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Recent experiments demonstrated that interfacial water dissociation (H 2O ⇆ H ++ OH -) could be accelerated exponentially by an electric field applied to graphene electrodes, a phenomenon related to the Wien effect. Here we report an order-of-magnitude acceleration of the interfacial water dissociation reaction under visible-light illumination. This process is accompanied by spatial separation of protons and hydroxide ions across one-atom-thick graphene and enhanced by strong interfacial electric fields. The found photoeffect is attributed to the combination of graphene's perfect selectivity with respect to protons, which prevents proton-hydroxide recombination, and to proton transport acceleration by the Wien effect, which occurs in synchrony with the water dissociation reaction. Our findings provide fundamental insights into ion dynamics near atomically thin proton-selective interfaces and suggest that strong interfacial fields can enhance and tune very fast ionic processes, which is of relevance for applications in photocatalysis and designing reconfigurable materials.

When two-dimensional crystals are brought into close proximity, their interaction results in reconstruction of electronic spectrum and crystal structure. Such reconstruction strongly depends on the twist angle between the crystals, which has received growing attention due to interesting electronic and optical properties that arise in graphene and transitional metal dichalcogenides. Here we study two insulating crystals of hexagonal boron nitride stacked at small twist angle. Using electrostatic force microscopy, we observe ferroelectric-like domains arranged in triangular superlattices with a large surface potential. The observation is attributed to interfacial elastic deformations that result in out-of-plane dipoles formed by pairs of boron and nitrogen atoms belonging to opposite interfacial surfaces. This creates a bilayer-thick ferroelectric with oppositely polarized (BN and NB) dipoles in neighbouring domains, in agreement with our modeling. These findings open up possibilities for designing van der Waals heterostructures and offer an alternative probe to study moiré-superlattice electrostatic potentials., Here, moiré superlattices generated by twisted insulating crystals of hexagonal boron nitride are shown to have a ferroelectric-like character, attributed to strain-induced polarized dipoles formed by pairs of interfacial boron and nitrogen atoms that create bilayer-thick ferroelectric domains.

In thermodynamic equilibrium, current in metallic systems is carried by electronic states near the Fermi energy whereas the filled bands underneath contribute little to conduction. Here we describe a very different regime in which carrier distribution in graphene and its superlattices is shifted so far from equilibrium that the filled bands start playing an essential role, leading to a critical-current behavior. The criticalities develop upon the velocity of electron flow reaching the Fermi velocity. Key signatures of the out-of-equilibrium state are current-voltage characteristics resembling those of superconductors, sharp peaks in differential resistance, sign reversal of the Hall effect, and a marked anomaly caused by the Schwinger-like production of hot electron-hole plasma. The observed behavior is expected to be common for all graphene-based superlattices., Comment: 22 pages, 11 figures

Electron-electron interactions play a critical role in many condensed matter phenomena, and it is tempting to find a way to control them by changing the interactions’ strength. One possible approach is to place a studied system in proximity of a metal, which induces additional screening and hence suppresses electron interactions. Here, using devices with atomically-thin gate dielectrics and atomically-flat metallic gates, we measure the electron-electron scattering length in graphene and report qualitative deviations from the standard behavior. The changes induced by screening become important only at gate dielectric thicknesses of a few nm, much smaller than a typical separation between electrons. Our theoretical analysis agrees well with the scattering rates extracted from measurements of electron viscosity in monolayer graphene and of umklapp electron-electron scattering in graphene superlattices. The results provide a guidance for future attempts to achieve proximity screening of many-body phenomena in two-dimensional systems., Experimental control of electron-electron interactions in materials is challenging. Here, the authors control the interactions by proximity screening with gate dielectrics of nanometer thickness, revealing qualitative changes in concentration and temperature dependences, and validating their analysis using electron hydrodynamics and umklapp scattering approaches.

In graphite crystals, layers of graphene reside in three equivalent, but distinct, stacking positions typically referred to as A, B, and C projections. The order in which the layers are stacked defines the electronic structure of the crystal, providing an exciting degree of freedom which can be exploited for designing graphitic materials with unusual properties including predicted higherature superconductivity and ferromagnetism. However, the lack of control of the stacking sequence limits most research to the stable ABA form of graphite. Here, we demonstrate a strategy to control the stacking order using van der Waals technology. To this end, we first visualize the distribution of stacking domains in graphite films and then perform directional encapsulation of ABC-rich graphite crystallites with hexagonal boron nitride (hBN). We found that hBN encapsulation, which is introduced parallel to the graphite zigzag edges, preserves ABC stacking, while encapsulation along the armchair edges transforms the stacking to ABA. The technique presented here should facilitate new research on the important properties of ABC graphite.

Two-dimensional crystals with angstrom-scale pores are widely considered as candidates for a next generation of molecular separation technologies aiming to provide extreme, exponentially large selectivity combined with high flow rates. No such pores have been demonstrated experimentally. Here we study gas transport through individual graphene pores created by low intensity exposure to low kV electrons. Helium and hydrogen permeate easily through these pores whereas larger species such as xenon and methane are practically blocked. Permeating gases experience activation barriers that increase quadratically with molecules’ kinetic diameter, and the effective diameter of the created pores is estimated as ∼2 angstroms, about one missing carbon ring. Our work reveals stringent conditions for achieving the long sought-after exponential selectivity using porous two-dimensional membranes and suggests limits on their possible performance., Two-dimensional membranes with angstrom-sized pores are predicted to combine high permeability with exceptional selectivity, but experimental demonstration has been challenging. Here the authors realize angstrom-sized pores in monolayer graphene and demonstrate gas transport with activation barriers increasing quadratically with the molecular kinetic diameter.

Oscillatory magnetoresistance measurements on graphene have revealed a wealth of novel physics. These phenomena are typically studied at low currents. At high currents, electrons are driven far from equilibrium with the atomic lattice vibrations so that their kinetic energy can exceed the thermal energy of the phonons. Here, we report three non-equilibrium phenomena in monolayer graphene at high currents: (i) a “Doppler-like” shift and splitting of the frequencies of the transverse acoustic (TA) phonons emitted when the electrons undergo inter-Landau level (LL) transitions; (ii) an intra-LL Mach effect with the emission of TA phonons when the electrons approach supersonic speed, and (iii) the onset of elastic inter-LL transitions at a critical carrier drift velocity, analogous to the superfluid Landau velocity. All three quantum phenomena can be unified in a single resonance equation. They offer avenues for research on out-of-equilibrium phenomena in other two-dimensional fermion systems., Magneto-oscillations have revealed many interesting phenomena in graphene and quantum Hall systems, but they are typically measured at low currents and in equilibrium. Here, the authors report several non-equilibrium quantum effects observed in magneto-oscillations in graphene at high currents.

We describe how the out-of-plane dielectric polarizability of monolayer graphene influences the electrostatics of bilayer graphene -- both Bernal (BLG) and twisted (tBLG). We compare the polarizability value computed using density functional theory with the output from previously published experimental data on the electrostatically controlled interlayer asymmetry potential in BLG and data on the on-layer density distribution in tBLG. We show that monolayers in tBLG are described well by polarizability $\alpha_{exp} = 10.8 \unicode{x212B}^3$ and effective out-of-plane dielectric susceptibility $\epsilon_z = 2.5$, including their on-layer electron density distribution at zero magnetic field and the inter-layer Landau level pinning at quantizing magnetic fields., Comment: 4 pages

A variety of physical phenomena associated with nanoscale electron transport often results in non-trivial spatial voltage and current patterns, particularly in nonlocal transport regimes. While numerous techniques have been devised to image electron flows, the need remains for a nanoscale probe capable of simultaneously imaging current and voltage distributions with high sensitivity and minimal invasiveness, in a magnetic field, across a broad range of temperatures and beneath an insulating surface. Here we present a technique for spatially mapping electron flows based on a nanotube single-electron transistor, which achieves high sensitivity for both voltage and current imaging. In a series of experiments using high-mobility graphene devices, we demonstrate the ability of our technique to visualize local aspects of intrinsically nonlocal transport, as in ballistic flows, which are not easily resolvable via existing methods. This technique should aid in understanding the physics of two-dimensional electronic devices and enable new classes of experiments that image electron flow through buried nanostructures in the quantum and interaction-dominated regimes.

2D nanoslit devices, where two crystals with atomically flat surfaces are separated by only a few nanometers, have attracted considerable attention because their tunable control over the confinement allows for the discovery of unusual transport behavior of gas, water, and ions. Here, the passage of double-stranded DNA molecules is studied through nanoslits fabricated from exfoliated 2D materials, such as graphene or hexagonal boron nitride, and the DNA polymer behavior is examined in this tight confinement. Two types of events are observed in the ionic current: long current blockades that signal DNA translocation and short spikes where DNA enters the slits but withdraws. DNA translocation events exhibit three distinct phases in their current-blockade traces—loading, translation, and exit. Coarse-grained molecular dynamics simulation allows the different polymer configurations of these phases to be identified. DNA molecules, including folds and knots in their polymer structure, are observed to slide through the slits with near-uniform velocity without noticeable frictional interactions of DNA with the confining graphene surfaces. It is anticipated that this new class of 2D-nanoslit devices will provide unique ways to study polymer physics and enable lab-on-a-chip biotechnology.

Van der Waals heterostructures display a rich variety of unique electronic properties. To identify novel transport mechanisms, nonlocal measurements have been widely used, wherein a voltage is measured at contacts placed far away from the expected classical flow of charge carriers. This approach was employed in search of dissipationless spin and valley transport, topological charge-neutral currents, hydrodynamic flows and helical edge modes. Monolayer, bilayer, and few-layer graphene, transition-metal dichalcogenides, and moire superlattices were found to display pronounced nonlocal effects. However, the origin of these effects is hotly debated. Graphene, in particular, exhibits giant nonlocality at charge neutrality, a prominent behavior that attracted competing explanations. Utilizing superconducting quantum interference device on a tip (SQUID-on-tip) for nanoscale thermal and scanning gate imaging, we demonstrate that the commonly-occurring charge accumulation at graphene edges leads to giant nonlocality, producing narrow conductive channels that support long-range currents. Unexpectedly, while the edge conductance has little impact on the current flow in zero magnetic field, it leads to field-induced decoupling between edge and bulk transport at moderate fields. The resulting giant nonlocality both at charge neutrality and away from it produces exotic flow patterns in which charges can flow against the global electric field. We have visualized surprisingly intricate patterns of nonlocal currents, which are sensitive to edge disorder. The observed one-dimensional edge transport, being generic and nontopological, is expected to support nonlocal transport in many electronic systems, offering insight into numerous controversies in the literature and linking them to long-range guided electronic states at system edges., Main text: 14 pages, 4 figures. Methods and Supplementary information: 27 pages, 6 figures. Supplementary videos: 9

Of the two stable forms of graphite, hexagonal (HG) and rhombohedral (RG), the former is more common and has been studied extensively. RG is less stable, which so far precluded its detailed investigation, despite many theoretical predictions about the abundance of exotic interaction-induced physics. Advances in van der Waals heterostructure technology have now allowed us to make high-quality RG films up to 50 graphene layers thick and study their transport properties. We find that the bulk electronic states in such RG are gapped and, at low temperatures, electron transport is dominated by surface states. Because of topological protection, the surface states are robust and of high quality, allowing the observation of the quantum Hall effect, where RG exhibits phase transitions between gapless semimetallic phase and gapped quantum spin Hall phase with giant Berry curvature. An energy gap can also be opened in the surface states by breaking their inversion symmetry via applying a perpendicular electric field. Moreover, in RG films thinner than 4 nm, a gap is present even without an external electric field. This spontaneous gap opening shows pronounced hysteresis and other signatures characteristic of electronic phase separation, which we attribute to emergence of strongly-correlated electronic surface states.

In quantizing magnetic fields, graphene superlattices exhibit a complex fractal spectrum often referred to as the Hofstadter butterfly. It can be viewed as a collection of Landau levels that arise from quantization of Brown-Zak minibands recurring at rational ($p/q$) fractions of the magnetic flux quantum per superlattice unit cell. Here we show that, in graphene-on-boron-nitride superlattices, Brown-Zak fermions can exhibit mobilities above 10$^6$ cm$^2$V$^{-1}$s$^{-1}$ and the mean free path exceeding several micrometers. The exceptional quality of our devices allows us to show that Brown-Zak minibands are $4q$ times degenerate and all the degeneracies (spin, valley and mini-valley) can be lifted by exchange interactions below 1K. We also found negative bend resistance at $1/q$ fractions for electrical probes placed as far as several micrometers apart. The latter observation highlights the fact that Brown-Zak fermions are Bloch quasiparticles propagating in high fields along straight trajectories, just like electrons in zero field., 16 pages, 13 figures

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Two-dimensional atomic crystals can radically change their properties in response to external influences such as substrate orientation or strain, resulting in essentially new materials in terms of the electronic structure. A striking example is the creation of flat-bands in bilayer-graphene for certain 'magic' twist-angles between the orientations of the two layers. The quenched kinetic-energy in these flat-bands promotes electron-electron interactions and facilitates the emergence of strongly-correlated phases such as superconductivity and correlated-insulators. However, the exquisite fine-tuning required for finding the magic-angle where flat-bands appear in twisted-bilayer graphene, poses challenges to fabrication and scalability. Here we present an alternative route to creating flat-bands that does not involve fine tuning. Using scanning tunneling microscopy and spectroscopy, together with numerical simulations, we demonstrate that graphene monolayers placed on an atomically-flat substrate can be forced to undergo a buckling-transition, resulting in a periodically modulated pseudo-magnetic field, which in turn creates a post-graphene material with flat electronic bands. Bringing the Fermi-level into these flat-bands by electrostatic doping, we observe a pseudogap-like depletion in the density-of-states, which signals the emergence of a correlated-state. The described approach of 2D crystal buckling offers a strategy for creating other superlattice systems and, in particular, for exploring interaction phenomena characteristic of flat-bands., 22 pages, 15 figures. arXiv admin note: substantial text overlap with arXiv:1904.10147

Defect-free graphene is impermeable to gases and liquids but highly permeable to thermal protons. Atomic-scale defects such as vacancies, grain boundaries, and Stone-Wales defects are predicted to enhance graphene's proton permeability and may even allow small ions through, whereas larger species such as gas molecules should remain blocked. These expectations have so far remained untested in experiment. Here, we show that atomically thin carbon films with a high density of atomic-scale defects continue blocking all molecular transport, but their proton permeability becomes similar to 1000 times higher than that of defect-free graphene. Lithium ions can also permeate through such disordered graphene. The enhanced proton and ion permeability is attributed to a high density of eight-carbon-atom rings. The latter pose approximately twice lower energy barriers for incoming protons compared to that of the six-atom rings of graphene and a relatively low barrier of similar to 0.6 eV for Li ions. Our findings suggest that disordered graphene could be of interest as membranes and protective barriers in various Li-ion and hydrogen technologies.

Blue energy converts the chemical potential difference from salinity gradients into electricity via reverse electrodialysis and provides a renewable source of clean energy. To achieve high energy conversion efficiency and power density, nanoporous membrane materials with both high ionic conductivity and ion selectivity are required. Here, we report ion transport through a network of holey-graphene-like sheets made by bottom-up polymerization. The resulting ultrathin membranes provide controlled pores of

When two-dimensional atomic crystals are brought into close proximity to form a van der Waals heterostructure, neighbouring crystals can start influencing each others electronic properties. Of particular interest is the situation when the periodicity of the two crystals closely match and a moir\'e pattern forms, which results in specific electron scattering, reconstruction of electronic and excitonic spectra, crystal reconstruction, and many other effects. Thus, formation of moir\'e patterns is a viable tool of controlling the electronic properties of 2D materials. At the same time, the difference in the interatomic distances for the two crystals combined, determines the range in which the electronic spectrum is reconstructed, and thus is a barrier to the low energy regime. Here we present a way which allows spectrum reconstruction at all energies. By using graphene which is aligned simultaneously to two hexagonal boron nitride layers, one can make electrons scatter in the differential moir\'e pattern, which can have arbitrarily small wavevector and, thus results in spectrum reconstruction at arbitrarily low energies. We demonstrate that the strength of such a potential relies crucially on the atomic reconstruction of graphene within the differential moir\'e super-cell. Such structures offer further opportunity in tuning the electronic spectra of two-dimensional materials., Comment: 35 pages, 15 figures

Detection of magnetic focusing peaks allows probing of minibands in the energy spectrum of twisted bilayer graphene., Magnetic fields force ballistic electrons injected from a narrow contact to move along skipping orbits and form caustics. This leads to pronounced resistance peaks at nearby voltage probes as electrons are effectively focused inside them, a phenomenon known as magnetic focusing. This can be used not only for the demonstration of ballistic transport but also to study the electronic structure of metals. Here, we use magnetic focusing to probe narrowbands in graphene bilayers twisted at ~2°. Their minibands are found to support long-range ballistic transport limited at low temperatures by intrinsic electron-electron scattering. A voltage bias between the layers causes strong minivalley splitting and allows selective focusing for different minivalleys, which is of interest for using this degree of freedom in frequently discussed valleytronics.

Ballistic Josephson junctions are predicted to support a number of exotic physics processess, providing an ideal system to inject the supercurrent in the quantum Hall regime. Herein, we demonstrate electrical transport measurements on ballistic superconductor–graphene–superconductor junctions by contacting graphene to niobium with a junction length up to 1.5 μm. Hexagonal boron nitride encapsulation and one-dimensional edge contacts guarantee high-quality graphene Josephson junctions with a mean free path of several micrometers and record-low contact resistance. Transports in normal states including the observation of Fabry–Perot oscillations and Sharvin resistance conclusively witness the ballistic propagation in the junctions. The critical current density JC is over one order of magnitude larger than that of the previously reported junctions. Away from the charge neutrality point, the ICRN product (IC is the critical current and RN the normal state resistance of junction) is nearly a constant, independent of carrier density n, which agrees well with the theory for ballistic Josephson junctions. Multiple Andreev reflections up to the third order are observed for the first time by measuring the differential resistance in the micrometer-long ballistic graphene Josephson junctions.

Defect-free monolayers of graphene and hexagonal boron nitride are surprisingly permeable to thermal protons, despite being completely impenetrable to all gases. It remains untested whether small ions can permeate through the two-dimensional crystals. Here we show that mechanically exfoliated graphene and hexagonal boron nitride exhibit perfect Nernst selectivity such that only protons can permeate through, with no detectable flow of counterions. In the experiments, we use suspended monolayers that have few, if any, atomic-scale defects, as shown by gas permeation tests, and place them to separate reservoirs filled with hydrochloric acid solutions. Protons account for all the electrical current and chloride ions are blocked. This result corroborates the previous conclusion that thermal protons can pierce defect-free two-dimensional crystals. Besides the importance for theoretical developments, our results are also of interest for research on various separation technologies based on two-dimensional materials., Defect-free monolayers of graphene and hexagonal boron nitride are highly permeable to thermal protons, but are impenetrable to gases. Here the authors show that mechanically exfoliated crystals exhibit perfect proton selectivity, corroborating proton transport through the bulk without atomic-scale defects.

Van der Waals materials and their heterostructures offer a versatile platform for studying a variety of quantum transport phenomena due to their unique crystalline properties and the exceptional ability in tuning their electronic spectrum. However, most experiments are limited to devices that have lateral dimensions of only a few micrometres. Here, we perform magnetotransport measurements on graphene/hexagonal boron-nitride Hall bars and show that wider devices reveal additional quantum effects. In devices wider than ten micrometres we observe distinct magnetoresistance oscillations that are caused by resonant scattering of Landau-quantised Dirac electrons by acoustic phonons in graphene. The study allows us to accurately determine graphene's low energy phonon dispersion curves and shows that transverse acoustic modes cause most of phonon scattering. Our work highlights the crucial importance of device width when probing quantum effects and also demonstrates a precise, spectroscopic method for studying electron-phonon interactions in van der Waals heterostructures., Comment: 23 pages and 9 figures, including supplementary information

The quantum Hall effect (QHE) originates from discrete Landau levels forming in a two-dimensional (2D) electron system in a magnetic field. In three dimensions (3D), the QHE is forbidden because the third dimension spreads Landau levels into multiple overlapping bands, destroying the quantisation. Here we report the QHE in graphite crystals that are up to hundreds of atomic layers thick - thickness at which graphite was believed to behave as a 3D bulk semimetal. We attribute the observation to a dimensional reduction of electron dynamics in high magnetic fields, such that the electron spectrum remains continuous only in the direction of the magnetic field, and only the last two quasi-one-dimensional (1D) Landau bands cross the Fermi level. In sufficiently thin graphite films, the formation of standing waves breaks these 1D bands into a discrete spectrum, giving rise to a multitude of quantum Hall plateaux. Despite a large number of layers, we observe a profound difference between films with even and odd numbers of graphene layers. For odd numbers, the absence of inversion symmetry causes valley polarisation of the standing-wave states within 1D Landau bands. This reduces QHE gaps, as compared to films of similar thicknesses but with even layer numbers because the latter retain the inversion symmetry characteristic of bilayer graphene. High-quality graphite films present a novel QHE system with a parity-controlled valley polarisation and intricate interplay between orbital, spin and valley states, and clear signatures of electron-electron interactions including the fractional QHE below 0.5 K.

Monolayers of graphene and hexagonal boron nitride (hBN) are highly permeable to thermal protons1,2. For thicker two-dimensional (2D) materials, proton conductivity diminishes exponentially, so that, for example, monolayer MoS2 that is just three atoms thick is completely impermeable to protons1. This seemed to suggest that only one-atom-thick crystals could be used as proton-conducting membranes. Here, we show that few-layer micas that are rather thick on the atomic scale become excellent proton conductors if native cations are ion-exchanged for protons. Their areal conductivity exceeds that of graphene and hBN by one to two orders of magnitude. Importantly, ion-exchanged 2D micas exhibit this high conductivity inside the infamous gap for proton-conducting materials3, which extends from ∼100 °C to 500 °C. Areal conductivity of proton-exchanged monolayer micas can reach above 100 S cm−2 at 500 °C, well above the current requirements for the industry roadmap4. We attribute the fast proton permeation to ~5-A-wide tubular channels that perforate micas’ crystal structure, which, after ion exchange, contain only hydroxyl groups inside. Our work indicates that there could be other 2D crystals5 with similar nanometre-scale channels, which could help close the materials gap in proton-conducting applications. Few-layer micas show proton permeation across the sheet, exceeding that of graphene and hBN by one to two orders of magnitude.

When two-dimensional electron gases (2DEGs) are exposed to magnetic field, they resonantly absorb electromagnetic radiation via electronic transitions between Landau levels (LLs). In 2DEGs with a Dirac spectrum, such as graphene, theory predicts an exceptionally high infrared magneto-absorption, even at zero doping. However, the measured LL magneto-optical effects in graphene have been much weaker than expected because of imperfections in the samples available so far for such experiments. Here we measure magneto-transmission and Faraday rotation in high-mobility encapsulated monolayer graphene using a custom designed setup for magneto-infrared microspectroscopy. Our results show a strongly enhanced magneto-optical activity in the infrared and terahertz ranges characterized by a maximum allowed (50%) absorption of light, a 100% magnetic circular dichroism as well as a record high Faraday rotation. Considering that sizeable effects have been already observed at routinely achievable magnetic fields, our findings demonstrate a new potential of magnetic tuning in 2D Dirac materials for long-wavelength optoelectronics and plasmonics., Comment: 14 pages, 4 figures

The study of atomically thin ferromagnetic crystals has led to the discovery of unusual magnetic behaviour and provided insight into the magnetic properties of bulk materials. However, the experimental techniques that have been used to explore ferromagnetism in such materials cannot probe the magnetic field directly. Here, we show that ballistic Hall micromagnetometry can be used to measure the magnetization of individual two-dimensional ferromagnets. Our devices are made by van der Waals assembly in such a way that the investigated ferromagnetic crystal is placed on top of a multi-terminal Hall bar made from encapsulated graphene. We use the micromagnetometry technique to study atomically thin chromium tribromide (CrBr3). We find that the material remains ferromagnetic down to monolayer thickness and exhibits strong out-of-plane anisotropy. We also find that the magnetic response of CrBr3 varies little with the number of layers and its temperature dependence cannot be described by the simple Ising model of two-dimensional ferromagnetism., 19 pages, 12 figures

The electronic properties of graphene superlattices have attracted intense interest that was further stimulated by the recent observation of novel many-body states at "magic" angles in twisted bilayer graphene (BLG). For very small ("marginal") twist angles of 0.1 deg, BLG has been shown to exhibit a strain-accompanied reconstruction that results in submicron-size triangular domains with the Bernal stacking. If the interlayer bias is applied to open an energy gap inside the domain regions making them insulating, marginally-twisted BLG is predicted to remain conductive due to a triangular network of chiral one-dimensional (1D) states hosted by domain boundaries. Here we study electron transport through this network and report giant Aharonov-Bohm oscillations persisting to temperatures above 100 K. At liquid helium temperatures, the network resistivity exhibits another kind of oscillations that appear as a function of carrier density and are accompanied by a sign-changing Hall effect. The latter are attributed to consecutive population of the flat minibands formed by the 2D network of 1D states inside the gap. Our work shows that marginally twisted BLG is markedly distinct from other 2D electronic systems, including BLG at larger twist angles, and offers a fascinating venue for further research., Comment: 11 pages, 8 figures

Topology is a powerful recent concept asserting that quantum states could be globally protected against local perturbations. Dissipationless topologically protected states are thus of major fundamental interest as well as of practical importance in metrology and quantum information technology. Although topological protection can be robust theoretically, in realistic devices it is often fragile against various dissipative mechanisms, which are difficult to probe directly because of their microscopic origins. By utilizing scanning nanothermometry, we visualize and investigate microscopic mechanisms undermining the apparent topological protection in the quantum Hall state in graphene. Our simultaneous nanoscale thermal and scanning gate microscopy shows that the dissipation is governed by crosstalk between counterpropagating pairs of downstream and upstream channels that appear at graphene boundaries because of edge reconstruction. Instead of local Joule heating, however, the dissipation mechanism comprises two distinct and spatially separated processes. The work generating process that we image directly and which involves elastic tunneling of charge carriers between the quantum channels, determines the transport properties but does not generate local heat. The independently visualized heat and entropy generation process, in contrast, occurs nonlocally upon inelastic resonant scattering off single atomic defects at graphene edges, while not affecting the transport. Our findings offer a crucial insight into the mechanisms concealing the true topological protection and suggest venues for engineering more robust quantum states for device applications., Comment: Main text: 12 pages, 3 figures. Supplementary information: 19 pages, 9 figures

Materials subjected to a magnetic field exhibit the Hall effect, a phenomenon studied and understood in fine detail. Here we report a qualitative breach of this classical behavior in electron systems with high viscosity. The viscous fluid in graphene is found to respond to non-quantizing magnetic fields by producing an electric field opposite to that generated by the classical Hall effect. The viscous contribution is large and identified by studying local voltages that arise in the vicinity of current-injecting contacts. We analyze the anomaly over a wide range of temperatures and carrier densities and extract the Hall viscosity, a dissipationless transport coefficient that was long identified theoretically but remained elusive in experiment. Good agreement with theory suggests further opportunities for studying electron magnetohydrodynamics., Comment: 18 pages, 9 figures

In electronic transport, umklapp processes play a fundamental role as the only intrinsic mechanism that allows electrons to transfer momentum to the crystal lattice and, therefore, provide a finite electrical resistance in pure metals1,2. However, umklapp scattering is difficult to demonstrate in experiment, as it is easily obscured by other dissipation mechanisms1–6. Here we show that electron–electron umklapp scattering dominates the transport properties of graphene-on-boron-nitride superlattices over a wide range of temperature and carrier density. The umklapp processes cause giant excess resistivity that rapidly increases with increasing superlattice period and are responsible for deterioration of the room-temperature mobility by more than an order of magnitude as compared to standard, non-superlattice graphene devices. The umklapp scattering exhibits a quadratic temperature dependence accompanied by a pronounced electron–hole asymmetry with the effect being much stronger for holes than electrons. In addition to being of fundamental interest, our results have direct implications for design of possible electronic devices based on heterostructures featuring superlattices. An increase in electrical resistance caused by the fundamental process of electrons scattering off of each other (umklapp scattering) is observed in graphene superlattice devices. This will limit the electrical properties of such devices.

Nanometre-scale graphitic capillaries with atomically flat walls are engineered and studied, revealing unexpectedly fast transport of liquid water through channels that accommodate only a few layers of water. Artificial nanometre-sized capillaries have enabled new research and led to the emergence of nanofluidics, but surface roughness in particular makes it very challenging to exactly control their dimensions. Andre Geim and colleagues now show that van der Waals assembly can produce narrow and smooth capillaries that have atomically flat top and bottom graphite sheets, separated by spacers made from a precisely controlled number of graphene layers. Water transport through the channels, which range in height from a single atomic plane to dozens of them, is unexpectedly fast and speeds up further in channels that accommodate only a few layers of water. The fabrication method is expected to give access to a wide range of capillaries with atomically precise sizes, and with permeation properties that are tunable by the choice of two-dimensional material used for creating the channel walls. Nanometre-scale pores and capillaries have long been studied because of their importance in many natural phenomena and their use in numerous applications1. A more recent development is the ability to fabricate artificial capillaries with nanometre dimensions, which has enabled new research on molecular transport and led to the emergence of nanofluidics2,3,4. But surface roughness in particular makes it challenging to produce capillaries with precisely controlled dimensions at this spatial scale. Here we report the fabrication of narrow and smooth capillaries through van der Waals assembly5, with atomically flat sheets at the top and bottom separated by spacers made of two-dimensional crystals6 with a precisely controlled number of layers. We use graphene and its multilayers as archetypal two-dimensional materials to demonstrate this technology, which produces structures that can be viewed as if individual atomic planes had been removed from a bulk crystal to leave behind flat voids of a height chosen with atomic-scale precision. Water transport through the channels, ranging in height from one to several dozen atomic planes, is characterized by unexpectedly fast flow (up to 1 metre per second) that we attribute to high capillary pressures (about 1,000 bar) and large slip lengths. For channels that accommodate only a few layers of water, the flow exhibits a marked enhancement that we associate with an increased structural order in nanoconfined water. Our work opens up an avenue to making capillaries and cavities with sizes tunable to angstrom precision, and with permeation properties further controlled through a wide choice of atomically flat materials available for channel walls.

Electrons that flow like a fluid Electrons inside a conductor are often described as flowing in response to an electric field. This flow rarely resembles anything like the familiar flow of water through a pipe, but three groups describe counterexamples (see the Perspective by Zaanen). Moll et al. found that the viscosity of the electron fluid in thin wires of PdCoO 2 had a major effect on the flow, much like what happens in regular fluids. Bandurin et al. found evidence in graphene of electron whirlpools similar to those formed by viscous fluid flowing through a small opening. Finally, Crossno et al. observed a huge increase of thermal transport in graphene, a signature of so-called Dirac fluids. Science , this issue p. 1061 , 1055 , 1058 ; see also p. 1026

Graphene on hexagonal boron-nitride (h-BN) is an atomically flat conducting system that is ideally suited for probing the effect of Zeeman splitting on electron transport. We demonstrate by magneto-transport measurements that a parallel magnetic field up to 30 Tesla does not affect the transport properties of graphene on h-BN even at charge neutrality where such an effect is expected to be maximal. The only magnetoresistance detected at low carrier concentrations is shown to be associated with a small perpendicular component of the field which cannot be fully eliminated in the experiment. Despite the high mobility of charge carries at low temperatures, we argue that the effects of Zeeman splitting are fully masked by electrostatic potential fluctuations at charge neutrality., Comment: v2: updated with some modifications/clarifications

Despite being only one-atom thick, defect-free graphene is considered to be completely impermeable to all gases and liquids1,2,3,4,5,6,7,8,9,10. This conclusion is based on theory3,4,5,6,7,8 and supported by experiments1,9,10 that could not detect gas permeation through micrometre-size membranes within a detection limit of 105 to 106 atoms per second. Here, using small monocrystalline containers tightly sealed with graphene, we show that defect-free graphene is impermeable with an accuracy of eight to nine orders of magnitude higher than in the previous experiments. We are capable of discerning (but did not observe) permeation of just a few helium atoms per hour, and this detection limit is also valid for all other gases tested (neon, nitrogen, oxygen, argon, krypton and xenon), except for hydrogen. Hydrogen shows noticeable permeation, even though its molecule is larger than helium and should experience a higher energy barrier. This puzzling observation is attributed to a two-stage process that involves dissociation of molecular hydrogen at catalytically active graphene ripples, followed by adsorbed atoms flipping to the other side of the graphene sheet with a relatively low activation energy of about 1.0 electronvolt, a value close to that previously reported for proton transport11,12. Our work provides a key reference for the impermeability of two-dimensional materials and is important from a fundamental perspective and for their potential applications.

Over the past decade, the ability to reduce the dimensions of fluidic devices to the nanometre scale (by using nanotubes 1–5 or nanopores 6–11 , for example) has led to the discovery of unexpected water- and ion-transport phenomena 12–14 . More recently, van der Waals assembly of two-dimensional materials 15 has allowed the creation of artificial channels with ångström-scale precision 16 . Such channels push fluid confinement to the molecular scale, wherein the limits of continuum transport equations 17 are challenged. Water films on this scale can rearrange into one or two layers with strongly suppressed dielectric permittivity 18,19 or form a room-temperature ice phase 20 . Ionic motion in such confined channels 21 is affected by direct interactions between the channel walls and the hydration shells of the ions, and water transport becomes strongly dependent on the channel wall material 22 . We explore how water and ionic transport are coupled in such confinement. Here we report measurements of ionic fluid transport through molecular-sized slit-like channels. The transport, driven by pressure and by an applied electric field, reveals a transistor-like electrohydrodynamic effect. An applied bias of a fraction of a volt increases the measured pressure-driven ionic transport (characterized by streaming mobilities) by up to 20 times. This gating effect is observed in both graphite and hexagonal boron nitride channels but exhibits marked material-dependent differences. We use a modified continuum framework accounting for the material-dependent frictional interaction of water molecules, ions and the confining surfaces to explain the differences observed between channels made of graphene and hexagonal boron nitride. This highly nonlinear gating of fluid transport under molecular-scale confinement may offer new routes to control molecular and ion transport, and to explore electromechanical couplings that may have a role in recently discovered mechanosensitive ionic channels 23 .

Controlled transport of water molecules through membranes and capillaries is important in areas as diverse as water purification and healthcare technologies1,2,3,4,5,6,7. Previous attempts to control water permeation through membranes (mainly polymeric ones) have concentrated on modulating the structure of the membrane and the physicochemical properties of its surface by varying the pH, temperature or ionic strength3,8. Electrical control over water transport is an attractive alternative; however, theory and simulations9,10,11,12,13,14 have often yielded conflicting results, from freezing of water molecules to melting of ice14,15,16 under an applied electric field. Here we report electrically controlled water permeation through micrometre-thick graphene oxide membranes17,18,19,20,21. Such membranes have previously been shown to exhibit ultrafast permeation of water17,22 and molecular sieving properties18,21, with the potential for industrial-scale production. To achieve electrical control over water permeation, we create conductive filaments in the graphene oxide membranes via controllable electrical breakdown. The electric field that concentrates around these current-carrying filaments ionizes water molecules inside graphene capillaries within the graphene oxide membranes, which impedes water transport. We thus demonstrate precise control of water permeation, from ultrafast permeation to complete blocking. Our work opens up an avenue for developing smart membrane technologies for artificial biological systems, tissue engineering and filtration.

Van der Waals heterostructures, which are composed of layered two-dimensional materials, offer a platform to investigate a diverse range of physical phenomena and could be of use in a variety of applications. Heterostructures containing two-dimensional ferromagnets, such as chromium triiodide (CrI3), have recently been reported, which could allow two-dimensional spintronic devices to be developed. Here we study tunnelling through thin ferromagnetic chromium tribromide (CrBr3) barriers that are sandwiched between graphene electrodes. In devices with non-magnetic barriers, conservation of momentum can be relaxed by phonon-assisted tunnelling or by tunnelling through localized states. In contrast, in the devices with ferromagnetic barriers, the major tunnelling mechanisms are the emission of magnons at low temperatures and the scattering of electrons on localized magnetic excitations at temperatures above the Curie temperature. Magnetoresistance in the graphene electrodes further suggests induced spin–orbit coupling and proximity exchange via the ferromagnetic barrier. Tunnelling with magnon emission offers the possibility of spin injection.

Plasmons, collective oscillations of electron systems, can efficiently couple light and electric current, and thus can be used to create sub-wavelength photodetectors, radiation mixers, and on-chip spectrometers. Despite considerable effort, it has proven challenging to implement plasmonic devices operating at terahertz frequencies. The material capable to meet this challenge is graphene as it supports long-lived electrically-tunable plasmons. Here we demonstrate plasmon-assisted resonant detection of terahertz radiation by antenna-coupled graphene transistors that act as both plasmonic Fabry-Perot cavities and rectifying elements. By varying the plasmon velocity using gate voltage, we tune our detectors between multiple resonant modes and exploit this functionality to measure plasmon wavelength and lifetime in bilayer graphene as well as to probe collective modes in its moir\'e minibands. Our devices offer a convenient tool for further plasmonic research that is often exceedingly difficult under non-ambient conditions (e.g. cryogenic temperatures and strong magnetic fields) and promise a viable route for various photonic applications., Comment: 19 pages, 12 figures

Electron-electron (e-e) collisions can impact transport in a variety of surprising and sometimes counterintuitive ways. Despite strong interest, experiments on the subject proved challenging because of the simultaneous presence of different scattering mechanisms that suppress or obscure consequences of e-e scattering. Only recently, sufficiently clean electron systems with transport dominated by e-e collisions have become available, showing behavior characteristic of highly viscous fluids. Here we study electron transport through graphene constrictions and show that their conductance below 150 K increases with increasing temperature, in stark contrast to the metallic character of doped graphene. Notably, the measured conductance exceeds the maximum conductance possible for free electrons. This anomalous behavior is attributed to collective movement of interacting electrons, which 'shields' individual carriers from momentum loss at sample boundaries. The measurements allow us to identify the conductance contribution arising due to electron viscosity and determine its temperature dependence. Besides fundamental interest, our work shows that viscous effects can facilitate high-mobility transport at elevated temperatures, a potentially useful behavior for designing graphene-based devices., Comment: Nature Physics 2017

Watching electrons lose steam in graphene Although graphene can be fabricated to be extremely clean, it still has a nonzero electrical resistance. Resistance is associated with turning electrons' energy into heat, but how exactly does this happen? Halbertal et al. used a tiny scanning temperature probe based on a superconducting quantum interference device to investigate this problem. As the current flowed through a square-shaped sample of graphene, electrons lost energy predominantly in the vicinity of atomic-scale defects, which were few and far between in the bulk but much more common on the edges of the sample. Science , this issue p. 1303

Many layered materials can be cleaved down to individual atomic planes, similar to graphene, but only a small minority of them are stable under ambient conditions. The rest reacts and decomposes in air, which has severely hindered their investigation and possible uses. Here we introduce a remedial approach based on cleavage, transfer, alignment and encapsulation of air-sensitive crystals, all inside a controlled inert atmosphere. To illustrate the technology, we choose two archetypal two-dimensional crystals unstable in air: black phosphorus and niobium diselenide. Our field-effect devices made from their monolayers are conductive and fully stable under ambient conditions, in contrast to the counterparts processed in air. NbSe2 remains superconducting down to the monolayer thickness. Starting with a trilayer, phosphorene devices reach sufficiently high mobilities to exhibit Landau quantization. The approach offers a venue to significantly expand the range of experimentally accessible two-dimensional crystals and their heterostructures., Comment: 4 figures

Graphene has recently been shown to be permeable to thermal protons, nuclei of hydrogen atoms, which sparked interest in its use as a proton-conducting membrane in relevant technologies. Here we report that proton transport through graphene can be enhanced strongly by iluminating it with visible light. Using electrical measurements and mass spectrometry, we find a photoresponsivity of ∼104 A W-1, which translates into a gain of ∼104 protons per photon, with response times in a microsecond range. These characteristics are competitive with thos of state-of-the-art photodetectors based on electron transport using silicon and novel two-dimensional materials. The photo-proton effect can be important for graphene's envisaged use in fuel cells and hydrogen isotope separation. Our observations can also be of interest for other applications such as light-iduced water splitting, photo-catalysis and novel photodetectors.

Graphene has recently been shown to be permeable to thermal protons 1 , the nuclei of hydrogen atoms, which sparked interest in its use as a proton-conducting membrane in relevant technologies 1-4 . However, the influence of light on proton permeation remains unknown. Here we report that proton transport through Pt-nanoparticle-decorated graphene can be enhanced strongly by illuminating it with visible light. Using electrical measurements and mass spectrometry, we find a photoresponsivity of ∼10 4 A W -1 , which translates into a gain of ∼10 4 protons per photon with response times in the microsecond range. These characteristics are competitive with those of state-of-the-art photodetectors that are based on electron transport using silicon and novel two-dimensional materials 5-7 . The photo-proton effect could be important for graphene's envisaged use in fuel cells and hydrogen isotope separation. Our observations may also be of interest for other applications such as light-induced water splitting, photocatalysis and novel photodetectors.

Understanding magnetoresistance, the change in electrical resistance upon an external magnetic field, at the atomic level is of great interest both fundamentally and technologically.

Heat-loving quantum oscillations The shape of the Fermi surface in a conductor can be gleaned through quantum oscillations—periodic changes in transport properties as an external magnetic field is varied. Like most quantum properties, the phenomenon can usually be observed only at very low temperatures. Krishna Kumar et al. report quantum oscillations in graphene that do not go away even at the temperature of boiling water. Although “ordinary,” low-temperature quantum oscillations die away, another oscillatory behavior sets in that is extremely robust to heating. These resilient oscillations appear only in samples in which graphene is nearly aligned with its hexagonal boron nitride substrate, indicating that they are caused by the potential of the moiré superlattice that forms in such circumstances. Science , this issue p. 181

Ion permeation and selectivity of graphene oxide membranes with sub-nm channels dramatically alters with the change in interlayer distance due to dehydration effects whereas permeation of water molecules remains largely unaffected. Graphene oxide membranes show exceptional molecular permeation properties, with promise for many applications1,2,3,4,5. However, their use in ion sieving and desalination technologies is limited by a permeation cutoff of ∼9 A (ref. 4), which is larger than the diameters of hydrated ions of common salts4,6. The cutoff is determined by the interlayer spacing (d) of ∼13.5 A, typical for graphene oxide laminates that swell in water2,4. Achieving smaller d for the laminates immersed in water has proved to be a challenge. Here, we describe how to control d by physical confinement and achieve accurate and tunable ion sieving. Membranes with d from ∼9.8 A to 6.4 A are demonstrated, providing a sieve size smaller than the diameters of hydrated ions. In this regime, ion permeation is found to be thermally activated with energy barriers of ∼10–100 kJ mol–1 depending on d. Importantly, permeation rates decrease exponentially with decreasing sieve size but water transport is weakly affected (by a factor of

Graphene oxide (GO) membranes continue to attract intense interest due to their unique molecular sieving properties combined with fast permeation rates. However, the membranes' use has been limited mostly to aqueous solutions because GO membranes appear to be impermeable to organic solvents, a phenomenon not fully understood yet. Here, we report efficient and fast filtration of organic solutions through GO laminates containing smooth two-dimensional (2D) capillaries made from flakes with large sizes of ~ 10-20 micron. Without sacrificing their sieving characteristics, such membranes can be made exceptionally thin, down to ~ 10 nm, which translates into fast permeation of not only water but also organic solvents. We attribute the organic solvent permeation and sieving properties of ultrathin GO laminates to the presence of randomly distributed pinholes that are interconnected by short graphene channels with a width of 1 nm. With increasing the membrane thickness, the organic solvent permeation rates decay exponentially but water continues to permeate fast, in agreement with previous reports. The application potential of our ultrathin laminates for organic-solvent nanofiltration is demonstrated by showing >99.9% rejection of various organic dyes with small molecular weights dissolved in methanol. Our work significantly expands possibilities for the use of GO membranes in purification, filtration and related technologies.

When a crystal is subjected to a periodic potential, under certain circumstances (such as when the period of the potential is close to the crystal periodicity; the potential is strong enough, etc.) it might adjust itself to follow the periodicity of the potential, resulting in a, so called, commensurate state. Such commensurate-incommensurate transitions are ubiquitous phenomena in many areas of condensed matter physics: from magnetism and dislocations in crystals, to vortices in superconductors, and atomic layers adsorbed on a crystalline surface. Of particular interest might be the properties of topological defects between the two commensurate phases: solitons, domain walls, and dislocation walls. Here we report a commensurate-incommensurate transition for graphene on top of hexagonal boron nitride (hBN). Depending on the rotational angle between the two hexagonal lattices, graphene can either stretch to adjust to a slightly different hBN periodicity (the commensurate state found for small rotational angles) or exhibit little adjustment (the incommensurate state). In the commensurate state, areas with matching lattice constants are separated by domain walls that accumulate the resulting strain. Such soliton-like objects present significant fundamental interest, and their presence might explain recent observations when the electronic, optical, Raman and other properties of graphene-hBN heterostructures have been notably altered.

Graphene is impermeable to all gases and liquids, and even such a small atom as hydrogen is not expected to penetrate through graphene's dense electronic cloud within billions of years. Here we show that monolayers of graphene and hexagonal boron nitride (hBN) are unexpectedly permeable to thermal protons, hydrogen ions under ambient conditions. As a reference, no proton transport could be detected for a monolayer of molybdenum disulfide, bilayer graphene or multilayer hBN. At room temperature, monolayer hBN exhibits the highest proton conductivity with a low activation energy of about 0.3 eV but graphene becomes a better conductor at elevated temperatures such that its resistivity to proton flow is estimated to fall below 10^-3 Ohm per cm2 above 250 C. The proton barriers can be further reduced by decorating monolayers with catalytic nanoparticles. These atomically thin proton conductors could be of interest for many hydrogen-based technologies., submitted, pre-edited version