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The intrathecally administered antisense oligonucleotide tofersen reduces synthesis of the superoxide dismutase 1 (SOD1) protein and is being studied in patients with amyotrophic lateral sclerosis (ALS) associated with mutations in SOD1 (SOD1 ALS).In this phase 3 trial, we randomly assigned adults with SOD1 ALS in a 2:1 ratio to receive eight doses of tofersen (100 mg) or placebo over a period of 24 weeks. The primary end point was the change from baseline to week 28 in the total score on the ALS Functional Rating Scale-Revised (ALSFRS-R; range, 0 to 48, with higher scores indicating better function) among participants predicted to have faster-progressing disease. Secondary end points included changes in the total concentration of SOD1 protein in cerebrospinal fluid (CSF), in the concentration of neurofilament light chains in plasma, in slow vital capacity, and in handheld dynamometry in 16 muscles. A combined analysis of the randomized component of the trial and its open-label extension at 52 weeks compared the results in participants who started tofersen at trial entry (early-start cohort) with those in participants who switched from placebo to the drug at week 28 (delayed-start cohort).A total of 72 participants received tofersen (39 predicted to have faster progression), and 36 received placebo (21 predicted to have faster progression). Tofersen led to greater reductions in concentrations of SOD1 in CSF and of neurofilament light chains in plasma than placebo. In the faster-progression subgroup (primary analysis), the change to week 28 in the ALSFRS-R score was -6.98 with tofersen and -8.14 with placebo (difference, 1.2 points; 95% confidence interval [CI], -3.2 to 5.5; P = 0.97). Results for secondary clinical end points did not differ significantly between the two groups. A total of 95 participants (88%) entered the open-label extension. At 52 weeks, the change in the ALSFRS-R score was -6.0 in the early-start cohort and -9.5 in the delayed-start cohort (difference, 3.5 points; 95% CI, 0.4 to 6.7); non-multiplicity-adjusted differences favoring early-start tofersen were seen for other end points. Lumbar puncture-related adverse events were common. Neurologic serious adverse events occurred in 7% of tofersen recipients.In persons with SOD1 ALS, tofersen reduced concentrations of SOD1 in CSF and of neurofilament light chains in plasma over 28 weeks but did not improve clinical end points and was associated with adverse events. The potential effects of earlier as compared with delayed initiation of tofersen are being further evaluated in the extension phase. (Funded by Biogen; VALOR and OLE ClinicalTrials.gov numbers, NCT02623699 and NCT03070119; EudraCT numbers, 2015-004098-33 and 2016-003225-41.).

Deep learning (DL) is an emerging analysis tool across the sciences and engineering. Encouraged by the successes of DL in revealing quantitative trends in massive imaging data, we applied this approach to nanoscale deeply subdiffractional images of propagating polaritonic waves in complex materials. Utilizing the convolutional neural network (CNN), we developed a practical protocol for the rapid regression of images that quantifies the wavelength and the quality factor of polaritonic waves. Using simulated near-field images as training data, the CNN can be made to simultaneously extract polaritonic characteristics and material parameters in a time scale that is at least 3 orders of magnitude faster than common fitting/processing procedures. The CNN-based analysis was validated by examining the experimental near-field images of charge-transfer plasmon polaritons at graphene/α-RuCl

Crystalline two-dimensional (2D) superconductors (SCs) with low carrier density are an exciting new class of materials in which electrostatic gating can tune superconductivity, electronic interactions play a prominent role, and electrical transport properties may directly reflect the topology of the Fermi surface. Here, we report the dramatic enhancement of superconductivity with decreasing thickness in semimetallic Td-MoTe2, with critical temperature (Tc) increasing up to 7.6 K for monolayers, a 60-fold increase with respect to the bulk Tc. We show that monolayers possess a similar electronic structure and density of states (DOS) as the bulk, implying that electronic interactions play a strong role in the enhanced superconductivity. Reflecting the low carrier density, the critical temperature, magnetic field, and current density are all tunable by an applied gate voltage. The response to high in-plane magnetic fields is distinct from that of other 2D SCs and reflects the canted spin texture of the electron pockets.

Quasi-periodic moiré patterns and their effect on electronic properties of twisted bilayer graphene have been intensely studied. At small twist angle θ, due to atomic reconstruction, the moiré superlattice morphs into a network of narrow domain walls separating micron-scale AB and BA stacking regions. We use scanning probe photocurrent imaging to resolve nanoscale variations of the Seebeck coefficient occurring at these domain walls. The observed features become enhanced in a range of mid-infrared frequencies where the hexagonal boron nitride substrate is optically hyperbolic. Our results illustrate the capabilities of the nano-photocurrent technique for probing nanoscale electronic inhomogeneities in two-dimensional materials., Here, the authors use scanning probe photocurrent imaging to resolve nanoscale variations of the Seebeck coefficient occurring at domain walls separating micron-scale AB and BA stacking regions in twisted bilayer graphene, and observe hyperbolic enhancement of the photocurrent pattern.

Patterning graphene with a spatially periodic potential provides a powerful means to modify its electronic properties1–3. In particular, in twisted bilayers, coupling to the resulting moire superlattice yields an isolated flat band that hosts correlated many-body phases4,5. However, both the symmetry and strength of the effective moire potential are constrained by the constituent crystals, limiting its tunability. Here, we have exploited the technique of dielectric patterning6 to subject graphene to a one-dimensional electrostatic superlattice (SL)1. We observed the emergence of multiple Dirac cones and found evidence that with increasing SL potential the main and satellite Dirac cones are sequentially flattened in the direction parallel to the SL basis vector, behaviour resulting from the interaction between the one-dimensional SL electric potential and the massless Dirac fermions hosted by graphene. Our results demonstrate the ability to induce tunable anisotropy in high-mobility two-dimensional materials, a long-desired property for novel electronic and optical applications7,8. Moreover, these findings offer a new approach to engineering flat energy bands where electron interactions can lead to emergent properties9. Dielectric patterning allows tunable anisotropy in high-mobility one-dimensional graphene electrostatic superlattices.

Twisted van der Waals heterostructures have latterly received prominent attention for their many remarkable experimental properties, and the promise that they hold for realising elusive states of matter in the laboratory. We propose that these systems can, in fact, be used as a robust quantum simulation platform that enables the study of strongly correlated physics and topology in quantum materials. Among the features that make these materials a versatile toolbox are the tunability of their properties through readily accessible external parameters such as gating, straining, packing and twist angle; the feasibility to realize and control a large number of fundamental many-body quantum models relevant in the field of condensed-matter physics; and finally, the availability of experimental readout protocols that directly map their rich phase diagrams in and out of equilibrium. This general framework makes it possible to robustly realize and functionalize new phases of matter in a modular fashion, thus broadening the landscape of accessible physics and holding promise for future technological applications., Comment: Invited to Nature Physics

Strongly correlated systems can give rise to spectacular phenomenology, from high-temperature superconductivity to the emergence of states of matter characterized by long-range quantum entanglement. Low-density flat-band systems play a vital role because the energy range of the band is so narrow that the Coulomb interactions dominate over kinetic energy, putting these materials in the strongly-correlated regime. Experimentally, when a band is narrow in both energy and momentum, its filling may be tuned in situ across the whole range, from empty to full. Recently, one particular flat-band system—that of van der Waals heterostructures, such as twisted bilayer graphene—has exhibited strongly correlated states and superconductivity, but it is still not clear to what extent the two are linked. Here, we review the status and prospects for flat-band engineering in van der Waals heterostructures and explore how both phenomena emerge from the moire flat bands. The identification of superconductivity and strong interactions in twisted bilayer 2D materials prompted many questions about the interplay of these phenomena. This Perspective presents the status of the field and the urgent issues for future study.

Topological spin textures are field arrangements that cannot be continuously deformed to a fully polarized state. In particular, merons are topological textures characterized by half-integer topological charge ±1/2 and vortex-like swirling patterns at large distances. Merons have been studied previously in the context of cosmology, fluid dynamics, condensed matter physics and plasmonics. Here, we visualized optical spin angular momentum of phonon polaritons that resembles nanoscale meron spin textures. Phonon polaritons, hybrids of infrared photons and phonons in hexagonal boron nitride, were excited by circularly polarized light incident on a ring-shaped antenna and imaged using infrared near-field techniques. The polariton field reveals a half-integer topological charge determined by the handedness of the incident beam. Our phonon polaritonic platform opens up new pathways to create, control, and visualize topological textures.

Twisted two-dimensional van der Waals (vdW) heterostructures have unlocked a new means for manipulating the properties of quantum materials. The resulting mesoscopic moiré superlattices are accessible to a wide variety of scanning probes. To date, spatially-resolved techniques have prioritized electronic structure visualization, with lattice response experiments only in their infancy. Here, we therefore investigate lattice dynamics in twisted layers of hexagonal boron nitride (hBN), formed by a minute twist angle between two hBN monolayers assembled on a graphite substrate. Nano-infrared (nano-IR) spectroscopy reveals systematic variations of the in-plane optical phonon frequencies amongst the triangular domains and domain walls in the hBN moiré superlattices. Our first-principles calculations unveil a local and stacking-dependent interaction with the underlying graphite, prompting symmetry-breaking between the otherwise identical neighboring moiré domains of twisted hBN., Here, the authors investigate the lattice dynamics of twisted hexagonal boron nitride layers via nano-infrared spectroscopy, showing local and stacking-dependent variations of the optical phonon frequencies associated to the interaction with the graphite substrate.

Hybrid superconductor/graphene (SC/g) junctions are excellent candidates for investigating correlations between Cooper pairs and quantum Hall (QH) edge modes. Experimental studies are challenging as Andreev reflections are extremely sensitive to junction disorder and high magnetic fields are required to form QH edge states. We fabricated low-resistance SC/g interfaces, composed of graphene edge contacted with NbN with a barrier strength of $Z\approx 0.4$, that remain superconducting under magnetic fields larger than $18$ T. We establish the role of graphene's Dirac band structure on zero-field Andreev reflections and demonstrate dynamic tunability of the Andreev reflection spectrum by moving the boundary between specular and retro Andreev reflections with parallel magnetic fields. Through the application of perpendicular magnetic fields, we observe an oscillatory suppression of the 2-probe conductance in the $\nu = 4$ Landau level attributed to the reduced efficiency of Andreev processes at the NbN/g interface, consistent with theoretical predictions.

Excitons play a dominant role in the optoelectronic properties of atomically thin van der Waals (vdW) semiconductors. These excitons are amenable to on-demand engineering with diverse control knobs, including dielectric screening, interlayer hybridization, and moiré potentials. However, external stimuli frequently yield heterogeneous excitonic responses at the nano- and meso-scales, making their spatial characterization with conventional diffraction-limited optics a formidable task. Here, we use a scattering-type scanning near-field optical microscope (s-SNOM) to acquire exciton spectra in atomically thin transition metal dichalcogenide microcrystals with previously unattainable 20 nm resolution. Our nano-optical data revealed material- and stacking-dependent exciton spectra of MoSe2, WSe2, and their heterostructures. Furthermore, we extracted the complex dielectric function of these prototypical vdW semiconductors. s-SNOM hyperspectral images uncovered how the dielectric screening modifies excitons at length scales as short as few nanometers. This work paves the way towards understanding and manipulation of excitons in atomically thin layers at the nanoscale., Excitons play an important role in the optical properties of 2D semiconductors, but their spatial characterization is usually constrained by the diffraction limit. Here, the authors report near-field optical spectroscopy of 2D transition metal dichalcogenides with 20 nm resolution, revealing their spatially dependent excitonic spectra and complex dielectric function.

Natural hyperbolic materials with dielectric permittivities of opposite signs along different principal axes can confine long-wavelength electromagnetic waves down to the nanoscale, well below the diffraction limit. Confined electromagnetic waves coupled to phonons in hyperbolic dielectrics including hexagonal boron nitride (hBN) and α-MoO3 are referred to as hyperbolic phonon polaritons (HPPs). HPP dissipation at ambient conditions is substantial, and its fundamental limits remain unexplored. Here, we exploit cryogenic nanoinfrared imaging to investigate propagating HPPs in isotopically pure hBN and naturally abundant α-MoO3 crystals. Close to liquid-nitrogen temperatures, losses for HPPs in isotopic hBN drop significantly, resulting in propagation lengths in excess of 8 μm, with lifetimes exceeding 5 ps, thereby surpassing prior reports on such highly confined polaritonic modes. Our nanoscale, temperature-dependent imaging reveals the relevance of acoustic phonons in HPP damping and will be instrumental in mitigating such losses for miniaturized mid-infrared technologies operating at liquid-nitrogen temperatures., Research at Columbia is supported by Vannevar Bush Faculty Fellowship ONR-VB: N00014-19-1-2630. We thank A. Sternbach and S. Zhang for helpful discussions. Exfoliation and transfer of hBN onto desired substrates and electron beam lithography of gold disks were performed by J.T.M. and supported by the National Science Foundation (DMR1904793). Additional structure fabrication was supported by the Center on Precision-Assembled Quantum Materials, funded through the U.S. National Science Foundation (NSF) Materials Research Science and Engineering Centers (award no. DMR-2011738). Initial simulations and experimental design from Vanderbilt were provided by J.D.C. in collaboration with the Columbia team (D.N.B. and G.N.) and was supported by the Office of Naval Research (N00014-18-1-2107). The hBN phonon band structure calculation was performed by R.C. and L.A. and supported by the Spanish MINECO/FEDER grant (MAT2015-71035- R). Cryogenics nano-optics experiments at Columbia were solely supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0019443. D.N.B is the Gordon and Betty Moore Foundation’s EPiQS Initiative Investigator no. 9455.

The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded the concept of topological order in physics bringing into focus the intimate relation between the “bulk” topology and the edge states. The QH effect in graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials. However, the broken-symmetry edge states have eluded spatial measurements. In this article, we spatially map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\nu }}={{0}},\pm {{1}}$$\end{document}ν=0,±1 across the quantum Hall edge boundary using high-resolution atomic force microscopy (AFM) and show a gapped ground state proceeding from the bulk through to the QH edge boundary. Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moiré superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields., The broken-symmetry edge states that are the hallmark of the quantum Hall effect in graphene have eluded spatial measurements. Here, the authors spatially map the quantum Hall broken-symmetry edge states using atomic force microscopy and show a gapped ground state proceeding from the bulk through to the quantum Hall edge boundary.

When light-matter polaritons travel in periodic media, they acquire properties akin to Bloch quasi-particles in crystals., Efficient control of photons is enabled by hybridizing light with matter. The resulting light-matter quasi-particles can be readily programmed by manipulating either their photonic or matter constituents. Here, we hybridized infrared photons with graphene Dirac electrons to form surface plasmon polaritons (SPPs) and uncovered a previously unexplored means to control SPPs in structures with periodically modulated carrier density. In these periodic structures, common SPPs with continuous dispersion are transformed into Bloch polaritons with attendant discrete bands separated by bandgaps. We explored directional Bloch polaritons and steered their propagation by dialing the proper gate voltage. Fourier analysis of the near-field images corroborates that this on-demand nano-optics functionality is rooted in the polaritonic band structure. Our programmable polaritonic platform paves the way for the much-sought benefits of on-the-chip photonic circuits.

Twisted bilayer graphene has recently emerged as a platform for hosting correlated phenomena. For twist angles near θ ≈ 1.1°, the low-energy electronic structure of twisted bilayer graphene features isolated bands with a flat dispersion1,2. Recent experiments have observed a variety of low-temperature phases that appear to be driven by electron interactions, including insulating states, superconductivity and magnetism3–6. Here we report electrical transport measurements up to room temperature for twist angles varying between 0.75° and 2°. We find that the resistivity, ρ, scales linearly with temperature, T, over a wide range of T before falling again owing to interband activation. The T-linear response is much larger than observed in monolayer graphene for all measured devices, and in particular increases by more than three orders of magnitude in the range where the flat band exists. Our results point to the dominant role of electron–phonon scattering in twisted bilayer graphene, with possible implications for the origin of the observed superconductivity. Transport measurements on twisted bilayer graphene show that a large linear-in-temperature increase in resistivity exists for many twist angles. This may have implications for the mechanism of superconductivity in this material.

We describe the development of a technique to transfer micrometer patterns of organic thin films with sub-50 nm edge resolution and sub-20 nm pattern fidelity. Large-area transfer of homopolymers, diblock copolymers, and small molecules films is demonstrated, and extended to multitudes of different shapes. Moreover, this technique is amenable to sequential printing (i.e. multilayer stacking) and can be integrated with 2D atomic crystals. This high-fidelity pattern transfer work has broad scope for potential uses from the construction of van der Waals heterostructures interfaced with self-assembled block copolymer thin films to the development of platforms to investigate the influence of hierarchical patterning on cell differentiation.

When monolayers of two-dimensional (2D) materials are stacked into van der Waals structures, interlayer electronic coupling can introduce entirely new properties, as exemplified by recent discoveries of moir\'e bands that host highly correlated electronic states and quantum dot-like interlayer exciton lattices. Here we show the magnetic control of interlayer electronic coupling, as manifested in tunable excitonic transitions, in an A-type antiferromagnetic 2D semiconductor CrSBr. Excitonic transitions in bilayer and above can be drastically changed when the magnetic order is switched from layered antiferromagnetic to the field-induced ferromagnetic state, an effect attributed to the spin-allowed interlayer hybridization of electron and hole orbitals in the latter, as revealed by GW-BSE calculations. Our work uncovers a magnetic approach to engineer electronic and excitonic effects in layered magnetic semiconductors., Comment: 16 pages, 4 figures, 10 pages SI

In moiré heterostructures, gate-tunable insulating phases driven by electronic correlations have been recently discovered. Here, we use transport measurements to characterize the gate-driven metal-insulator transitions and the metallic phase in twisted WSe2 near half filling of the first moiré subband. We find that the metal-insulator transition as a function of both density and displacement field is continuous. At the metal-insulator boundary, the resistivity displays strange metal behaviour at low temperature with dissipation comparable to the Planckian limit. Further into the metallic phase, Fermi-liquid behaviour is recovered at low temperature which evolves into a quantum critical fan at intermediate temperatures before eventually reaching an anomalous saturated regime near room temperature. An analysis of the residual resistivity indicates the presence of strong quantum fluctuations in the insulating phase. These results establish twisted WSe2 as a new platform to study doping and bandwidth controlled metal-insulator quantum phase transitions on the triangular lattice.

Charge separated interlayer excitons in transition metal dichalcogenide heterobilayers are being explored for moir\'e exciton lattices and exciton condensates. The presence of permanent dipole moments and the poorly screened Coulomb interaction make many-body interactions particularly strong for interlayer excitons. Here we reveal two distinct phase transitions for interlayer excitons in the ${\mathrm{MoSe}}_{2}/{\mathrm{WSe}}_{2}$ heterobilayer using time and spatially resolved photoluminescence imaging: from trapped excitons in the moir\'e potential to the modestly mobile exciton gas as exciton density increases to ${n}_{ex}\ensuremath{\sim}{10}^{11}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}$ and from the exciton gas to the highly mobile charge separated electron-hole plasma for ${n}_{ex}g{10}^{12}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}$. The latter is the Mott transition and is confirmed in photoconductivity measurements. These findings set fundamental limits for achieving quantum states of interlayer excitons.

Significance Micrometer-sized uniform four-layer (ABCA) rhombohedral graphene is realized by introducing a small twist angle between two bilayers of Bernal graphene. By means of scanning tunneling spectroscopy we observe an extremely sharp van Hove singularity of 3–5-meV half-width and a correlated many-body gap of 9.5 meV at neutrality, thus making small twisted double-bilayer graphene a unique platform to realize electronic correlations in the absence of a moiré potential. Furthermore, ABCA graphene domain walls display tunable topological edge states, of great interest in Floquet engineering., Atomically thin van der Waals materials stacked with an interlayer twist have proven to be an excellent platform toward achieving gate-tunable correlated phenomena linked to the formation of flat electronic bands. In this work we demonstrate the formation of emergent correlated phases in multilayer rhombohedral graphene––a simple material that also exhibits a flat electronic band edge but without the need of having a moiré superlattice induced by twisted van der Waals layers. We show that two layers of bilayer graphene that are twisted by an arbitrary tiny angle host large (micrometer-scale) regions of uniform rhombohedral four-layer (ABCA) graphene that can be independently studied. Scanning tunneling spectroscopy reveals that ABCA graphene hosts an unprecedentedly sharp van Hove singularity of 3–5-meV half-width. We demonstrate that when this van Hove singularity straddles the Fermi level, a correlated many-body gap emerges with peak-to-peak value of 9.5 meV at charge neutrality. Mean-field theoretical calculations for model with short-ranged interactions indicate that two primary candidates for the appearance of this broken symmetry state are a charge-transfer excitonic insulator and a ferrimagnet. Finally, we show that ABCA graphene hosts surface topological helical edge states at natural interfaces with ABAB graphene which can be turned on and off with gate voltage, implying that small-angle twisted double-bilayer graphene is an ideal programmable topological quantum material.

Near the boundary between ordered and disordered quantum phases, several experiments have demonstrated metallic behaviour that defies the Landau Fermi paradigm1–5. In moire heterostructures, gate-tuneable insulating phases driven by electronic correlations have been recently discovered6–23. Here, we use transport measurements to characterize metal–insulator transitions (MITs) in twisted WSe2 near half filling of the first moire subband. We find that the MIT as a function of both density and displacement field is continuous. At the metal–insulator boundary, the resistivity displays strange metal behaviour at low temperatures, with dissipation comparable to that at the Planckian limit. Further into the metallic phase, Fermi liquid behaviour is recovered at low temperature, and this evolves into a quantum critical fan at intermediate temperatures, before eventually reaching an anomalous saturated regime near room temperature. An analysis of the residual resistivity indicates the presence of strong quantum fluctuations in the insulating phase. These results establish twisted WSe2 as a new platform to study doping and bandwidth-controlled metal–insulator quantum phase transitions on the triangular lattice. Metal-to-insulator transitions are characterized in twisted WSe, revealing strange metal behaviour and quantum criticality at low temperatures.

Nanoscale charge control is a key enabling technology in plasmonics, electronic band structure engineering, and the topology of two-dimensional materials. By exploiting the large electron affinity of α-RuCl3, we are able to visualize and quantify massive charge transfer at graphene/α-RuCl3 interfaces through generation of charge-transfer plasmon polaritons (CPPs). We performed nanoimaging experiments on graphene/α-RuCl3 at both ambient and cryogenic temperatures and discovered robust plasmonic features in otherwise ungated and undoped structures. The CPP wavelength evaluated through several distinct imaging modalities offers a high-fidelity measure of the Fermi energy of the graphene layer: EF = 0.6 eV (n = 2.7 × 1013 cm–2). Our first-principles calculations link the plasmonic response to the work function difference between graphene and α-RuCl3 giving rise to CPPs. Our results provide a novel general strategy for generating nanometer-scale plasmonic interfaces without resorting to external contacts or chemical doping., Research at Columbia was supported as part of the Energy Frontier Research Center on Programmable Quantum Materials funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. DE-SC0019443. J.Z., L.X., and A.R. were supported by the European Research Council (ERC-2015-AdG694097), the Cluster of Excellence “Advanced Imaging of Matter” (AIM) EXC 2056 - 390715994, funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under RTG 2247, Grupos Consolidados (IT1249-19) and SFB925 “Light induced dynamics and control of correlated quantum systems”. J.Z. acknowledges funding received from the European Union Horizon 2020 research and innovation program under Marie Sklodowska-Curie Grant Agreement 886291 (PeSD-NeSL). J.Z., L.X., and A.R. would like to acknowledge Nicolas Tancogne-Dejean for fruitful discussions and also acknowledge support by the Max Planck Institute-New York City Center for Non-Equilibrium Quantum Phenomena. The Flatiron Institute is a division of the Simons Foundation. D.G.M. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS Initiative, Grant GBMF9069. Work at ORNL was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, Grant JPMXP0112101001, JSPS KAKENHI Grant JP20H00354, and the CREST (JPMJCR15F3), JST. S.E.N. was supported by the Division of Scientific User Facilities of the U.S. DOE Basic Energy Sciences. M.M.F. acknowledges support from the Office of Naval Research Grant N00014-18-1-2722. D.N.B. is the Vannevar Bush Faculty ONR-VB: N00014-19-1-2630 and Moore investigator in Quantum Materials EPIQS program #9455. A.S.M acknowledges support from award 80NSSC19K1210 under the NASA Laboratory Analysis of Returned Samples program.

Twisted van der Waals heterostructures with flat electronic bands have recently emerged as a platform for realizing correlated and topological states with an extraordinary degree of control and tunability. In graphene-based moir\'e heterostructures, the correlated phase diagram and band topology depend strongly on the number of graphene layers, their relative stacking arrangement, and details of the external environment from the encapsulating crystals. Here, we report that the system of twisted monolayer-bilayer graphene (tMBG) hosts a variety of correlated metallic and insulating states, as well as topological magnetic states. Because of its low symmetry, the phase diagram of tMBG approximates that of twisted bilayer graphene when an applied perpendicular electric field points from the bilayer towards the monolayer graphene, or twisted double bilayer graphene when the field is reversed. In the former case, we observe correlated states which undergo an orbitally driven insulating transition above a critical perpendicular magnetic field. In the latter case, we observe the emergence of electrically tunable ferromagnetism at one-quarter filling of the conduction band, with a large associated anomalous Hall effect. Uniquely, the magnetization direction can be switched purely with electrostatic doping at zero magnetic field. Our results establish tMBG as a highly tunable platform for investigating a wide array of tunable correlated and topological states., Comment: 21 Pages, 20 Figures

In narrow electron bands in which the Coulomb interaction energy becomes comparable to the bandwidth, interactions can drive new quantum phases. Such flat bands in twisted graphene-based systems result in correlated insulator, superconducting and topological states. Here we report evidence of low-energy flat bands in twisted bilayer WSe2, with signatures of collective phases observed over twist angles that range from 4 to 5.1°. At half-band filling, a correlated insulator appeared that is tunable with both twist angle and displacement field. At a 5.1° twist, zero-resistance pockets were observed on doping away from half filling at temperatures below 3 K, which indicates a possible transition to a superconducting state. The observation of tunable collective phases in a simple band, which hosts only two holes per unit cell at full filling, establishes twisted bilayer transition metal dichalcogenides as an ideal platform to study correlated physics in two dimensions on a triangular lattice., Studies of the tunable correlated states in the twisted bilayer WSe2 were supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award DE-SC0019443. The synthesis of the WSe2 crystals was supported by the NSF MRSEC programme through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634). The theoretical work was supported by the European Research Council (ERC-2015-AdG694097), cluster of Excellence AIM, SFB925 and Grupos Consolidados (IT1249-19). The Flatiron Institute is a division of the Simons Foundation. We acknowledge support from the Max Planck–New York Center for Non-Equilibrium Quantum Phenomena.

The recent discovery of two-dimensional (2D) magnets offers unique opportunities for the experimental exploration of low-dimensional magnetism4 and the magnetic proximity effects, and for the development of novel magnetoelectric, magnetooptic and spintronic devices. These advancements call for 2D materials with diverse magnetic structures as well as effective probes for their magnetic symmetries, which is key to understanding intralayer magnetic order and interlayer magnetic coupling. Here we apply second harmonic generation (SHG), a technique acutely sensitive to symmetry breaking, to probe the magnetic structure of a new 2D magnetic semiconductor, CrSBr. We find that CrSBr monolayers are ferromagnetically ordered below 146 K, an observation enabled by the discovery of a giant magnetic dipole SHG effect in the centrosymmetric 2D structure. In multilayers, the ferromagnetic monolayers are coupled antiferromagnetically, with the N\'eel temperature notably increasing with decreasing layer number. The magnetic structure of CrSBr, comprising spins co-aligned in-plane with rectangular unit cell, differs markedly from the prototypical 2D hexagonal magnets CrI3 and Cr2Ge2Te6 with out-of-plane moments. Moreover, our SHG analysis suggests that the order parameters of the ferromagnetic monolayer and the antiferromagnetic bilayer are the magnetic dipole and the magnetic toroidal moments, respectively. These findings establish CrSBr as an exciting 2D magnetic semiconductor and SHG as a powerful tool to probe 2D magnetic symmetry, opening the door to the exploration of coupling between magnetic order and excitonic/electronic properties, as well as the magnetic toroidal moment, in a broad range of applications., Comment: 15 pages, 4 figures, +27 pages Supporting Information

Graphene-based heterostructures display a variety of phenomena that are strongly tunable by electrostatic local gates. Monolayer graphene (MLG) exhibits tunable surface plasmon polaritons, as revealed by scanning nano-infrared experiments. In bilayer graphene (BLG), an electronic gap is induced by a perpendicular displacement field. Gapped BLG is predicted to display unusual effects such as plasmon amplification and domain wall plasmons with significantly larger lifetime than MLG. Furthermore, a variety of correlated electronic phases highly sensitive to displacement fields have been observed in twisted graphene structures. However, applying perpendicular displacement fields in nano-infrared experiments has only recently become possible [Li, H.; Nano Lett. 2020, 20, 3106-3112]. In this work, we fully characterize two approaches to realizing nano-optics compatible top gates: bilayer MoS2 and MLG. We perform nano-infrared imaging on both types of structures and evaluate their strengths and weaknesses. Our work paves the way for comprehensive near-field experiments of correlated phenomena and plasmonic effects in graphene-based heterostructures.

Monolayer (ML) semiconducting transition-metal dichalcogenides (TMDs) represent a unique class of two-dimensional (2D) electron systems. Their atomically thin structure -- just like graphene -- facilitates gate-tunability, while the sizable band gap and strong spin-orbit coupling hold promise for properties beyond graphene. Measurements under large magnetic fields have revealed an unusual LL structure, distinct from other 2D electron systems. However, owing to limited sample quality and poor electrical contact, probing the lowest Landau levels (LLs) has been challenging, and observation of electron correlations within the fractionally filled LLs regime has not been possible. Here, through bulk electronic compressibility measurements, we investigate the LL structure of ML WSe$_2$ in the extreme quantum limit, and observe fractional quantum Hall (FQH) states in the lowest three LLs. The odd-denominator FQH sequences demonstrate a systematic evolution with the LL orbital index, which has not been observed in any other system but is consistent with generic theoretical expectations. In addition, we observe an even-denominator state in the second LL that is expected to host non-Abelian statistics. Our results suggest that the 2D semiconductors can provide an experimental platform that closely resembles idealized theoretical models in the quantum Hall regime., typos in v1 corrected

Plasmon polaritons are hybrid excitations of light and mobile electrons that can confine the energy of long-wavelength radiation at the nanoscale. Plasmon polaritons may enable many enigmatic quantum effects, including lasing 1 , topological protection2,3 and dipole-forbidden absorption 4 . A necessary condition for realizing such phenomena is a long plasmonic lifetime, which is notoriously difficult to achieve for highly confined modes 5 . Plasmon polaritons in graphene—hybrids of Dirac quasiparticles and infrared photons—provide a platform for exploring light–matter interaction at the nanoscale6,7. However, plasmonic dissipation in graphene is substantial 8 and its fundamental limits remain undetermined. Here we use nanometre-scale infrared imaging to investigate propagating plasmon polaritons in high-mobility encapsulated graphene at cryogenic temperatures. In this regime, the propagation of plasmon polaritons is primarily restricted by the dielectric losses of the encapsulated layers, with a minor contribution from electron–phonon interactions. At liquid-nitrogen temperatures, the intrinsic plasmonic propagation length can exceed 10 micrometres, or 50 plasmonic wavelengths, thus setting a record for highly confined and tunable polariton modes. Our nanoscale imaging results reveal the physics of plasmonic dissipation and will be instrumental in mitigating such losses in heterostructure engineering applications. The fundamental limits to plasmon damping in graphene are determined using nanoscale infrared imaging at cryogenic temperatures, and plasmon polaritons are observed to propagate over 10 micrometres in high-mobility encapsulated graphene.

Monolayers (MLs) of transition metal dichalcogenides (TMDs) exhibit unusual electrical behavior under magnetic fields due to their intrinsic spin-orbit coupling and lack of inversion symmetry. While recent experiments have also identified the critical role of carrier interactions within these materials, a complete mapping of the ambipolar Landau level (LL) sequence has remained elusive. Here, we use single-electron transistors to perform LL spectroscopy in ML WSe$_2$, for the first time providing a comprehensive picture of the electronic structure of a ML TMD for both electrons and holes. We find that the LLs differ notably between the two bands, and follow a unique sequence in the valence band (VB) that is dominated by strong Zeeman effects. The Zeeman splitting in the VB is several times higher than the cyclotron energy, far exceeding the predictions of a single-particle model, and moreover tunes significantly with doping. This implies exceptionally strong many-body interactions, and suggests that ML WSe$_2$ can serve as a host for new correlated-electron phenomena., Comment: 22 pages, 11 figures

The multi-component nature of bilayer graphene (BLG), together with the ability to controllably tune between the various ground state orders, makes it a rich system in which to explore interaction driven phenomena. In the fractional quantum Hall effect (FQHE) regime, the unique Landau level spectrum of BLG is anticipated to support a non-Abelian even-denominator state that is tunable by both electric and magnetic fields. However, observation of this state, which is anticipated to be stronger than in conventional systems, has been conspicuously difficult. Here we report transport measurements of a robust even denominator FQHE in high-mobility, dual gated BLG devices. We confirm that the stability of the energy gap can be sensitively tuned and map the phase diagram. Our results establish BLG as a dynamic new platform to study topological ground states with possible non-Abelian excitations., Comment: 6 pages, 4 figures. v2, a typo has been corrected

Monolayer MoS2, among many other transition metal dichalcogenides, holds great promise for future applications in nanoelectronics and optoelectronics due to its ultrathin nature, flexibility, sizable band gap, and unique spin-valley coupled physics. However, careful study of these properties at low temperature has been hindered by an inability to achieve low-temperature Ohmic contacts to monolayer MoS2, particularly at low carrier densities. In this work, we report a new contact scheme that utilizes cobalt (Co) with a monolayer of hexagonal boron nitride (h-BN) that has the following two functions: modifies the work function of Co and acts as a tunneling barrier. We measure a flat-band Schottky barrier of 16 meV, which makes thin tunnel barriers upon doping the channels, and thus achieve low-T contact resistance of 3 kΩ.μm at a carrier density of 5.3 × 1012/cm2. This further allows us to observe Shubnikov–de Haas oscillations in monolayer MoS2 at much lower carrier densities compared to previous work.

Photonic crystals are commonly implemented in media with periodically varying optical properties. Photonic crystals enable exquisite control of light propagation in integrated optical circuits, and also emulate advanced physical concepts. However, common photonic crystals are unfit for in-operando on/off controls. We overcome this limitation and demonstrate a broadly tunable two-dimensional photonic crystal for surface plasmon polaritons. Our platform consists of a continuous graphene monolayer integrated in a back-gated platform with nano-structured gate insulators. Infrared nano-imaging reveals the formation of a photonic bandgap and strong modulation of the local plasmonic density of states that can be turned on/off or gradually tuned by the applied gate voltage. We also implement an artificial domain wall which supports highly confined one-dimensional plasmonic modes. Our electrostatically-tunable photonic crystals are derived from standard metal oxide semiconductor field effect transistor technology and pave a way for practical on-chip light manipulation., Traditional photonic crystals consist of periodic media with a pre-defined optical response. Here, the authors combine nanostructured back-gate insulators with a continuous layer of graphene to demonstrate an electrically tunable two-dimensional photonic crystal suitable for controlling the propagation of surface plasmon polaritons.

Controlling two-dimensional twist In heterostructures assembled from two-dimensional materials such as graphene, electron tunneling between layers varies strongly with the rotation angle between the crystal lattices. Usually, the twist angle between layers is fixed after assembly. Ribeiro-Palau et al. encapsulated graphene with boron nitride, but the top boron nitride flake was shaped so that an atomic force microscope tip could push on it to vary the twist angle by as little as 0.2°. They observed variations with twist angle in properties such as the charge neutrality point, which would be difficult to observe in static rotated structures. Science , this issue p. 690

In heterostructures consisting of atomically thin crystals layered on top of one another, lattice mismatch or rotation between the layers results in long-wavelength moir\'e superlattices. These moir\'e patterns can drive significant band structure reconstruction of the composite material, leading to a wide range of emergent phenomena including superconductivity, magnetism, fractional Chern insulating states, and moir\'e excitons. Here, we investigate monolayer graphene encapsulated between two crystals of boron nitride (BN), where the rotational alignment between all three components can be varied. We find that band gaps in the graphene arising from perfect rotational alignment with both BN layers can be modified substantially depending on whether the relative orientation of the two BN layers is 0 or 60 degrees, suggesting a tunable transition between the absence or presence of inversion symmetry in the heterostructure. Small deviations ($, Comment: 14 Pages, 12 Figures

International audience; We report experimental observation of the reentrant integer quantum Hall effect in graphene, appearing in the N=2 Landau level. Similar to high-mobility GaAs/AlGaAs heterostructures, the effect is due to a competition between incompressible fractional quantum Hall states, and electron solid phases. The tunability of graphene allows us to measure the B-T phase diagram of the electron solid phase. The hierarchy of reentrant states suggests spin and valley degrees of freedom play a role in determining the ground state energy. We find that the melting temperature scales with magnetic field, and construct a phase diagram of the electron liquid-solid transition.

The physical properties of two-dimensional van der Waals (2D vdW) crystals depend sensitively on the interlayer coupling, which is intimately connected to the stacking arrangement and the interlayer spacing. For example, simply changing the twist angle between graphene layers can induce a variety of correlated electronic phases, which can be controlled further in a continuous manner by applying hydrostatic pressure to decrease the interlayer spacing. In the recently discovered 2D magnets, theory suggests that the interlayer exchange coupling strongly depends on layer separation, while the stacking arrangement can even change the sign of the magnetic exchange, thus drastically modifying the ground state. Here, we demonstrate pressure tuning of magnetic order in the 2D magnet CrI3. We probe the magnetic states using tunneling and scanning magnetic circular dichroism microscopy measurements. We find that the interlayer magnetic coupling can be more than doubled by hydrostatic pressure. In bilayer CrI3, pressure induces a transition from layered antiferromagnetic to ferromagnetic phases. In trilayer CrI3, pressure can create coexisting domains of three phases, one ferromagnetic and two distinct antiferromagnetic. The observed changes in magnetic order can be explained by changes in the stacking arrangement. Such coupling between stacking order and magnetism provides ample opportunities for designer magnetic phases and functionalities.

Electrons transmitted across a ballistic semiconductor junction are expected to undergo refraction, analogous to light rays across an optical boundary. In graphene, the linear dispersion and zero-gap band structure admit highly transparent p-n junctions by simple electrostatic gating. Here, we employ transverse magnetic focusing to probe the propagation of carriers across an electrostatically defined graphene junction. We find agreement with the predicted Snell’s law for electrons, including the observation of both positive and negative refraction. Resonant transmission across the p-n junction provides a direct measurement of the angle-dependent transmission coefficient. Comparing experimental data with simulations reveals the crucial role played by the effective junction width, providing guidance for future device design. Our results pave the way for realizing electron optics based on graphene p-n junctions.

Andreev reflection occurs at the interface of a metal and a superconductor when an incident electron in the metal gets ‘reflected’ as a hole travelling on the same path. Replace the metal with graphene and specular reflection may instead take place. Electrons incident from a normal metal onto a superconductor are reflected back as holes—a process called Andreev reflection1,2,3. In a normal metal where the Fermi energy is much larger than a typical superconducting gap, the reflected hole retraces the path taken by the incident electron. In graphene with low disorder, however, the Fermi energy can be tuned to be smaller than the superconducting gap. In this unusual limit, the holes are expected to be reflected specularly at the superconductor–graphene interface owing to the onset of interband Andreev processes, where the effective mass of the reflected holes changes sign4,5. Here we present measurements of gate-modulated Andreev reflections across the low-disorder van der Waals interface formed between graphene and the superconducting NbSe2. We find that the conductance across the graphene–superconductor interface exhibits a characteristic suppression when the Fermi energy is tuned to values smaller than the superconducting gap, a hallmark for the transition between intraband retro Andreev reflections and interband specular Andreev reflections.

Mixing interactions and superlattices Under the influence of an external magnetic field, the energies of electrons in two-dimensional systems group into the so-called Landau levels. In the cleanest samples, interactions among electrons lead to fractional quantum Hall (FQH) states. If such a system is then subjected to a superlattice potential, it is unclear whether the fragile FQH states will survive. To address this question, Wang et al. sandwiched graphene between two layers of hexagonal boron nitride. Transport measurements on the superlattice showed that some FQH states did survive. Furthermore, the interplay between interactions and the superlattice potential produced additional, anomalous states. Science , this issue p. 1231

We present the characterization of ballistic graphene field-effect transistors (GFETs) with an effective oxide thickness of 3.5 nm. Graphene channels are fully encapsulated within hexagonal boron nitride, and self-aligned contacts are formed to the edge of the single-layer graphene. Devices of channel lengths ( $L_{G})$ down to 67 nm are fabricated, and a virtual-source transport model is used to model the resulting current–voltage characteristics. The mobility and source-injection velocity as a function of $L_{G}$ yields a mean-free-path, ballistic velocity, and effective mobility of 850 nm, $9.3\times 10^{7}$ cm/s, and 13 700 cm2/Vs, respectively, which are among the highest velocities and mobilities reported for GFETs. Despite these best-in-class attributes, these devices achieve transconductance ( $g_{m})$ and output conductance ( $g_{{\mathrm{ds}}})$ of only 600 and 300 $\mu \text{S}/\mu \text{m}$ , respectively, due to the fundamental limitations of graphene’s quantum capacitance and zero-bandgap. $g_{m}$ values, which are less than those of comparable ballistic silicon devices, benefit from the high ballistic velocity in graphene but are degraded by an effective gate capacitance reduced by the quantum capacitance. The $g_{{\mathrm{ds}}}$ values, which limit the effective power gain achievable in these devices, are significantly worse than comparable silicon devices due to the properties of the zero-bandgap graphene channel.

We report on quantum capacitance measurements of high quality, graphite- and hexagonal boron nitride encapsulated Bernal stacked trilayer graphene devices. At zero applied magnetic field, we observe a number of electron density- and electrical displacement-tuned features in the electronic compressibility associated with changes in Fermi surface topology. At high displacement field and low density, strong trigonal warping gives rise to emergent Dirac gullies centered near the corners of the hexagonal Brillouin and related by three fold rotation symmetry. At low magnetic fields of $B=1.25$~T, the gullies manifest as a change in the degeneracy of the Landau levels from two to three. Weak incompressible states are also observed at integer filling within these triplets Landau levels, which a Hartree-Fock analysis indicates are associated with Coulomb-driven nematic phases that spontaneously break rotation symmetry., Main text: 5 pages, 3 Figures. Supplements: 8 pages, 5 figures

Heterostructures of atomically-thin materials have attracted significant interest owing to their ability to host novel electronic properties fundamentally distinct from their constituent layers. In the case of graphene on boron nitride, the closely-matched lattices yield a moir\'e superlattice that modifies the graphene electron dispersion and opens gaps both at the primary Dirac point (DP) and the moir\'e-induced secondary Dirac point (SDP) in the valence band. While significant effort has focused on controlling the superlattice period via the rotational stacking order, the role played by the magnitude of the interlayer coupling has received comparatively little attention. Here, we modify the interaction between graphene and boron nitride by tuning their separation with hydrostatic pressure. We observe a dramatic enhancement of the DP gap with increasing pressure, but little change in the SDP gap. Our surprising results identify the critical role played by atomic-scale structural deformations of the graphene lattice and reveal new opportunities for band structure engineering in van der Waals heterostructures., Comment: 26 Pages, 16 Figures. (v2) Main text and figures are updated

The ability to manipulate two-dimensional (2D) electrons with external electric fields provides a route to synthetic band engineering. By imposing artificially designed and spatially periodic superlattice (SL) potentials, 2D electronic properties can be further engineered beyond the constraints of naturally occurring atomic crystals. Here we report a new approach to fabricate high mobility SL devices by integrating surface dielectric patterning with atomically thin van der Waals materials. By separating the device assembly and SL fabrication processes, we address the intractable tradeoff between device processing and mobility degradation that constrains SL engineering in conventional systems. The improved electrostatics of atomically thin materials moreover allows smaller wavelength SL patterns than previously achieved. Replica Dirac cones in ballistic graphene devices with sub 40nm wavelength SLs are demonstrated, while under large magnetic fields we report the fractal Hofstadter spectra from SLs with designed lattice symmetries vastly different from that of the host crystal. Our results establish a robust and versatile technique for band structure engineering of graphene and related van der Waals materials with dynamic tunability., 15 pages, 4 figures

The high magnetic field electronic structure of bilayer graphene is enhanced by the spin, valley isospin, and an accidental orbital degeneracy, leading to a complex phase diagram of broken symmetry states. Here, we present a technique for measuring the layer-resolved charge density, from which we directly determine the valley and orbital polarization within the zero energy Landau level. Layer polarization evolves in discrete steps across 32 electric field-tuned phase transitions between states of different valley, spin, and orbital order, including previously unobserved orbitally polarized states stabilized by skew interlayer hopping. We fit our data to a model that captures both single-particle and interaction-induced anisotropies, providing a complete picture of this correlated electron system. The resulting roadmap to symmetry breaking paves the way for deterministic engineering of fractional quantum Hall states, while our layer-resolved technique is readily extendable to other two-dimensional materials where layer polarization maps to the valley or spin quantum numbers., United States. Department of Energy. Office of Basic Energy Sciences (Contract FG02-08ER46514), Gordon and Betty Moore Foundation (Grant GBMF2931)

Coulomb interaction between two closely spaced parallel layers of electron system can generate the frictional drag effect by interlayer Coulomb scattering. Employing graphene double layers separated by few layer hexagonal boron nitride (hBN), we investigate density tunable magneto- and Hall-drag under strong magnetic fields. The observed large magneto-drag and Hall-drag signals can be related with Laudau level (LL) filling status of the drive and drag layers. We find that the sign and magnitude of the magneto- and Hall-drag resistivity tensor can be quantitatively correlated to the variation of magneto-resistivity tensors in the drive and drag layers, confirming a theoretical formula for magneto-drag in the quantum Hall regime. The observed weak temperature dependence and $\sim B^2$ dependence of the magneto-drag are qualitatively explained by Coulomb scattering phase-space argument., 5 pages, 3 figures