Strongly coupled edge states in a graphene quantum Hall interferometer.

Electronic interferometers using the chiral, one-dimensional (1D) edge channels of the quantum Hall effect (QHE) can demonstrate a wealth of fundamental phenomena. The recent observation of phase jumps in a Fabry-Pérot (FP) interferometer revealed anyonic quasiparticle exchange statistics in the fractional QHE. When multiple integer edge channels are involved, FP interferometers have exhibited anomalous Aharonov-Bohm (AB) interference frequency doubling, suggesting putative pairing of electrons into 2 e quasiparticles. Here, we use a highly tunable graphene-based QHE FP interferometer to observe the connection between interference phase jumps and AB frequency doubling, unveiling how strong repulsive interaction between edge channels leads to the apparent pairing phenomena. By tuning electron density in-situ from filling factor ν < 2 to ν > 7 , we tune the interaction strength and observe periodic interference phase jumps leading to AB frequency doubling. Our observations demonstrate that the combination of repulsive interaction between the spin-split ν = 2 edge channels and charge quantization is sufficient to explain the frequency doubling, through a near-perfect charge screening between the localized and extended edge channels. Our results show that interferometers are sensitive probes of microscopic interactions and enable future experiments studying correlated electrons in 1D channels using density-tunable graphene.

On-chip multi-degree-of-freedom control of two-dimensional materials.

Two-dimensional materials (2DM) and their heterostructures offer tunable electrical and optical properties, primarily modifiable through electrostatic gating and twisting. Although electrostatic gating is a well-established method for manipulating 2DM, achieving real-time control over interfacial properties remains challenging in exploring 2DM physics and advanced quantum device technology1-6. Current methods, often reliant on scanning microscopes, are limited in their scope of application, lacking the accessibility and scalability of electrostatic gating at the device level. Here we introduce an on-chip platform for 2DM with in situ adjustable interfacial properties, using a microelectromechanical system (MEMS). This platform comprises compact and cost-effective devices with the ability of precise voltage-controlled manipulation of 2DM, including approaching, twisting and pressurizing actions. We demonstrate this technology by creating synthetic topological singularities, such as merons, in the nonlinear optical susceptibility of twisted hexagonal boron nitride (h-BN)7-10. A key application of this technology is the development of integrated light sources with real-time and wide-range tunable polarization. Furthermore, we predict a quantum analogue that can generate entangled photon pairs with adjustable entanglement properties. Our work extends the abilities of existing technologies in manipulating low-dimensional quantum materials and paves the way for new hybrid two- and three-dimensional devices, with promising implications in condensed-matter physics, quantum optics and related fields.

Hunting for Majoranas.

Over the past decade, there have been considerable efforts to observe non-abelian quasiparticles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasiparticles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this Review, we focus on efforts to create topological superconducting phases that host Majorana zero modes. We consider the lessons learned from existing experimental efforts, which are motivating both improvements to present platforms and the exploration of new approaches. Although the experimental detection of non-abelian quasiparticles remains challenging, the knowledge gained thus far and the opportunities ahead offer high potential for discovery and advances in this exciting area of quantum physics.

Stabilizing Fluctuating Spin-Triplet Superconductivity in Graphene via Induced Spin-Orbit Coupling.

A recent experiment showed that a proximity-induced Ising spin-orbit coupling enhances the spin-triplet superconductivity in Bernal bilayer graphene. Here, we show that, due to the nearly perfect spin rotation symmetry of graphene, the fluctuations of the spin orientation of the triplet order parameter suppress the superconducting transition to nearly zero temperature. Our analysis shows that both an Ising spin-orbit coupling and an in-plane magnetic field can eliminate these low-lying fluctuations and can greatly enhance the transition temperature, consistent with the recent experiment. Our model also suggests the possible existence of a phase at small anisotropy and magnetic field which exhibits quasilong-range ordered spin-singlet charge 4e superconductivity, even while the triplet 2e superconducting order only exhibits short-ranged correlations. Finally, we discuss relevant experimental signatures.

Surface Cooper-Pair Spin Waves in Triplet Superconductors.

We study the electrodynamics of spin triplet superconductors including dipolar interactions, which give rise to an interplay between the collective spin dynamics of the condensate and orbital Meissner screening currents. Within this theory, we identify a class of spin waves that originate from the coupled dynamics of the spin-symmetry breaking triplet order parameter and the electromagnetic field. In particular, we study magnetostatic spin wave modes that are localized to the sample surface. We show that these surface modes can be excited and detected using experimental techniques such as microwave spin wave resonance spectroscopy or nitrogen-vacancy magnetometry, and propose that the detection of these modes offers a means for the identification of spin triplet superconductivity.

The Magnetic Genome of Two-Dimensional van der Waals Materials.

Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.

Superconductivity in a quintuple-layer square-planar nickelate.

Since the discovery of high-temperature superconductivity in copper oxide materials1, there have been sustained efforts to both understand the origins of this phase and discover new cuprate-like superconducting materials2. One prime materials platform has been the rare-earth nickelates and, indeed, superconductivity was recently discovered in the doped compound Nd0.8Sr0.2NiO2 (ref. 3). Undoped NdNiO2 belongs to a series of layered square-planar nickelates with chemical formula Ndn+1NinO2n+2 and is known as the 'infinite-layer' (n = ∞) nickelate. Here we report the synthesis of the quintuple-layer (n = 5) member of this series, Nd6Ni5O12, in which optimal cuprate-like electron filling (d8.8) is achieved without chemical doping. We observe a superconducting transition beginning at ~13 K. Electronic structure calculations, in tandem with magnetoresistive and spectroscopic measurements, suggest that Nd6Ni5O12 interpolates between cuprate-like and infinite-layer nickelate-like behaviour. In engineering a distinct superconducting nickelate, we identify the square-planar nickelates as a new family of superconductors that can be tuned via both doping and dimensionality.

Fractional Chern insulators in magic-angle twisted bilayer graphene.

Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states that may provide a new avenue towards manipulating non-Abelian excitations. Early theoretical studies1-7 have predicted their existence in systems with flat Chern bands and highlighted the critical role of a particular quantum geometry. However, FCI states have been observed only in Bernal-stacked bilayer graphene (BLG) aligned with hexagonal boron nitride (hBN)8, in which a very large magnetic field is responsible for the existence of the Chern bands, precluding the realization of FCIs at zero field. By contrast, magic-angle twisted BLG9-12 supports flat Chern bands at zero magnetic field13-17, and therefore offers a promising route towards stabilizing zero-field FCIs. Here we report the observation of eight FCI states at low magnetic field in magic-angle twisted BLG enabled by high-resolution local compressibility measurements. The first of these states emerge at 5 T, and their appearance is accompanied by the simultaneous disappearance of nearby topologically trivial charge density wave states. We demonstrate that, unlike the case of the BLG/hBN platform, the principal role of the weak magnetic field is merely to redistribute the Berry curvature of the native Chern bands and thereby realize a quantum geometry favourable for the emergence of FCIs. Our findings strongly suggest that FCIs may be realized at zero magnetic field and pave the way for the exploration and manipulation of anyonic excitations in flat moiré Chern bands.

The development of microfabricated solenoids with magnetic cores for micromagnetic neural stimulation.

Electrical stimulation via invasive microelectrodes is commonly used to treat a wide range of neurological and psychiatric conditions. Despite its remarkable success, the stimulation performance is not sustainable since the electrodes become encapsulated by gliosis due to foreign body reactions. Magnetic stimulation overcomes these limitations by eliminating the need for a metal-electrode contact. Here, we demonstrate a novel microfabricated solenoid inductor (80 µm × 40 µm) with a magnetic core that can activate neuronal tissue. The characterization and proof-of-concept of the device raise the possibility that micromagnetic stimulation solenoids that are small enough to be implanted within the brain may prove to be an effective alternative to existing electrode-based stimulation devices for chronic neural interfacing applications.

A magnon scattering platform.

Scattering experiments have revolutionized our understanding of nature. Examples include the discovery of the nucleus [R. G. Newton, Scattering Theory of Waves and Particles (1982)], crystallography [U. Pietsch, V. Holý, T. Baumback, High-Resolution X-Ray Scattering (2004)], and the discovery of the double-helix structure of DNA [J. D. Watson, F. H. C. Crick, Nature 171, 737-738]. Scattering techniques differ by the type of particles used, the interaction these particles have with target materials, and the range of wavelengths used. Here, we demonstrate a two-dimensional table-top scattering platform for exploring magnetic properties of materials on mesoscopic length scales. Long-lived, coherent magnonic excitations are generated in a thin film of yttrium iron garnet and scattered off a magnetic target deposited on its surface. The scattered waves are then recorded using a scanning nitrogen vacancy center magnetometer that allows subwavelength imaging and operation under conditions ranging from cryogenic to ambient environment. While most scattering platforms measure only the intensity of the scattered waves, our imaging method allows for spatial determination of both amplitude and phase of the scattered waves, thereby allowing for a systematic reconstruction of the target scattering potential. Our experimental results are consistent with theoretical predictions for such a geometry and reveal several unusual features of the magnetic response of the target, including suppression near the target edges and a gradient in the direction perpendicular to the direction of surface wave propagation. Our results establish magnon scattering experiments as a platform for studying correlated many-body systems.

Phase-induced topological superconductivity in a planar heterostructure.

Topological superconductivity in quasi-one-dimensional systems is a novel phase of matter with possible implications for quantum computation. Despite years of effort, a definitive signature of this phase in experiments is still debated. A major cause of this ambiguity is the side effects of applying a magnetic field: induced in-gap states, vortices, and alignment issues. Here we propose a planar semiconductor-superconductor heterostructure as a platform for realizing topological superconductivity without applying a magnetic field to the two-dimensional electron gas hosting the topological state. Time-reversal symmetry is broken only by phase biasing the proximitizing superconductors, which can be achieved using extremely small fluxes or bias currents far from the quasi-one-dimensional channel. Our platform is based on interference between this phase biasing and the phase arising from strong spin-orbit coupling in closed electron trajectories. The principle is demonstrated analytically using a simple model, and then shown numerically for realistic devices. We show a robust topological phase diagram, as well as explicit wavefunctions of Majorana zero modes. We discuss experimental issues regarding the practical implementation of our proposal, establishing it as an accessible scheme with contemporary experimental techniques.

Aharonov-Bohm effect in graphene-based Fabry-Pérot quantum Hall interferometers.

Interferometers probe the wave-nature and exchange statistics of indistinguishable particles-for example, electrons in the chiral one-dimensional edge channels of the quantum Hall effect (QHE). Quantum point contacts can split and recombine these channels, enabling interference of charged particles. Such quantum Hall interferometers (QHIs) can unveil the exchange statistics of anyonic quasi-particles in the fractional quantum Hall effect (FQHE). Here, we present a fabrication technique for QHIs in van der Waals (vdW) materials and realize a tunable, graphene-based Fabry-Pérot (FP) QHI. The graphite-encapsulated architecture allows observation of FQHE at a magnetic field of 3T and precise partitioning of integer and fractional edge modes. We measure pure Aharonov-Bohm interference in the integer QHE, a major technical challenge in small FP interferometers, and find that edge modes exhibit high-visibility interference due to large velocities. Our results establish vdW heterostructures as a versatile alternative to GaAs-based interferometers for future experiments targeting anyonic quasi-particles.

High-energy quasiparticle injection into mesoscopic superconductors.

At non-zero temperatures, superconductors contain excitations known as Bogoliubov quasiparticles (QPs). The mesoscopic dynamics of QPs inform the design of quantum information processors, among other devices. Knowledge of these dynamics stems from experiments in which QPs are injected in a controlled fashion, typically at energies comparable to the pairing energy1-5. Here we perform tunnel spectroscopy of a mesoscopic superconductor under high electric fields. We observe QP injection due to field-emitted electrons with 106 times the pairing energy, an unexplored regime of QP dynamics. Upon application of a gate voltage, the QP injection decreases the critical current and, at sufficiently high electric field, a field-emission current (<0.1 nA in our device) switches the mesoscopic superconductor into the normal state, consistent with earlier observations6. We expect that high-energy injection will be useful for developing QP-tolerant quantum information processors, will allow rapid control of resonator quality factors and will enable the design of electric-field-controlled superconducting devices with new functionality.

Data-driven studies of magnetic two-dimensional materials.

We use a data-driven approach to study the magnetic and thermodynamic properties of van der Waals (vdW) layered materials. We investigate monolayers of the form [Formula: see text], based on the known material [Formula: see text], using density functional theory (DFT) calculations and machine learning methods to determine their magnetic properties, such as magnetic order and magnetic moment. We also examine formation energies and use them as a proxy for chemical stability. We show that machine learning tools, combined with DFT calculations, can provide a computationally efficient means to predict properties of such two-dimensional (2D) magnetic materials. Our data analytics approach provides insights into the microscopic origins of magnetic ordering in these systems. For instance, we find that the X site strongly affects the magnetic coupling between neighboring A sites, which drives the magnetic ordering. Our approach opens new ways for rapid discovery of chemically stable vdW materials that exhibit magnetic behavior.

Imaging viscous flow of the Dirac fluid in graphene.

The electron-hole plasma in charge-neutral graphene is predicted to realize a quantum critical system in which electrical transport features a universal hydrodynamic description, even at room temperature1,2. This quantum critical 'Dirac fluid' is expected to have a shear viscosity close to a minimum bound3,4, with an interparticle scattering rate saturating1 at the Planckian time, the shortest possible timescale for particles to relax. Although electrical transport measurements at finite carrier density are consistent with hydrodynamic electron flow in graphene5-8, a clear demonstration of viscous flow at the charge-neutrality point remains elusive. Here we directly image viscous Dirac fluid flow in graphene at room temperature by measuring the associated stray magnetic field. Nanoscale magnetic imaging is performed using quantum spin magnetometers realized with nitrogen vacancy centres in diamond. Scanning single-spin and wide-field magnetometry reveal a parabolic Poiseuille profile for electron flow in a high-mobility graphene channel near the charge-neutrality point, establishing the viscous transport of the Dirac fluid. This measurement is in contrast to the conventional uniform flow profile imaged in a metallic conductor and also in a low-mobility graphene channel. Via combined imaging and transport measurements, we obtain viscosity and scattering rates, and observe that these quantities are comparable to the universal values expected at quantum criticality. This finding establishes a nearly ideal electron fluid in charge-neutral, high-mobility graphene at room temperature4. Our results will enable the study of hydrodynamic transport in quantum critical fluids relevant to strongly correlated electrons in high-temperature superconductors9. This work also highlights the capability of quantum spin magnetometers to probe correlated electronic phenomena at the nanoscale.

A cantilever torque magnetometry method for the measurement of Hall conductivity of highly resistive samples.

We present the first measurements of Hall conductivity utilizing a torque magnetometry method. A Corbino disk exhibits a magnetic dipole moment proportional to Hall conductivity when voltage is applied across a test material. This magnetic dipole moment can be measured through torque magnetometry. The symmetry of this contactless technique allows for the measurement of Hall conductivity in previously inaccessible materials. Finally, we calculate a low-temperature noise bound, demonstrate the lack of systematic errors, and measure the Hall conductivity of sputtered indium tin oxide.

Nanoscale Detection of Magnon Excitations with Variable Wavevectors Through a Quantum Spin Sensor.

We report the optical detection of magnons with a broad range of wavevectors in magnetic insulator Y3Fe5O12 thin films by proximate nitrogen-vacancy (NV) single-spin sensors. Through multimagnon scattering processes, the excited magnons generate fluctuating magnetic fields at the NV electron spin resonance frequencies, which accelerate the relaxation of NV spins. By measuring the variation of the emitted spin-dependent photoluminescence of the NV centers, magnons with variable wavevectors up to ∼5 × 107 m-1 can be optically accessed, providing an alternative perspective to reveal the underlying spin behaviors in magnetic systems. Our results highlight the significant opportunities offered by NV single-spin quantum sensors in exploring nanoscale spin dynamics of emergent spintronic materials.

Topological superconductivity in a phase-controlled Josephson junction.

Topological superconductors can support localized Majorana states at their boundaries1-5. These quasi-particle excitations obey non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner6,7. Although signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scaled to large numbers of states8-21. Here we present an experimental approach towards a two-dimensional architecture of Majorana bound states. Using a Josephson junction made of a HgTe quantum well coupled to thin-film aluminium, we are able to tune the transition between a trivial and a topological superconducting state by controlling the phase difference across the junction and applying an in-plane magnetic field22. We determine the topological state of the resulting superconductor by measuring the tunnelling conductance at the edge of the junction. At low magnetic fields, we observe a minimum in the tunnelling spectra near zero bias, consistent with a trivial superconductor. However, as the magnetic field increases, the tunnelling conductance develops a zero-bias peak, which persists over a range of phase differences that expands systematically with increasing magnetic field. Our observations are consistent with theoretical predictions for this system and with full quantum mechanical numerical simulations performed on model systems with similar dimensions and parameters. Our work establishes this system as a promising platform for realizing topological superconductivity and for creating and manipulating Majorana modes and probing topological superconducting phases in two-dimensional systems.

Electrical generation and detection of spin waves in a quantum Hall ferromagnet.

Spin waves are collective excitations of magnetic systems. An attractive setting for studying long-lived spin-wave physics is the quantum Hall (QH) ferromagnet, which forms spontaneously in clean two-dimensional electron systems at low temperature and in a perpendicular magnetic field. We used out-of-equilibrium occupation of QH edge channels in graphene to excite and detect spin waves in magnetically ordered QH states. Our experiments provide direct evidence for long-distance spin-wave propagation through different ferromagnetic phases in the N = 0 Landau level, as well as across the insulating canted antiferromagnetic phase. Our results will enable experimental investigation of the fundamental magnetic properties of these exotic two-dimensional electron systems.

Crystallographic Orientation Dependent Reactive Ion Etching in Single Crystal Diamond.

Sculpturing desired shapes in single crystal diamond is ever more crucial in the realization of complex devices for nanophotonics, quantum computing, and quantum optics. The crystallographic orientation dependent wet etch of single crystalline silicon in potassium hydroxide (KOH) allows a range of shapes to be formed and has significant impacts on microelectromechanical systems (MEMS), atomic force microscopy (AFM), and microfluidics. Here, a crystal direction dependent dry etching principle in an inductively coupled plasma reactive ion etcher is presented, which selectively reveals desired crystal planes in monocrystalline diamond by controlling the etching conditions. Using this principle, monolithic diamond nanopillars for magnetometry using nitrogen vacancy centers are fabricated. In these nanopillars, a half-tapering angle up to 21° is achieved, the highest angle reported in the literature, which leads to a high photon efficiency and high mechanical strength of the nanopillar. These results represent the first demonstration of a crystallographic orientation dependent reactive ion etching principle, which opens a new window for shaping specific nanostructures which is at the heart of nanotechnology. It is believed that this principle will prove to be valuable for the structuring and patterning of other single crystal materials as well.