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Operation speed and coherence time are two core measures for the viability of a qubit. Strong spin-orbit interaction (SOI) and relatively weak hyperfine interaction make holes in germanium (Ge) intriguing candidates for spin qubits with rapid, all-electrical coherent control. Here we report ultrafast single-spin manipulation in a hole-based double quantum dot in a germanium hut wire (GHW). Mediated by the strong SOI, a Rabi frequency exceeding 540 MHz is observed at a magnetic field of 100 mT, setting a record for ultrafast spin qubit control in semiconductor systems. We demonstrate that the strong SOI of heavy holes (HHs) in our GHW, characterized by a very short spin-orbit length of 1.5 nm, enables the rapid gate operations we accomplish. Our results demonstrate the potential of ultrafast coherent control of hole spin qubits to meet the requirement of DiVincenzo’s criteria for a scalable quantum information processor. Hole-spin qubits in germanium are promising candidates for rapid, all-electrical qubit control. Here the authors report Rabi oscillations with the record frequency of 540 MHz in a hole-based double quantum dot in a germanium hut wire, which is attributed to strong spin-orbit interaction of heavy holes.

The investigation of orbital angular momentum (OAM) of delocalised Bloch electrons has advanced our understanding of magnetic, transport, and optical phenomena in crystals, drawing widespread interest across various materials science domains, from metals and semiconductors to topological and magnetic materials. Here, we review OAM dynamics in depth, focusing on key concepts and non-equilibrium systems, and laying the groundwork for the thriving field of orbitronics. We review briefly the conventional understanding of the equilibrium OAM based on the modern theory of orbital magnetisation. Following this, we explore recent theoretical and experimental developments in out-of-equilibrium systems. We focus on the generation of an OAM density via the orbital magneto-electric, or Edelstein effect, the generation of an OAM current via the orbital Hall effect, the orbital torque resulting from them, along with their reciprocal non-equilibrium counterparts - the inverse orbital Edelstein and inverse orbital Hall effects, as well as OAM conservation. We discuss the most salient achievements and the most pressing challenges in this rapidly evolving field, and in closing we highlight the future prospects of orbitronics.

Strong spin-orbit interactions make hole quantum dots central to the quest for electrical spin qubit manipulation enabling fast, low-power, scalable quantum computation. Yet it is important to establish to what extent spin-orbit coupling exposes qubits to electrical noise, facilitating decoherence. Here, taking Ge as an example, we show that group IV gate-defined hole spin qubits generically exhibit optimal operation points, defined by the top gate electric field, at which they are both fast and long-lived: the dephasing rate vanishes to first order in the electric field noise along with all directions in space, the electron dipole spin resonance strength is maximized, while relaxation is drastically reduced at small magnetic fields. The existence of optimal operation points is traced to group IV crystal symmetry and properties of the Rashba spin-orbit interaction unique to spin-3/2 systems. Our results overturn the conventional wisdom that fast operation implies reduced lifetimes and suggest group IV hole spin qubits as ideal platforms for ultra-fast, highly coherent scalable quantum computing.

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 10 4 to 10 5 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. Spin qubits in systems with strong spin–orbit coupling can be electrically controlled, but are usually affected by short coherence times. Here, coherence times up to 10 ms are obtained for strain-engineered hole states bound to boron acceptors in silicon 28.

Silicon quantum dots are considered an excellent platform for spin qubits, partly due to their weak spin-orbit interaction. However, the sharp interfaces in the heterostructures induce a small but significant spin-orbit interaction that degrades the performance of the qubits or, when understood and controlled, could be used as a powerful resource. To understand how to control this interaction, we build a detailed profile of the spin-orbit interaction of a silicon metal-oxide-semiconductor double quantum-dot system. We probe the derivative of the Stark shift,g-factor andg-factor difference for two single-electron quantum-dot qubits as a function of external magnetic field and find that they are dominated by spin-orbit interactions originating from the vector potential, consistent with recent theoretical predictions. Conversely, by populating the double dot with two electrons, we probe the mixing of singlet and spin-polarized triplet states during electron tunneling, which we conclude is dominated by momentum-term spin-orbit interactions that vary from 1.85 MHz up to 27.5 MHz depending on the magnetic field orientation. Finally, we exploit the tunability of the derivative of the Stark shift of one of the dots to reduce its sensitivity to electric noise and observe an 80% increase inT2*. We conclude that the tuning of the spin-orbit interaction will be crucial for scalable quantum computing in silicon and that the optimal setting will depend on the exact mode of qubit operations used.

Fluid dynamics is one of the cornerstones of modern physics and has recently found applications in the transport of electrons in solids. In most solids, electron transport is dominated by extrinsic factors, such as sample geometry and scattering from impurities. However, in the hydrodynamic regime, Coulomb interactions transform the electron motion from independent particles to the collective motion of a viscous “electron fluid.” The fluid viscosity is an intrinsic property of the electron system, determined solely by the electron-electron interactions. Resolving the universal intrinsic viscosity is challenging, as it affects the resistance only through interactions with the sample boundaries, whose roughness not only is unknown but also varies from device to device. Here, we eliminate all unknown parameters by fabricating samples with smooth sidewalls to achieve the perfect slip boundary condition, which has been elusive in both molecular fluids and electronic systems. We engineer the device geometry to create viscous dissipation and reveal the true intrinsic hydrodynamic properties of a 2D system. We observe a clear transition from ballistic to hydrodynamic electron motion, driven by both temperature and magnetic field. We directly measure the viscosity and electron-electron scattering lifetime (the Fermi quasiparticle lifetime) over a wide temperature range without fitting parameters and show they have a strong dependence on electron density that cannot be explained by conventional theories based on the random phase approximation.

The highly efficient torques generated by 3D topological insulators make them a favourable platform for faster and more efficient magnetic memory devices. Recently, research into harnessing orbital angular momentum in orbital torques has received significant attention. Here we study the orbital Hall effect in topological insulators. We find that the bulk states give rise to a sizeable orbital Hall effect that is up to 3 orders of magnitude larger than the spin Hall effect in topological insulators. This is partially because the orbital angular momentum that each conduction electron carries is up to an order of magnitude larger than the ℏ /2 carried by its spin. Our results imply that the large torques measured in topological insulator/ferromagnet devices can be further enhanced through careful engineering of the heterostructure to optimise orbital-to-spin conversion.

The origins of the spin-orbit torque (SOT) at ferromagnet/topological insulator interfaces are incompletely understood. The theory has overwhelmingly focussed on the Edelstein effect due to the surface states in the presence of a scalar scattering potential. We investigate here the contribution to the SOT due to extrinsic spin-orbit (SO) scattering of the surface states, focusing on the case of an out-of-plane magnetization. We show that SO scattering brings about a sizable renormalization of the field-like SOT, which exceeds 20 % at larger strengths of the extrinsic SO parameter. The resulting SOT exhibits a maximum as a function of the Fermi energy, magnetization, and extrinsic SO strength. The field-like SOT decreases with increasing disorder strength, while the damping-like SOT is independent of the impurity density. With experimental observation in mind we also determine the role of extrinsic SO scattering on the anomalous Hall effect. Our results suggest extrinsic SO scattering is a significant contributor to the surface SOT stemming from the Edelstein effect when the magnetization is out of the plane.

2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the existence of 1D spin–momentum locked metallic edge states—both helical and chiral—surrounding an electrically insulating bulk. Forty years since the first discoveries of topological phases in condensed matter, the abstract concept of band topology has sprung into realization with several materials now available in which sizable bulk energy gaps—up to a few hundred meV—promise to enable topology for applications even at room-temperature. Further, the possibility of combining 2D TIs in heterostructures with functional materials such as multiferroics, ferromagnets, and superconductors, vastly extends the range of applicability beyond their intrinsic properties. While 2D TIs remain a unique testbed for questions of fundamental condensed matter physics, proposals seek to control the topologically protected bulk or boundary states electrically, or even induce topological phase transitions to engender switching functionality. Induction of superconducting pairing in 2D TIs strives to realize non-Abelian quasiparticles, promising avenues towards fault-tolerant topological quantum computing. This roadmap aims to present a status update of the field, reviewing recent advances and remaining challenges in theoretical understanding, materials synthesis, physical characterization and, ultimately, device perspectives.

The spin-Hall effect underpins some of the most active topics in modern physics, including spin torques and the inverse spin-Hall effect, yet it lacks a proper theoretical description. This makes it difficult to differentiate the SHE from other mechanisms, as well as differentiate band structure and disorder contributions. Here, by exploiting recent analytical breakthroughs in the understanding of the intrinsic spin-Hall effect, we devise a density functional theory method for evaluating the conserved (proper) spin current in a generic system. Spin non-conservation makes the conventional spin current physically meaningless, while the conserved spin current has been challenging to evaluate since it involves the position operator between Bloch bands. The novel method we introduce here can handle band structures with arbitrary degeneracies and incorporates all matrix elements of the position operator, including the notoriously challenging diagonal elements, which are associated with Fermi surface, group velocity, and dipolar effects but often diverge if not treated correctly. We apply this method to the most important classes of spin-Hall materials: topological insulators, 2D quantum spin-Hall insulators, non-collinear antiferromagnets, and strongly spin-orbit coupled metals. We demonstrate that the torque dipole systematically suppresses contributions to the conventional spin current such that, the proper spin current is generally smaller in magnitude and often has a different sign. Remarkably, its energy-dependence is relatively flat and featureless, and its magnitude is comparable in all classes of materials studied. These findings will guide the experiment in characterizing charge-to-spin interconversion in spintronic and orbitronic devices. We also discuss briefly a potential generalization of the method to calculate extrinsic spin currents generated by disorder scattering.