Indistinguishable telecom band photons from a single Er ion in the solid state.

Atomic defects in the solid state are a key component of quantum repeater networks for long-distance quantum communication1. Recently, there has been significant interest in rare earth ions2-4, in particular Er3+ for its telecom band optical transition5-7 that allows long-distance transmission in optical fibres. However, the development of repeater nodes based on rare earth ions has been hampered by optical spectral diffusion, precluding indistinguishable single-photon generation. Here, we implant Er3+ into CaWO4, a material that combines a non-polar site symmetry, low decoherence from nuclear spins8 and is free of background rare earth ions, to realize significantly reduced optical spectral diffusion. For shallow implanted ions coupled to nanophotonic cavities with large Purcell factor, we observe single-scan optical linewidths of 150 kHz and long-term spectral diffusion of 63 kHz, both close to the Purcell-enhanced radiative linewidth of 21 kHz. This enables the observation of Hong-Ou-Mandel interference9 between successively emitted photons with a visibility of V = 80(4)%, measured after a 36 km delay line. We also observe spin relaxation times T1,s = 3.7 s and T2,s > 200 µs, with the latter limited by paramagnetic impurities in the crystal instead of nuclear spins. This represents a notable step towards the construction of telecom band quantum repeater networks with single Er3+ ions.

One-dimensional Luttinger liquids in a two-dimensional moiré lattice.

The Luttinger liquid (LL) model of one-dimensional (1D) electronic systems provides a powerful tool for understanding strongly correlated physics, including phenomena such as spin-charge separation1. Substantial theoretical efforts have attempted to extend the LL phenomenology to two dimensions, especially in models of closely packed arrays of 1D quantum wires2-13, each being described as a LL. Such coupled-wire models have been successfully used to construct two-dimensional (2D) anisotropic non-Fermi liquids2-6, quantum Hall states7-9, topological phases10,11 and quantum spin liquids12,13. However, an experimental demonstration of high-quality arrays of 1D LLs suitable for realizing these models remains absent. Here we report the experimental realization of 2D arrays of 1D LLs with crystalline quality in a moiré superlattice made of twisted bilayer tungsten ditelluride (tWTe2). Originating from the anisotropic lattice of the monolayer, the moiré pattern of tWTe2 hosts identical, parallel 1D electronic channels, separated by a fixed nanoscale distance, which is tuneable by the interlayer twist angle. At a twist angle of approximately 5 degrees, we find that hole-doped tWTe2 exhibits exceptionally large transport anisotropy with a resistance ratio of around 1,000 between two orthogonal in-plane directions. The across-wire conductance exhibits power-law scaling behaviours, consistent with the formation of a 2D anisotropic phase that resembles an array of LLs. Our results open the door for realizing a variety of correlated and topological quantum phases based on coupled-wire models and LL physics.

Catalogue of flat-band stoichiometric materials.

Topological electronic flattened bands near or at the Fermi level are a promising route towards unconventional superconductivity and correlated insulating states. However, the related experiments are mostly limited to engineered materials, such as moiré systems1-3. Here we present a catalogue of the naturally occuring three-dimensional stoichiometric materials with flat bands around the Fermi level. We consider 55,206 materials from the Inorganic Crystal Structure Database catalogued using the Topological Quantum Chemistry website4,5, which provides their structural parameters, space group, band structure, density of states and topological characterization. We combine several direct signatures and properties of band flatness with a high-throughput analysis of all crystal structures. In particular, we identify materials hosting line-graph or bipartite sublattices-in either two or three dimensions-that probably lead to flat bands. From this trove of information, we create the Materials Flatband Database website, a powerful search engine for future theoretical and experimental studies. We use the database to extract a curated list of 2,379 high-quality flat-band materials, from which we identify 345 promising candidates that potentially host flat bands with charge centres that are not strongly localized on the atomic sites. We showcase five representative materials and provide a theoretical explanation for the origin of their flat bands close to the Fermi energy using the S-matrix method introduced in a parallel work6.

Landau quantization and highly mobile fermions in an insulator.

In strongly correlated materials, quasiparticle excitations can carry fractional quantum numbers. An intriguing possibility is the formation of fractionalized, charge-neutral fermions-for example, spinons1 and fermionic excitons2,3-that result in neutral Fermi surfaces and Landau quantization4,5 in an insulator. Although previous experiments in quantum spin liquids1, topological Kondo insulators6-8 and quantum Hall systems3,9 have hinted at charge-neutral Fermi surfaces, evidence for their existence remains inconclusive. Here we report experimental observation of Landau quantization in a two-dimensional insulator, monolayer tungsten ditelluride (WTe2), a large-gap topological insulator10-13. Using a detection scheme that avoids edge contributions, we find large quantum oscillations in the material's magnetoresistance, with an onset field as small as about 0.5 tesla. Despite the huge resistance, the oscillation profile, which exhibits many periods, mimics the Shubnikov-de Haas oscillations in metals. At ultralow temperatures, the observed oscillations evolve into discrete peaks near 1.6 tesla, above which the Landau quantized regime is fully developed. Such a low onset field of quantization is comparable to the behaviour of high-mobility conventional two-dimensional electron gases. Our experiments call for further investigation of the unusual ground state of the WTe2 monolayer, including the influence of device components and the possible existence of mobile fermions and charge-neutral Fermi surfaces inside its insulating gap.

Diamond surface functionalization via visible light-driven C-H activation for nanoscale quantum sensing.

Nitrogen-vacancy (NV) centers in diamond are a promising platform for nanoscale NMR sensing. Despite significant progress toward using NV centers to detect and localize nuclear spins down to the single spin level, NV-based spectroscopy of individual, intact, arbitrary target molecules remains elusive. Such sensing requires that target molecules are immobilized within nanometers of NV centers with long spin coherence. The inert nature of diamond typically requires harsh functionalization techniques such as thermal annealing or plasma processing, limiting the scope of functional groups that can be attached to the surface. Solution-phase chemical methods can be readily generalized to install diverse functional groups, but they have not been widely explored for single-crystal diamond surfaces. Moreover, realizing shallow NV centers with long spin coherence times requires highly ordered single-crystal surfaces, and solution-phase functionalization has not yet been shown with such demanding conditions. In this work, we report a versatile strategy to directly functionalize C-H bonds on single-crystal diamond surfaces under ambient conditions using visible light, forming C-F, C-Cl, C-S, and C-N bonds at the surface. This method is compatible with NV centers within 10 nm of the surface with spin coherence times comparable to the state of the art. As a proof-of-principle demonstration, we use shallow ensembles of NV centers to detect nuclear spins from surface-bound functional groups. Our approach to surface functionalization opens the door to deploying NV centers as a tool for chemical sensing and single-molecule spectroscopy.

Electron doping of a double-perovskite flat-band system.

Electronic structure calculations indicate that the Sr2FeSbO6 double perovskite has a flat-band set just above the Fermi level that includes contributions from ordinary subbands with weak kinetic electron hopping plus a flat subband that can be attributed to the lattice geometry and orbital interference. To place the Fermi energy in that flat band, electron-doped samples with formulas Sr2-xLaxFeSbO6 (0 ≤ x ≤ 0.3) were synthesized, and their magnetism and ambient temperature crystal structures were determined by high-resolution synchrotron X-ray powder diffraction. All materials appear to display an antiferromagnetic-like maximum in the magnetic susceptibility, but the dominant spin coupling evolves from antiferromagnetic to ferromagnetic on electron doping. Which of the three subbands or combinations is responsible for the behavior has not been determined.

Geometrical frustration versus Kitaev interactions in BaCo2(AsO4)2.

Recently, Co-based honeycomb magnets have been proposed as promising candidate materials to host the Kitaev spin liquid (KSL) state. One of the front-runners is BaCo2(AsO4)2 (BCAO), where it was suggested that the exchange processes between Co2+ ions via the surrounding edge-sharing oxygen octahedra could give rise to bond-dependent Kitaev interactions. In this work, we present and analyze a comprehensive inelastic neutron scattering (INS) study of BCAO with fields in the honeycomb plane. Combining the constraints from the magnon excitations in the high-field polarized state and the inelastic spin structure factor measured in zero magnetic field, we examine two leading theoretical models: the Kitaev-type [Formula: see text] model and the XXZ[Formula: see text]model. We show that the existing experimental data can be consistently accounted for by the XXZ[Formula: see text]model but not by the [Formula: see text] model, and we discuss the implications of these results for the realization of a spin liquid phase in BCAO and more generally for the realization of the Kitaev model in cobaltates.

Observation of the nonlinear Hall effect under time-reversal-symmetric conditions.

The electrical Hall effect is the production, upon the application of an electric field, of a transverse voltage under an out-of-plane magnetic field. Studies of the Hall effect have led to important breakthroughs, including the discoveries of Berry curvature and topological Chern invariants1,2. The internal magnetization of magnets means that the electrical Hall effect can occur in the absence of an external magnetic field2; this 'anomalous' Hall effect is important for the study of quantum magnets2-7. The electrical Hall effect has rarely been studied in non-magnetic materials without external magnetic fields, owing to the constraint of time-reversal symmetry. However, only in the linear response regime-when the Hall voltage is linearly proportional to the external electric field-does the Hall effect identically vanish as a result of time-reversal symmetry; the Hall effect in the nonlinear response regime is not subject to such symmetry constraints8-10. Here we report observations of the nonlinear Hall effect10 in electrical transport in bilayers of the non-magnetic quantum material WTe2 under time-reversal-symmetric conditions. We show that an electric current in bilayer WTe2 leads to a nonlinear Hall voltage in the absence of a magnetic field. The properties of this nonlinear Hall effect are distinct from those of the anomalous Hall effect in metals: the nonlinear Hall effect results in a quadratic, rather than linear, current-voltage characteristic and, in contrast to the anomalous Hall effect, the nonlinear Hall effect results in a much larger transverse than longitudinal voltage response, leading to a nonlinear Hall angle (the angle between the total voltage response and the applied electric field) of nearly 90 degrees. We further show that the nonlinear Hall effect provides a direct measure of the dipole moment10 of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe2. Our results demonstrate a new type of Hall effect and provide a way of detecting Berry curvature in non-magnetic quantum materials.

Evidence of magnetism-induced topological protection in the axion insulator candidate EuSn2P2.

We unravel the interplay of topological properties and the layered (anti)ferromagnetic ordering in EuSn2P2, using spin and chemical selective electron and X-ray spectroscopies supported by first-principle calculations. We reveal the presence of in-plane long-range ferromagnetic order triggering topological invariants and resulting in the multiple protection of topological Dirac states. We provide clear evidence that layer-dependent spin-momentum locking coexists with ferromagnetism in this material, a cohabitation that promotes EuSn2P2 as a prime candidate axion insulator for topological antiferromagnetic spintronics applications.

Evidence of Temperature-Dependent Interplay between Spin and Orbital Moment in van der Waals Ferromagnet VI3.

van der Waals materials provide a versatile toolbox for the emergence of new quantum phenomena and fabrication of functional heterostructures. Among them, the trihalide VI3 stands out for its unique magnetic and structural landscape. Here we investigate the spin and orbital magnetic degrees of freedom in the layered ferromagnet VI3 by means of temperature-dependent X-ray absorption spectroscopy and X-ray magnetic circular and linear dichroism. We detect localized electronic states and reduced magnetic dimensionality, due to electronic correlations. We furthermore provide experimental evidence of (a) an unquenched orbital magnetic moment (up to 0.66(7) µB/V atom) in the ferromagnetic state and (b) an instability of the orbital moment in the proximity of the spin reorientation transition. Our results support a coherent picture where electronic correlations give rise to a strong magnetic anisotropy and a large orbital moment and establish VI3 as a prime candidate for the study of orbital quantum effects.