Electrically Tunable, Rapid Spin-Orbit Torque Induced Modulation of Colossal Magnetoresistance in Mn3Si2Te6 Nanoflakes.

As a quasi-layered ferrimagnetic material, Mn3Si2Te6 nanoflakes exhibit magnetoresistance behavior that is fundamentally different from their bulk crystal counterparts. They offer three key properties crucial for spintronics. First, at least 106 times faster response compared to that exhibited by bulk crystals has been observed in current-controlled resistance and magnetoresistance. Second, ultralow current density is required for resistance modulation (∼5 A/cm2). Third, electrically gate-tunable magnetoresistance has been realized. Theoretical calculations reveal that the unique magnetoresistance behavior in the Mn3Si2Te6 nanoflakes arises from a magnetic field induced band gap shift across the Fermi level. The rapid current induced resistance variation is attributed to spin-orbit torque, an intrinsically ultrafast process (∼nanoseconds). This study suggests promising avenues for spintronic applications. In addition, it highlights Mn3Si2Te6 nanoflakes as a suitable platform for investigating the intriguing physics underlying chiral orbital moments, magnetic field induced band variation, and spin torque.

Dominance of Extrinsic Scattering Mechanisms in the Orbital Hall Effect: Graphene, Transition Metal Dichalcogenides, and Topological Antiferromagnets.

The theory of the orbital Hall effect (OHE), a transverse flow of orbital angular momentum (OAM) in response to an electric field, has concentrated on intrinsic mechanisms. Here, using a quantum kinetic formulation, we determine the full OHE in the presence of short-range disorder using 2D massive Dirac fermions as a prototype. We find that, in doped systems, extrinsic effects associated with the Fermi surface (skew scattering and side jump) provide ≈95% of the OHE. This suggests that, at experimentally relevant transport densities, the OHE is primarily extrinsic.

Nonlinear Valley Hall Effect.

The valley Hall effect arises from valley-contrasting Berry curvature and requires inversion symmetry breaking. Here, we propose a nonlinear mechanism to generate a valley Hall current in systems with both inversion and time-reversal symmetry, where the linear and second-order charge Hall currents vanish along with the linear valley Hall current. We show that a second-order valley Hall signal emerges from the electric field correction to the Berry curvature, provided a valley-contrasting anisotropic dispersion is engineered. We demonstrate the nonlinear valley Hall effect in tilted massless Dirac fermions in strained graphene and organic semiconductors. Our Letter opens up the possibility of controlling the valley degree of freedom in inversion symmetric systems via nonlinear valleytronics.

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.

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.

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.

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 kBT 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.

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.

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.

Nonlinear Ballistic Response of Quantum Spin Hall Edge States.

Topological edge states (TES) exhibit dissipationless transport, yet their dispersion has never been probed. Here we show that the nonlinear electrical response of ballistic TES ascertains the presence of symmetry breaking terms, such as deviations from nonlinearity and tilted spin quantization axes. The nonlinear response stems from discontinuities in the band occupation on either side of a Zeeman gap, and its direction is set by the spin orientation with respect to the Zeeman field. We determine the edge dispersion for several classes of TES and discuss experimental measurement.

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.

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.

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.

Sign Change in the Anomalous Hall Effect and Strong Transport Effects in a 2D Massive Dirac Metal Due to Spin-Charge Correlated Disorder.

The anomalous Hall effect (AHE) is highly sensitive to disorder in the metallic phase. Here we show that statistical correlations between the charge-spin disorder sectors strongly affect the conductivity and the sign or magnitude of AHE. As the correlation between the charge and gauge-mass components increases, so does the AHE, achieving its universal value, and even exceeding it, although the system is an impure metal. The AHE can change sign when the anticorrelations reverse the sign of the effective Dirac mass, a possible mechanism behind the sign change seen in recent experiments.

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.

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.

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.

Valley Phase and Voltage Control of Coherent Manipulation in Si Quantum Dots.

With any roughness at the interface of an indirect-bandgap semiconducting dot, the phase of the valley-orbit coupling can take on a random value. This random value, in double quantum dots, causes a large change in the exchange splitting. We demonstrate a simple analytical method to calculate the phase, and thus the exchange splitting and singlet-triplet qubit frequency, for an arbitrary interface. We then show that, with lateral control of the position of a quantum dot using a gate voltage, the valley-orbit phase can be controlled over a wide range, so that variations in the exchange splitting can be controlled for individual devices. Finally, we suggest experiments to measure the valley phase and the concomitant gate voltage control.

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/AlxGa1-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.

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.