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.

One-Dimensional Magnetic Conduction Channels across Zigzag Graphene Nanoribbon/Hexagonal Boron Nitride Heterojunctions.

We examine the electronic structure of recently fabricated in-plane heterojunctions of zigzag graphene nanoribbons embedded in hexagonal boron nitride. We focus on hitherto unexplored interface configurations in which both edges of the nanoribbon are bonded to the same chemical species, either boron or nitrogen atoms. Using ab initio and mean-field Hubbard model calculations, we reveal the emergence of one-dimensional magnetic conducting channels at these interfaces. These channels originate from the energy shift of the magnetic interface states that is induced by charge transfer between the nanoribbon and hexagonal boron nitride. We further address the response of these heterojunctions to external electric and magnetic fields, demonstrating the tunability of energy and spin splittings in the electronic structure. Our findings establish that zigzag graphene nanoribbon/hexagonal boron nitride heterojunctions are a suitable platform for exploring and engineering spin transport in the atomically thin limit, with potential applications in integrated spintronic devices.

Twisto-Electrochemical Activity Volcanoes in Trilayer Graphene.

In this work, we develop a twist-dependent electrochemical activity map, combining a low-energy continuum electronic structure model with modified Marcus-Hush-Chidsey kinetics in trilayer graphene. We identify a counterintuitive rate enhancement region spanning the magic angle curve and incommensurate twists in the system geometry. We find a broad activity peak with a ruthenium hexamine redox couple in regions corresponding to both magic angles and incommensurate angles, a result qualitatively distinct from the twisted bilayer case. Flat bands and incommensurability offer new avenues for reaction rate enhancements in electrochemical transformations.

Charge order landscape and competition with superconductivity in kagome metals.

In the kagome metals AV3Sb5 (A = K, Rb, Cs), three-dimensional charge order is the primary instability that sets the stage for other collective orders to emerge, including unidirectional stripe order, orbital flux order, electronic nematicity and superconductivity. Here, we use high-resolution angle-resolved photoemission spectroscopy to determine the microscopic structure of three-dimensional charge order in AV3Sb5 and its interplay with superconductivity. Our approach is based on identifying an unusual splitting of kagome bands induced by three-dimensional charge order, which provides a sensitive way to refine the spatial charge patterns in neighbouring kagome planes. We found a marked dependence of the three-dimensional charge order structure on composition and doping. The observed difference between CsV3Sb5 and the other compounds potentially underpins the double-dome superconductivity in CsV3(Sb,Sn)5 and the suppression of Tc in KV3Sb5 and RbV3Sb5. Our results provide fresh insights into the rich phase diagram of AV3Sb5.

Operando electron microscopy investigation of polar domain dynamics in twisted van der Waals homobilayers.

Conventional antiferroelectric materials with atomic-scale anti-aligned dipoles undergo a transition to a ferroelectric (FE) phase under strong electric fields. The moiré superlattice formed in the twisted stacks of van der Waals crystals exhibits polar domains alternating in moiré length with anti-aligned dipoles. In this moiré domain antiferroelectic (MDAF) arrangement, the distribution of electric dipoles is distinguished from that of two-dimensional FEs, suggesting dissimilar domain dynamics. Here we performed an operando transmission electron microscopy investigation on twisted bilayer WSe2 to observe the polar domain dynamics in real time. We find that the topological protection, provided by the domain wall network, prevents the MDAF-to-FE transition. As one decreases the twist angle, however, this transition occurs as the domain wall network disappears. Exploiting stroboscopic operando transmission electron microscopy on the FE phase, we measure a maximum domain wall velocity of 300 µm s-1. Domain wall pinnings by various disorders limit the domain wall velocity and cause Barkhausen noises in the polarization hysteresis loop. Atomic-scale analysis of the pinning disorders provides structural insight on how to improve the switching speed of van der Waals FEs.

Unconventional superconductivity in magic-angle graphene superlattices.

The behaviour of strongly correlated materials, and in particular unconventional superconductors, has been studied extensively for decades, but is still not well understood. This lack of theoretical understanding has motivated the development of experimental techniques for studying such behaviour, such as using ultracold atom lattices to simulate quantum materials. Here we report the realization of intrinsic unconventional superconductivity-which cannot be explained by weak electron-phonon interactions-in a two-dimensional superlattice created by stacking two sheets of graphene that are twisted relative to each other by a small angle. For twist angles of about 1.1°-the first 'magic' angle-the electronic band structure of this 'twisted bilayer graphene' exhibits flat bands near zero Fermi energy, resulting in correlated insulating states at half-filling. Upon electrostatic doping of the material away from these correlated insulating states, we observe tunable zero-resistance states with a critical temperature of up to 1.7 kelvin. The temperature-carrier-density phase diagram of twisted bilayer graphene is similar to that of copper oxides (or cuprates), and includes dome-shaped regions that correspond to superconductivity. Moreover, quantum oscillations in the longitudinal resistance of the material indicate the presence of small Fermi surfaces near the correlated insulating states, in analogy with underdoped cuprates. The relatively high superconducting critical temperature of twisted bilayer graphene, given such a small Fermi surface (which corresponds to a carrier density of about 1011 per square centimetre), puts it among the superconductors with the strongest pairing strength between electrons. Twisted bilayer graphene is a precisely tunable, purely carbon-based, two-dimensional superconductor. It is therefore an ideal material for investigations of strongly correlated phenomena, which could lead to insights into the physics of high-critical-temperature superconductors and quantum spin liquids.

Correlated insulator behaviour at half-filling in magic-angle graphene superlattices.

A van der Waals heterostructure is a type of metamaterial that consists of vertically stacked two-dimensional building blocks held together by the van der Waals forces between the layers. This design means that the properties of van der Waals heterostructures can be engineered precisely, even more so than those of two-dimensional materials. One such property is the 'twist' angle between different layers in the heterostructure. This angle has a crucial role in the electronic properties of van der Waals heterostructures, but does not have a direct analogue in other types of heterostructure, such as semiconductors grown using molecular beam epitaxy. For small twist angles, the moiré pattern that is produced by the lattice misorientation between the two-dimensional layers creates long-range modulation of the stacking order. So far, studies of the effects of the twist angle in van der Waals heterostructures have concentrated mostly on heterostructures consisting of monolayer graphene on top of hexagonal boron nitride, which exhibit relatively weak interlayer interaction owing to the large bandgap in hexagonal boron nitride. Here we study a heterostructure consisting of bilayer graphene, in which the two graphene layers are twisted relative to each other by a certain angle. We show experimentally that, as predicted theoretically, when this angle is close to the 'magic' angle the electronic band structure near zero Fermi energy becomes flat, owing to strong interlayer coupling. These flat bands exhibit insulating states at half-filling, which are not expected in the absence of correlations between electrons. We show that these correlated states at half-filling are consistent with Mott-like insulator states, which can arise from electrons being localized in the superlattice that is induced by the moiré pattern. These properties of magic-angle-twisted bilayer graphene heterostructures suggest that these materials could be used to study other exotic many-body quantum phases in two dimensions in the absence of a magnetic field. The accessibility of the flat bands through electrical tunability and the bandwidth tunability through the twist angle could pave the way towards more exotic correlated systems, such as unconventional superconductors and quantum spin liquids.

Heterointerface effects in the electrointercalation of van der Waals heterostructures.

Molecular-scale manipulation of electronic and ionic charge accumulation in materials is the backbone of electrochemical energy storage1-4. Layered van der Waals (vdW) crystals are a diverse family of materials into which mobile ions can electrochemically intercalate into the interlamellar gaps of the host atomic lattice5,6. The structural diversity of such materials enables the interfacial properties of composites to be optimized to improve ion intercalation for energy storage and electronic devices7-12. However, the ability of heterolayers to modify intercalation reactions, and their role at the atomic level, are yet to be elucidated. Here we demonstrate the electrointercalation of lithium at the level of individual atomic interfaces of dissimilar vdW layers. Electrochemical devices based on vdW heterostructures 13 of stacked hexagonal boron nitride, graphene and molybdenum dichalcogenide (MoX2; X = S, Se) layers are constructed. We use transmission electron microscopy, in situ magnetoresistance and optical spectroscopy techniques, as well as low-temperature quantum magneto-oscillation measurements and ab initio calculations, to resolve the intermediate stages of lithium intercalation at heterointerfaces. The formation of vdW heterointerfaces between graphene and MoX2 results in a more than tenfold greater accumulation of charge in MoX2 when compared to MoX2/MoX2 homointerfaces, while enforcing a more negative intercalation potential than that of bulk MoX2 by at least 0.5 V. Beyond energy storage, our combined experimental and computational methodology for manipulating and characterizing the electrochemical behaviour of layered systems opens new pathways to control the charge density in two-dimensional electronic and optoelectronic devices.

Dirac Half-Semimetallicity and Antiferromagnetism in Graphene Nanoribbon/Hexagonal Boron Nitride Heterojunctions.

Half-metals have been envisioned as active components in spintronic devices by virtue of their completely spin-polarized electrical currents. Actual materials hosting half-metallic phases, however, remain scarce. Here, we predict that recently fabricated heterojunctions of zigzag nanoribbons embedded in two-dimensional hexagonal boron nitride are half-semimetallic, featuring fully spin-polarized Dirac points at the Fermi level. The half-semimetallicity originates from the transfer of charges from hexagonal boron nitride to the embedded graphene nanoribbon. These charges give rise to opposite energy shifts of the states residing at the two edges, while preserving their intrinsic antiferromagnetic exchange coupling. Upon doping, an antiferromagnetic-to-ferrimagnetic phase transition occurs in these heterojunctions, with the sign of the excess charge controlling the spatial localization of the net magnetic moments. Our findings demonstrate that such heterojunctions realize tunable one-dimensional conducting channels of spin-polarized Dirac fermions seamlessly integrated into a two-dimensional insulator, thus holding promise for the development of carbon-based spintronics.

Modulating the Electrochemical Intercalation of Graphene Interfaces with α-RuCl3 as a Solid-State Electron Acceptor.

Intercalation reactions modify the charge density in van der Waals (vdW) materials through coupled electronic-ionic charge accumulation and are susceptible to modulation by interlayer hybridization in vdW heterostructures. Here, we demonstrate that charge transfer between graphene and α-RuCl3, which hole-dopes the graphene, greatly favors the intercalation of lithium ions into graphene-based vdW heterostructures. We systematically tune this effect on Li+ ion intercalation, modulating the intercalation potential, by using varying thicknesses of hexagonal boron nitride (hBN) as spacer layers between graphene and α-RuCl3. Confocal Raman spectroscopy and electronic transport measurements are used to monitor electrochemical intercalation, and density functional theory computations help quantify charge transfer to both α-RuCl3 and graphene upon Li intercalation. This work demonstrates a versatile approach for systematically modulating the electrochemical intercalation behavior of two-dimensional layers akin to electron donating/withdrawing substituent effects used to tune molecular redox potentials.

Lattice Reconstruction in MoSe2-WSe2 Heterobilayers Synthesized by Chemical Vapor Deposition.

Vertical van der Waals heterostructures of semiconducting transition metal dichalcogenides realize moiré systems with rich correlated electron phases and moiré exciton phenomena. For material combinations with small lattice mismatch and twist angles as in MoSe2-WSe2, however, lattice reconstruction eliminates the canonical moiré pattern and instead gives rise to arrays of periodically reconstructed nanoscale domains and mesoscopically extended areas of one atomic registry. Here, we elucidate the role of atomic reconstruction in MoSe2-WSe2 heterostructures synthesized by chemical vapor deposition. With complementary imaging down to the atomic scale, simulations, and optical spectroscopy methods, we identify the coexistence of moiré-type cores and extended moiré-free regions in heterostacks with parallel and antiparallel alignment. Our work highlights the potential of chemical vapor deposition for applications requiring laterally extended heterosystems of one atomic registry or exciton-confining heterostack arrays.

Domain-Dependent Surface Adhesion in Twisted Few-Layer Graphene: Platform for Moiré-Assisted Chemistry.

Twisted van der Waals multilayers are widely regarded as a rich platform to access novel electronic phases thanks to the multiple degrees of freedom available for controlling their electronic and chemical properties. Here, we propose that the stacking domains that form naturally due to the relative twist between successive layers act as an additional "knob" for controlling the behavior of these systems and report the emergence and engineering of stacking domain-dependent surface chemistry in twisted few-layer graphene. Using mid-infrared near-field optical microscopy and atomic force microscopy, we observe a selective adhesion of metallic nanoparticles and liquid water at the domains with rhombohedral stacking configurations of minimally twisted double bi- and trilayer graphene. Furthermore, we demonstrate that the manipulation of nanoparticles located at certain stacking domains can locally reconfigure the moiré superlattice in their vicinity at the micrometer scale. Our findings establish a new approach to controlling moiré-assisted chemistry and nanoengineering.

Unveiling and Manipulating Hidden Symmetries in Graphene Nanoribbons.

Armchair graphene nanoribbons are a highly promising class of semiconductors for all-carbon nanocircuitry. Here, we present a new perspective on their electronic structure from simple model Hamiltonians and ab initio calculations. We focus on a specific set of nanoribbons of width n=3p+2, where n is the number of carbon atoms across the nanoribbon axis and p is a positive integer. We demonstrate that the energy-gap opening in these nanoribbons originates from the breaking of a previously unidentified hidden symmetry by long-ranged hopping of π electrons and structural distortions occurring at the edges. This hidden symmetry can be restored or manipulated through the application of in-plane lattice strain, which enables continuous energy-gap tuning, the emergence of Dirac points at the Fermi level, and topological quantum phase transitions. Our work establishes an original interpretation of the semiconducting character of armchair graphene nanoribbons and offers guidelines for rationally designing their electronic structure.

Hydrogen Atoms on Zigzag Graphene Nanoribbons: Chemistry and Magnetism Meet at the Edge.

Although the unconventional π-magnetism at the zigzag edges of graphene holds promise for a wide array of applications, whether and to what degree it plays a role in their chemistry remains poorly understood. Here, we investigate the addition of a hydrogen atom─the simplest yet the most experimentally relevant adsorbate─to zigzag graphene nanoribbons (ZGNRs). We show that the π-magnetism governs the chemistry of ZGNRs, giving rise to a site-dependent reactivity of the carbon atoms and driving the hydrogenation process to the nanoribbon edges. Conversely, the chemisorbed hydrogen atom governs the π-magnetism of ZGNRs, acting as a spin-1/2 paramagnetic center in the otherwise antiferromagnetic ground state and spin-polarizing the charge carriers at the band extrema. Our findings establish a comprehensive picture of the peculiar interplay between chemistry and magnetism that emerges at the zigzag edges of graphene.

Modulation Doping of Single-Layer Semiconductors for Improved Contact at Metal Interfaces.

Single layers of two-dimensional (2D) materials hold the promise for further miniaturization of semiconductor electronic devices. However, the metal-semiconductor contact resistance limits device performance. To mitigate this problem, we propose modulation doping, specifically a doping layer placed on the opposite side of a metal-semiconductor interface. Using first-principles calculations to obtain the band alignment, we show that the Schottky barrier height and, consequently, the contact resistance at the metal-semiconductor interface can be reduced by modulation doping. We demonstrate the feasibility of this approach for a single-layer tungsten diselenide (WSe2) channel and 2D MXene modulation doping layers, interfaced with several different metal contacts. Our results indicate that the Fermi level of the metal can be shifted across the entire band gap. This approach can be straight-forwardly generalized for other 2D semiconductors and a wide variety of doping layers.

Modeling the effect of the vaccination campaign on the COVID-19 pandemic.

Population-wide vaccination is critical for containing the SARS-CoV-2 (COVID-19) pandemic when combined with restrictive and prevention measures. In this study we introduce SAIVR, a mathematical model able to forecast the COVID-19 epidemic evolution during the vaccination campaign. SAIVR extends the widely used Susceptible-Infectious-Removed (SIR) model by considering the Asymptomatic (A) and Vaccinated (V) compartments. The model contains several parameters and initial conditions that are estimated by employing a semi-supervised machine learning procedure. After training an unsupervised neural network to solve the SAIVR differential equations, a supervised framework then estimates the optimal conditions and parameters that best fit recent infectious curves of 27 countries. Instructed by these results, we performed an extensive study on the temporal evolution of the pandemic under varying values of roll-out daily rates, vaccine efficacy, and a broad range of societal vaccine hesitancy/denial levels. The concept of herd immunity is questioned by studying future scenarios which involve different vaccination efforts and more infectious COVID-19 variants.

Electrically Induced Dirac Fermions in Graphene Nanoribbons.

Graphene nanoribbons are widely regarded as promising building blocks for next-generation carbon-based devices. A critical issue to their prospective applications is whether their electronic structure can be externally controlled. Here, we combine simple model Hamiltonians with extensive first-principles calculations to investigate the response of armchair graphene nanoribbons to transverse electric fields. Such fields can be achieved either upon laterally gating the nanoribbon or incorporating ambipolar chemical codopants along the edges. We reveal that the field induces a semiconductor-to-semimetal transition with the semimetallic phase featuring zero-energy Dirac fermions that propagate along the armchair edges. The transition occurs at critical fields that scale inversely with the width of the nanoribbons. These findings are universal to group-IV honeycomb lattices, including silicene and germanene nanoribbons, irrespective of the type of edge termination. Overall, our results create new opportunities to electrically engineer Dirac semimetallic phases in otherwise semiconducting graphene-like nanoribbons.

Dirac fermions and flat bands in the ideal kagome metal FeSn.

A kagome lattice of 3d transition metal ions is a versatile platform for correlated topological phases hosting symmetry-protected electronic excitations and magnetic ground states. However, the paradigmatic states of the idealized two-dimensional kagome lattice-Dirac fermions and flat bands-have not been simultaneously observed. Here, we use angle-resolved photoemission spectroscopy and de Haas-van Alphen quantum oscillations to reveal coexisting surface and bulk Dirac fermions as well as flat bands in the antiferromagnetic kagome metal FeSn, which has spatially decoupled kagome planes. Our band structure calculations and matrix element simulations demonstrate that the bulk Dirac bands arise from in-plane localized Fe-3d orbitals, and evidence that the coexisting Dirac surface state realizes a rare example of fully spin-polarized two-dimensional Dirac fermions due to spin-layer locking in FeSn. The prospect to harness these prototypical excitations in a kagome lattice is a frontier of great promise at the confluence of topology, magnetism and strongly correlated physics.

Correlated Insulating States and Transport Signature of Superconductivity in Twisted Trilayer Graphene Superlattices.

Layers of two-dimensional materials stacked with a small twist angle give rise to beating periodic patterns on a scale much larger than the original lattice, referred to as a "moiré superlattice." Here, we demonstrate a higher-order "moiré of moiré" superlattice in twisted trilayer graphene with two consecutive small twist angles. We report correlated insulating states near the half filling of the moiré of moiré superlattice at an extremely low carrier density (∼10^{10} cm^{-2}), near which we also report a zero-resistance transport behavior typically expected in a 2D superconductor. The full-occupancy (ν=-4 and ν=4) states are semimetallic and gapless, distinct from the twisted bilayer systems.

Ultraheavy and Ultrarelativistic Dirac Quasiparticles in Sandwiched Graphenes.

Electrons in quantum materials exhibiting coexistence of dispersionless (flat) bands piercing dispersive (steep) bands give rise to strongly correlated phenomena and are associated with unconventional superconductivity. We show that in twisted sandwiched graphene (TSWG)-a three-layer van der Waals heterostructure with a twisted middle layer-steep Dirac cones can coexist with dramatic band flattening at the same energy scale, if twisted by 1.5°. This phenomenon is not stable in the simplified continuum models. The key result of this Letter is that the flat bands become stable only as a consequence of lattice relaxation processes included in our atomistic calculations. Further on, external fields can change the relative energy offset between the Dirac cone vertex and the flat bands and enhance band hybridization, which could permit controlling correlated phases. Our work establishes twisted sandwiched graphene as a new platform for research into strongly interacting two-dimensional quantum matter.