transitions associated with the global properties of the system measured by the location of the topological edge states. Specifically, we show that the location of the topological edge states exhibits a versatile tunability as a function of the interface orientation, the strength of the interface tunnel coupling between a topological graphene nanoribbon and a normal graphene nanoribbon, the spin-orbit coupling strength in the normal graphene nanoribbon, and the width of the system. For zigzag and bearded graphene nanoribbons, the topological edge states can be tuned to be either at the interface or outer edge of the normal ribbon. For armchair graphene nanoribbons, the potential location of the topological edge state can be further shifted to the edge of or within the normal ribbon, to the interface, or diving into the topological graphene nanoribbon. We further show that the topological phase diagram established for the prototypical graphene heterostructures can also explain the intriguing quantum phase transition reported recently in other topological-insulator heterostructures. We also discuss potential experimental realizations of the predicted topological proximity effects, which may pave the way for integrating the salient functionality of topological insulators and graphene in future device applications.

Electrically driven spin qubit based on valley mixing

The electrical control of single spin qubits based on semiconductor quantum dots is of great interest for scalable quantum computing since electric fields provide an alternative mechanism for qubit control compared with magnetic fields and can also be easier to produce. Here we outline the mechanism for a drastic enhancement in the electrically-driven spin rotation frequency for silicon quantum dot qubits in the presence of a step at a heterointerface. The enhancement is due to the strong coupling between the ground and excited states which occurs when the electron wave function overcomes the potential barrier induced by the interface step. We theoretically calculate single qubit gate times tπ of 170 ns for a quantum dot confined at a silicon/silicon-dioxide interface. The engineering of such steps could be used to achieve fast electrical rotation and entanglement of spin qubits despite the weak spin-orbit coupling in silicon.

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.

Electrical Control of the Zeeman Spin Splitting in Two-Dimensional Hole Systems

Semiconductor holes with strong spin-orbit coupling allow all-electrical spin control, with broad applications ranging from spintronics to quantum computation. Using a two-dimensional hole system in a gallium arsenide quantum well, we demonstrate a new mechanism of electrically controlling the Zeeman splitting, which is achieved through altering the hole wave vector k. We find a threefold enhancement of the in-plane g-factor g_{∥}(k). We introduce a new method for quantifying the Zeeman splitting from magnetoresistance measurements, since the conventional tilted field approach fails for two-dimensional systems with strong spin-orbit coupling. Finally, we show that the Rashba spin-orbit interaction suppresses the in-plane Zeeman interaction at low magnetic fields. The ability to control the Zeeman splitting with electric fields opens up new possibilities for future quantum spin-based devices, manipulating non-Abelian geometric phases, and realizing Majorana systems in p-type superconductor systems.

Room-Temperature Magnetic Phase Transition in an Electrically Tuned van der Waals Ferromagnet

Finding tunable van der Waals (vdW) ferromagnets that operate at above room temperature is an important research focus in physics and materials science. Most vdW magnets are only intrinsically magnetic far below room temperature and magnetism with square-shaped hysteresis at room temperature has yet to be observed. Here, we report magnetism in a quasi-2D magnet Cr_{1.2}Te_{2} observed at room temperature (290 K). This magnetism was tuned via a protonic gate with an electron doping concentration up to 3.8×10^{21}  cm^{-3}. We observed nonmonotonic evolutions in both coercivity and anomalous Hall resistivity. Under increased electron doping, the coercivities and anomalous Hall effects (AHEs) vanished, indicating a doping-induced magnetic phase transition. This occurred up to room temperature. DFT calculations showed the formation of an antiferromagnetic (AFM) phase caused by the intercalation of protons which induced significant electron doping in the Cr_{1.2}Te_{2}. The tunability of the magnetic properties and phase in room temperature magnetic vdW Cr_{1.2}Te_{2} is a significant step towards practical spintronic devices.

Progress in Epitaxial Thin-Film Na3 Bi as a Topological Electronic Material

Trisodium bismuthide (Na₃ Bi) is the first experimentally verified topological Dirac semimetal, and is a 3D analogue of graphene hosting relativistic Dirac fermions. Its unconventional momentum-energy relationship is interesting from a fundamental perspective, yielding exciting physical properties such as chiral charge carriers, the chiral anomaly, and weak anti-localization. It also shows promise for realizing topological electronic devices such as topological transistors. Herein, an overview of the substantial progress achieved in the last few years on Na₃ Bi is presented, with a focus on technologically relevant large-area thin films synthesized via molecular beam epitaxy. Key theoretical aspects underpinning the unique electronic properties of Na₃ Bi are introduced. Next, the growth process on different substrates is reviewed. Spectroscopic and microscopic features are illustrated, and an analysis of semiclassical and quantum transport phenomena in different doping regimes is provided. The emergent properties arising from confinement in two dimensions, including thickness-dependent and electric-field-driven topological phase transitions, are addressed, with an outlook toward current challenges and expected future progress.

Strong Spin-Orbit Contribution to the Hall Coefficient of Two-Dimensional Hole Systems

Classical charge transport, such as longitudinal and Hall currents in weak magnetic fields, is usually not affected by quantum phenomena. Yet relativistic quantum mechanics is at the heart of the spin-orbit interaction, which has been at the forefront of efforts to realize spin-based electronics, new phases of matter, and topological quantum computing. In this work we demonstrate that quantum spin dynamics induced by the spin-orbit interaction is directly observable in classical charge transport. We determine the Hall coefficient R_{H} of two-dimensional hole systems at low magnetic fields and show that it has a sizable spin-orbit contribution, which depends on the density p, is independent of temperature, is a strong function of the top gate electric field, and can reach ∼20% of the total. We provide a general method for extracting the spin-orbit parameter from magnetotransport data, applicable even at higher temperatures where Shubnikov-de Haas oscillations and weak antilocalization are difficult to observe. Our work will enable experimentalists to measure spin-orbit parameters without requiring large magnetic fields, ultralow temperatures, or optical setups.

Unconventional Temperature Dependence of the Anomalous Hall Effect in HgCr_{2}Se_{4}

At sufficiently low temperatures, many quantum effects, such as weak localization, electron-electron interaction (EEI), and Kondo screening, can lead to pronounced corrections to the semiclassical electron transport. Although low temperature corrections to longitudinal resistivity, ordinary Hall resistivity, or anomalous Hall (AH) resistivity are often observed, the corrections to three of them have never been simultaneously detected in a single sample. Here, we report on the observation of sqrt[T]-type temperature dependences of the longitudinal, ordinary Hall and AH resistivities at temperatures down to at least 20 mK in n-type HgCr_{2}Se_{4}, a half-metallic ferromagnetic semiconductor that can reach extremely low carrier densities. For the samples with moderate disorder, the longitudinal and ordinary Hall conductivities can be satisfactorily described by the EEI theory developed by Altshuler et al., whereas the large corrections to AH conductivity are inconsistent with the existing theory, which predicts vanishing and finite corrections to AH conductivity for EEI and weak localization, respectively.

Spin-orbit torques due to topological insulator surface states: an in-plane magnetization as a probe of extrinsic spin-orbit scattering

Topological insulator (TI) surface states exert strong spin-orbit torques. When the magnetization is in the plane its interaction with the TI conduction electrons is non-trivial, and is influenced by extrinsic spin-orbit scattering. This is expected to be strong in TIs but is difficult to calculate and to measure unambiguously. Here we show that extrinsic spin-orbit scattering sizably renormalizes the surface state spin-orbit torque resulting in a strong density dependence. The magnitude of the renormalization of the spin torque and the effect of spin-orbit scattering on the relative sizes of the in-plane and out-of-plane field-like torques have strong implications for experiment: We propose two separate experimental signatures for the measurement of its presence.