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Coulomb drag between adjacent electron and hole gases has attracted considerable attention, being studied in various two-dimensional systems, including semiconductor and graphene heterostructures. Here we report measurements of electron-hole drag in the Planckian plasma that develops in monolayer graphene in the vicinity of its Dirac point above liquid-nitrogen temperatures. The frequent electron-hole scattering forces minority carriers to move against the applied electric field due to the drag induced by majority carriers. This unidirectional transport of electrons and holes results in nominally negative mobility for the minority carriers. The electron-hole drag is found to be strongest near-room temperature, despite being notably affected by phonon scattering. Our findings provide better understanding of the transport properties of charge-neutral graphene, reveal limits on its hydrodynamic description and also offer insight into quantum-critical systems in general.

Two dimensional (2D) crystals have attracted strong interest as a new class of proton conducting materials that can block atoms, molecules and ions while allowing proton transport through the atomically thin basal planes. Although 2D materials exhibit this perfect selectivity, the reported proton conductivities have been relatively low. Here we show that vacancy-rich titania monolayers are highly permeable to protons while remaining impermeable to helium with proton conductivity exceeding 100 S cm-2 at 200 C and surpassing targets set by industry roadmaps. The fast and selective proton transport is attributed to an extremely high density of titanium-atom vacancies (one per square nm), which effectively turns titania monolayers into angstrom-scale sieves. Our findings highlight the potential of 2D oxides as membrane materials for hydrogen-based technologies.

Water is essential for almost every aspect of life on our planet and, unsurprisingly, its properties have been studied in great detail. However, disproportionately little remains known about the electrical properties of interfacial and strongly confined water where its structure deviates from that of bulk water, becoming distinctly layered. The structural change is expected to affect water's conductivity and particularly its polarizability, which in turn modifies intermolecular forces that play a crucial role in many physical and chemical processes. Here we use scanning dielectric microscopy to probe the in-plane electrical properties of water confined between atomically flat surfaces separated by distances down to 1 nm. For confinement exceeding a few nm, water exhibits an in-plane dielectric constant close to that of bulk water and its proton conductivity is notably enhanced, gradually increasing with decreasing water thickness. This trend abruptly changes when the confined water becomes only a few molecules thick. Its in-plane dielectric constant reaches giant, ferroelectric-like values of about 1,000 whereas the conductivity peaks at a few S/m, close to values characteristic of superionic liquids. We attribute the enhancement to strongly disordered hydrogen bonding induced by the few-layer confinement, which facilitates both easier in-plane polarization of molecular dipoles and faster proton exchange. This insight into the electrical properties of nanoconfined water is important for understanding many phenomena that occur at aqueous interfaces and in nanoscale pores.

The ongoing efforts to optimize Li-ion batteries led to the interest in intercalation of nanoscale layered compounds, including bilayer graphene. Its lithium intercalation has been demonstrated recently but the mechanisms underpinning the storage capacity remain poorly understood. Here, using magnetotransport measurements, we report in-operando intercalation dynamics of bilayer graphene. Unexpectedly, we find four distinct intercalation stages that correspond to well-defined Li-ion densities. We refer to these stages as 'in-plane', with no in-plane analogues in bulk graphite. The fully intercalated bilayers represent a stoichiometric compound C14LiC14 with a Li density of 2.7x10^{14} cm^{-2}, notably lower than fully intercalated graphite. Combining the experimental findings and DFT calculations, we show that the critical step in bilayer intercalation is a transition from AB to AA stacking which occurs at a density of 0.9x10^{14} cm^{-2}. Our findings reveal the mechanism and limits for electrochemical intercalation of bilayer graphene and suggest possible avenues for increasing the Li storage capacity., Comment: 30 pages, 17 figures

Extensive efforts have been undertaken to combine superconductivity and the quantum Hall effect so that Cooper-pair transport between superconducting electrodes in Josephson junctions is mediated by one-dimensional edge states. This interest has been motivated by prospects of finding new physics, including topologically-protected quasiparticles, but also extends into metrology and device applications. So far it has proven challenging to achieve detectable supercurrents through quantum Hall conductors. Here we show that domain walls in minimally twisted bilayer graphene support exceptionally robust proximity superconductivity in the quantum Hall regime, allowing Josephson junctions to operate in fields close to the upper critical field of superconducting electrodes. The critical current is found to be non-oscillatory and practically unchanging over the entire range of quantizing fields, with its value being limited by the quantum conductance of ballistic, strictly one-dimensional electronic channels residing within the domain walls. The system described is unique in its ability to support Andreev bound states at quantizing fields and offers many interesting directions for further exploration., Comment: 24 pages, 14 figures

Biological nanostructures change their shape and function in response to external stimuli, and significant efforts have been made to design artificial biomimicking devices operating on similar principles. In this work we demonstrate a programmable nanofluidic switch, driven by elastocapillarity, and based on nanochannels built from layered two-dimensional nanomaterials possessing atomically smooth surfaces and exceptional mechanical properties. We explore operational modes of the nanoswitch and develop a theoretical framework to explain the phenomenon. By predicting the switching-reversibility phase diagram - based on material, interfacial and wetting properties, as well as the geometry of the nanofluidic circuit - we rationally design switchable nano-capsules capable of enclosing zeptoliter volumes of liquid, as small as the volumes enclosed in viruses. The nanoswitch will find useful application as an active element in integrated nanofluidic circuitry and could be used to explore nanoconfined chemistry and biochemistry, or be incorporated into shape-programmable materials.

Two-dimensional (2D) materials offer a prospect of membranes that combine negligible gas permeability with high proton conductivity and could outperform the existing proton exchange membranes used in various applications including fuel cells. Graphene oxide (GO), a well-known 2D material, facilitates rapid proton transport along its basal plane but proton conductivity across it remains unknown. It is also often presumed that individual GO monolayers contain a large density of nanoscale pinholes that lead to considerable gas leakage across the GO basal plane. Here we show that relatively large, micrometer-scale areas of monolayer GO are impermeable to gases, including helium, while exhibiting proton conductivity through the basal plane which is nearly two orders of magnitude higher than that of graphene. These findings provide insights into the key properties of GO and demonstrate that chemical functionalization of 2D crystals can be utilized to enhance their proton transparency without compromising gas impermeability.

Boundaries between structural twins of bilayer graphene (so-called AB/BA domain walls) are often discussed in terms of the formation of topologically protected valley-polarised chiral states. Here, we show that, depending on the width of the AB/BA boundary, the latter can also support non-chiral one-dimensional (1D) states that are confined to the domain wall at low energies and take the form of quasi-bound states at higher energies, where the 1D bands cross into the two-dimensional spectral continuum. We present the results of modeling of electronic properties of AB/BA domain walls with and without magnetic field as a function of their width and interlayer bias.

Insights into the fundamental properties of graphene's Dirac-Weyl fermions have emerged from studies of electron tunnelling transistors in which an atomically thin layer of hexagonal boron nitride (hBN) is sandwiched between two layers of high purity graphene. Here, we show that when a single defect is present within the hBN tunnel barrier, it can inject electrons into the graphene layers and its sharply defined energy level acts as a high resolution spectroscopic probe of electron-electron interactions in graphene. We report a magnetic field dependent suppression of the tunnel current flowing through a single defect below temperatures of $\sim$ 2 K. This is attributed to the formation of a magnetically-induced Coulomb gap in the spectral density of electrons tunnelling into graphene due to electron-electron interactions.

Defect-free graphene is impermeable to all atoms and ions at ambient conditions. Experiments that can resolve gas flows of a few atoms per hour through micrometre-sized membranes found that monocrystalline graphene is completely impermeable to helium, the smallest of atoms. Such membranes were also shown to be impermeable to all ions, including the smallest one, lithium. On the other hand, graphene was reported to be highly permeable to protons, nuclei of hydrogen atoms. There is no consensus, however, either on the mechanism behind the unexpectedly high proton permeability or even on whether it requires defects in graphene's crystal lattice. Here using high resolution scanning electrochemical cell microscopy (SECCM), we show that, although proton permeation through mechanically-exfoliated monolayers of graphene and hexagonal boron nitride cannot be attributed to any structural defects, nanoscale non-flatness of 2D membranes greatly facilitates proton transport. The spatial distribution of proton currents visualized by SECCM reveals marked inhomogeneities that are strongly correlated with nanoscale wrinkles and other features where strain is accumulated. Our results highlight nanoscale morphology as an important parameter enabling proton transport through 2D crystals, mostly considered and modelled as flat, and suggest that strain and curvature can be used as additional degrees of freedom to control the proton permeability of 2D materials.

Graphite is one of the most chemically inert materials. Its elementary constituent, monolayer graphene, is generally expected to inherit most of the parent material's properties including chemical inertness. Here we show that, unlike graphite, defect-free monolayer graphene exhibits a strong activity with respect to splitting molecular hydrogen, which is comparable to that of metallic and other known catalysts for this reaction. We attribute the unexpected catalytic activity to surface corrugations (nanoscale ripples), a conclusion supported by theory. Nanoripples are likely to play a role in other chemical reactions involving graphene and, because nanorippling is inherent to atomically thin crystals, can be important for two dimensional materials in general.

Periodic systems feature the Hofstadter butterfly spectrum produced by Brown--Zak minibands of electrons formed when magnetic field flux through the lattice unit cell is commensurate with flux quantum and manifested by magneto-transport oscillations. Quantum oscillations, such as Shubnikov -- de Haas effect and Aharonov--Bohm effect, are also characteristic for electronic systems with closed orbits in real space and reciprocal space. Here we show the intricate relation between these two phenomena by tracing quantum magneto-oscillations to Lifshitz transitions in graphene superlattices, where they persist even at relatively low fields and very much above liquid-helium temperatures. The oscillations originate from Aharonov--Bohm interference on cyclotron trajectories that form a kagom\'e-shaped network characteristic for Lifshitz transitions. In contrast to Shubnikov - de Haas oscillations, the kagom\'e oscillations are robust against thermal smearing and they can be detected even when the Hofstadter butterfly spectrum is undermined by electron's scattering. We expect that kagom\'e quantum oscillations are generic to rotationally-symmetric two-dimensional crystals close to Lifshitz transitions., Comment: 7+7 pages

The most recognizable feature of graphene's electronic spectrum is its Dirac point around which interesting phenomena tend to cluster. At low temperatures, the intrinsic behavior in this regime is often obscured by charge inhomogeneity but thermal excitations can overcome the disorder at elevated temperatures and create electron-hole plasma of Dirac fermions. The Dirac plasma has been found to exhibit unusual properties including quantum critical scattering and hydrodynamic flow. However, little is known about the plasma's behavior in magnetic fields. Here we report magnetotransport in this quantum-critical regime. In low fields, the plasma exhibits giant parabolic magnetoresistivity reaching >100% in 0.1 T even at room temperature. This is orders of magnitude higher than magnetoresistivity found in any other system at such temperatures. We show that this behavior is unique to monolayer graphene, being underpinned by its massless spectrum and ultrahigh mobility, despite frequent (Planckian-limit) scattering. With the onset of Landau quantization in a few T, where the electron-hole plasma resides entirely on the zeroth Landau level, giant linear magnetoresistivity emerges. It is nearly independent of temperature and can be suppressed by proximity screening, indicating a many-body origin. Clear parallels with magnetotransport in strange metals and so-called quantum linear magnetoresistance predicted for Weyl metals offer an interesting playground to further explore relevant physics using this well-defined quantum-critical 2D system., Comment: 8 pages, 3 figures

Van der Waals assembly enables exquisite design of electronic states in two-dimensional (2D) materials, often by superimposing a long-wavelength periodic potential on a crystal lattice using moir\'e superlattices. Here we show that electronic states in three-dimensional (3D) crystals such as graphite can also be tuned by the superlattice potential arising at the interface with another crystal, namely, crystallographically aligned hexagonal boron nitride. Such alignment is found to result in a multitude of Lifshitz transitions and Brown-Zak oscillations for near-surface 2D states whereas, in high magnetic fields, fractal states of Hofstadter's butterfly extend deep into graphite's bulk. Our work shows a venue to control 3D spectra by using the approach of 2D twistronics.

Recent experiments have shown that the out-of-plane dielectric constant of water confined in nanoslits of graphite and hexagonal boron nitride (hBN) is vanishingly small. Despite extensive effort based mainly on classical force-field molecular dynamics (FFMD) approaches, the origin of this phenomenon is under debate. Here we used ab initio molecular dynamics simulations (AIMD) and AIMD-trained machine learning potentials to explore the structure and electronic properties of water confined inside graphene and hBN slits. We found that the reduced dielectric constant arises mainly from the anti-parallel alignment of the water dipoles in the perpendicular direction to the surface in the first two water layers near the solid interface. Although the water molecules retain liquid-like mobility, the interfacial layers exhibit a net ferroelectric ordering and constrained hydrogen-bonding orientations which lead to much reduced polarization fluctuations in the out-of-plane direction at room temperature. Importantly, we show that this effect is independent of the distance between the two confining surfaces of the slit, and it originates in the spontaneous polarization of interfacial water. Our calculations also show no significant variations in the structure and polarization of water near graphene and hBN, despite their different electronic structures. These results are important as they offer new insight into a property of water that plays a critical role in the long-range interactions between surfaces, the electric double-layer formation, ion solvation and transport, as well as biomolecular functioning.

Recent experiments demonstrated that interfacial water dissociation (H2O = 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 photo-effect 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 photo-catalysis and designing reconfigurable materials.

Strong electric fields can accelerate molecular dissociation reactions. The phenomenon known as the Wien effect was previously observed using high-voltage electrolysis cells that produced fields of about 10^7 V m-1, sufficient to accelerate the dissociation of weakly bound molecules (e.g., organics and weak electrolytes). The observation of the Wien effect for the common case of water dissociation (H2O = H+ + OH-) has remained elusive. Here we study the dissociation of interfacial water adjacent to proton-permeable graphene electrodes and observe strong acceleration of the reaction in fields reaching above 10^8 V m-1. The use of graphene electrodes allow measuring the proton currents arising exclusively from the dissociation of interfacial water, while the electric field driving the reaction is monitored through the carrier density induced in graphene by the same field. The observed exponential increase in proton currents is in quantitative agreement with Onsager's theory. Our results also demonstrate that graphene electrodes can be valuable for the investigation of various interfacial phenomena involving proton transport.

Materials that are capable of extracting gold from complex sources, especially electronic waste (e-waste) with high efficiency are needed for gold resource sustainability and effective e-waste recycling. However, it remains challenging to achieve high extraction capacity to trace amount of gold, and precise selectivity to gold over a wide range of complex co-existing elements. Here we report a reduced graphene oxide (rGO) material that has an ultrahigh extraction capacity for trace amounts of gold (1,850 mg/g and 1,180 mg/g to 10 ppm and 1 ppm gold). The excellent gold extraction behavior is accounted to the graphene areas and oxidized regions of rGO. The graphene areas spontaneously reduce gold ions to metallic gold, and the oxidized regions provide a good dispersibility so that efficient adsorption and reduction of gold ions by the graphene area can be realized. The rGO is also highly selective to gold ions. By controlling the protonation process of the functional groups on the oxidized regions of rGO, it shows an exclusive gold extraction without adsorption of 14 co-existing elements seen in e-waste. These discoveries are further exploited in highly efficient, continuous gold recycling from e-waste with good scalability and economic viability, as exemplified by extracting gold from e-waste using a rGO membrane based flow-through process.

Nanoporous membranes based on two dimensional materials are predicted to provide highly selective gas transport in combination with extreme permeability. Here we investigate membranes made from multilayer graphdiyne, a graphene-like crystal with a larger unit cell. Despite being nearly a hundred of nanometers thick, the membranes allow fast, Knudsen-type permeation of light gases such as helium and hydrogen whereas heavy noble gases like xenon exhibit strongly suppressed flows. Using isotope and cryogenic temperature measurements, the seemingly conflicting characteristics are explained by a high density of straight-through holes (direct porosity of ~0.1%), in which heavy atoms are adsorbed on the walls, partially blocking Knudsen flows. Our work offers important insights into intricate transport mechanisms playing a role at nanoscale.

Van der Waals (vdW) heterostructures continue to attract intense interest as a route of designing materials with novel properties that cannot be found in naturally occurring materials. Unfortunately, this approach is currently limited to only a few layers that can be stacked on top of each other. Here we report a bulk material consisting of superconducting monolayers interlayered with monolayers displaying charge density waves (CDW). This bulk vdW heterostructure is created by phase transition of 1T-TaS2 to 6R at 800 {\deg}C in an inert atmosphere. Electron microscopy analysis directly shows the presence of alternating 1T and 1H monolayers within the resulting bulk 6R phase. Its superconducting transition (Tc) is found at 2.6 K, exceeding the Tc of the bulk 2H phase of TaS2. The superconducting temperature can be further increased to 3.6 K by exfoliating 6R-TaS2 and then restacking its layers. Using first-principles calculations, we argue that the coexistence of superconductivity and CDW within 6R-TaS2 stems from amalgamation of the properties of adjacent 1H and 1T monolayers, where the former dominates the superconducting state and the latter the CDW behavior.

Fine-tuned ion transport across nanoscale pores is key to many biological processes such as neurotransmission. Recent advances have enabled the confinement of water and ions to two dimensions, unveiling transport properties unreachable at larger scales and triggering hopes to reproduce the ionic machinery of biological systems. Here we report experiments demonstrating the emergence of memory in the transport of aqueous electrolytes across (sub)nanoscale channels. We unveiled two types of nanofluidic memristors, depending on channel material and confinement, with memory from minutes to hours. We explained how large timescales could emerge from interfacial processes like ionic self-assembly or surface adsorption. Such behavior allowed us to implement Hebbian learning with nanofluidic systems. This result lays the ground for biomimetic computations on aqueous electrolytic chips.

Optical device is a key component in our lives and organic liquid crystals are nowadays widely used to reduce human imprint. However, this technology still suffers from relatively high costs, toxicity and other environmental impacts, and cannot fully meet the demand of future sustainable society. Here we describe an alternative approach to colour-tuneable optical devices, which is based on sustainable inorganic liquid crystals derived from two-dimensional mineral materials abundant in nature. The prototypical two-dimensional mineral of vermiculite is massively produced by a green method, possessing size-to-thickness ratios of >103, in-plane magnetisation of >10 emu g-1, and an optical bandgap of >3 eV. These characteristics endow two-dimensional vermiculite with sensitive magneto-birefringence response, which is several orders of magnitude larger than organic counterparts, as well as capability of broad-spectrum modulation. Our finding consequently permits the fabrication of various chromic devices with low or even zero-energy consumption, which can be used for sustainable optics., Comment: 16 pages, 4 figures

Electrical resistance usually originates from lattice imperfections. However, even a perfect lattice has a fundamental resistance limit, given by the Landauer conductance caused by a finite number of propagating electron modes. This resistance, shown by Sharvin to appear at the contacts of electronic devices, sets the ultimate conductance limit of non-interacting electrons. Recent years have seen growing evidence of hydrodynamic electronic phenomena, prompting recent theories to ask whether an electronic fluid can radically break the fundamental Landauer-Sharvin limit. Here, we use single-electron transistor imaging of electronic flow in high-mobility graphene Corbino disk devices to answer this question. First, by imaging ballistic flows at liquid-helium temperatures, we observe a Landauer-Sharvin resistance that does not appear at the contacts but is instead distributed throughout the bulk. This underpins the phase-space origin of this resistance - as emerging from spatial gradients in the number of conduction modes. At elevated temperatures, by identifying and accounting for electron-phonon scattering, we reveal the details of the purely hydrodynamic flow. Strikingly, we find that electron hydrodynamics eliminates the bulk Landuer-Sharvin resistance. Finally, by imaging spiraling magneto-hydrodynamic Corbino flows, we reveal the key emergent length scale predicted by hydrodynamic theories - the Gurzhi length. These observations demonstrate that electronic fluids can dramatically transcend the fundamental limitations of ballistic electrons, with important implications for fundamental science and future technologies

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.

Twisted heterostructures of two-dimensional crystals offer almost unlimited scope for the design of novel metamaterials. Here we demonstrate a room-temperature ferroelectric semiconductor that is assembled using mono- or few- layer MoS2. These van der Waals heterostructures feature broken inversion symmetry, which, together with the asymmetry of atomic arrangement at the interface of two 2D crystals, enables ferroelectric domains with alternating out-of-plane polarisation arranged into a twist-controlled network. The latter can be moved by applying out-of-plane electrical fields, as visualized in situ using channelling contrast electron microscopy. The interfacial charge transfer for the observed ferroelectric domains is quantified using Kelvin probe force microscopy and agrees well with theoretical calculations. The movement of domain walls and their bending rigidity also agrees well with our modelling results. Furthermore, we demonstrate proof-of-principle field-effect transistors, where the channel resistance exhibits a pronounced hysteresis governed by pinning of ferroelectric domain walls. Our results show a potential venue towards room temperature electronic and optoelectronic semiconductor devices with built-in ferroelectric memory functions., Comment: 15 pages, 3 figures

Research on graphene is proving to have more lives than a cat, repeatedly coming back in new incarnations including graphene's recent alter ego, two-dimensional emptiness.

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

We demonstrate that spin-orbit coupling (SOC) strength for electrons near the conduction band edge in few-layer $\gamma$-InSe films can be tuned over a wide range. This tunability is the result of a competition between film-thickness-dependent intrinsic and electric-field-induced SOC, potentially, allowing for electrically switchable spintronic devices. Using a hybrid $\mathbf{k\cdot p}$ tight-binding model, fully parameterized with the help of density functional theory computations, we quantify SOC strength for various geometries of InSe-based field-effect transistors. The theoretically computed SOC strengths are compared with the results of weak antilocalization measurements on dual-gated multilayer InSe films, interpreted in terms of Dyakonov-Perel spin relaxation due to SOC, showing a good agreement between theory and experiment.

Superconductors with nontrivial band structure topology represent a class of materials with unconventional and potentially useful properties. Recent years have seen much success in creating artificial hybrid structures exhibiting main characteristics of two-dimensional (2D) topological superconductors. Yet, bulk materials known to combine inherent superconductivity with nontrivial topology remain scarce, largely because distinguishing their central characteristic -- topological surface states -- proved challenging due to a dominant contribution from the superconducting bulk. Reported here is a highly anomalous behaviour of surface superconductivity in topologically nontrivial 3D superconductor In2Bi where the surface states result from its nontrivial band structure, which itself is a consequence of the non-symmorphic crystal symmetry and strong spin-orbit coupling. In contrast to smoothly decreasing diamagnetic susceptibility above the bulk critical field Hc2, associated with surface superconductivity in conventional superconductors, we observe near-perfect, Meissner-like screening of low-frequency magnetic fields well above Hc2. The enhanced diamagnetism disappears at a new phase transition close to the critical field of surface superconductivity Hc3. Using theoretical modelling, we show that the anomalous screening is consistent with modification of surface superconductivity due to the presence of topological surface states. The demonstrated possibility to detect signatures of the surface states using macroscopic magnetization measurements provides an important new tool for discovery and identification of topological superconductors., Comment: 30 pages, 4 main figures, 11 supporting figures

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.

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., Comment: Main text: 14 pages, 4 figures. Methods and Supplementary information: 27 pages, 6 figures. Supplementary videos: 9

When two-dimensional crystals are brought into close proximity, their interaction results in strong reconstruction of electronic spectrum and local crystal structure. Such reconstruction strongly depends on the twist angle between the two crystals and has received growing attention due to new interesting electronic and optical properties that arise in graphene and transitional metal dichalcogenides. Similarly, novel and potentially useful properties are expected to appear in insulating crystals. Here we study two insulating crystals of hexagonal boron nitride (hBN) stacked at a small twist angle. Using electrostatic force microscopy, we observe ferroelectric-like domains arranged in triangular superlattices with a large surface potential that is independent on the size and orientation of the domains as well as the thickness of the twisted hBN crystals. The observation is attributed to interfacial elastic deformations that result in domains with a large density of out-of-plane polarized dipoles formed by pairs of boron and nitrogen atoms belonging to the opposite interfacial surfaces. This effectively creates a bilayer-thick ferroelectric with oppositely polarized (BN and NB) dipoles in neighbouring domains, in agreement with our modelling. The demonstrated electrostatic domains and their superlattices offer many new possibilities in designing novel van der Waals heterostructures.

In van der Waals heterostructures, electronic bands of two-dimensional (2D) materials, their nontrivial topology, and electron-electron interactions can be dramatically changed by a moire pattern induced by twist angles between different layers. Such process is referred to as twistronics, where the tuning of twist angle can be realized through mechanical manipulation of 2D materials. Here we demonstrate an experimental technique that can achieve in situ dynamical rotation and manipulation of 2D materials in van der Waals heterostructures. Using this technique we fabricated heterostructures where graphene is perfectly aligned with both top and bottom encapsulating layers of hexagonal boron nitride. Our technique enables twisted 2D material systems in one single stack with dynamically tunable optical, mechanical, and electronic properties.

The rectification of electromagnetic waves to direct currents is a crucial process for energy harvesting, beyond-5G wireless communications, ultra-fast science, and observational astronomy. As the radiation frequency is raised to the sub-terahertz (THz) domain, ac-to-dc conversion by conventional electronics becomes challenging and requires alternative rectification protocols. Here we address this challenge by tunnel field-effect transistors made of bilayer graphene (BLG). Taking advantage of BLG's electrically tunable band structure, we create a lateral tunnel junction and couple it to an antenna exposed to THz radiation. The incoming radiation is then down-converted by the tunnel junction nonlinearity, resulting in high-responsivity (> 4 kV/W) and low-noise (0.2 pW/$\sqrt{\mathrm{Hz}}$}) detection. We demonstrate how switching from intraband Ohmic to interband tunneling regime can raise detectors' responsivity by few orders of magnitude, in agreement with the developed theory. Our work demonstrates a potential application of tunnel transistors for THz detection and reveals BLG as a promising platform therefor.

Capillary condensation of water is ubiquitous in nature and technology. It routinely occurs in granular and porous media, can strongly alter such properties as adhesion, lubrication, friction and corrosion, and is important in many processes employed by microelectronics, pharmaceutical, food and other industries. The century-old Kelvin equation is commonly used to describe condensation phenomena and shown to hold well for liquid menisci with diameters as small as several nm. For even smaller capillaries that are involved in condensation under ambient humidity and, hence, of particular practical interest, the Kelvin equation is expected to break down, because the required confinement becomes comparable to the size of water molecules. Here we take advantage of van der Waals assembly of two-dimensional crystals to create atomic-scale capillaries and study condensation inside. Our smallest capillaries are less than 4 angstroms in height and can accommodate just a monolayer of water. Surprisingly, even at this scale, the macroscopic Kelvin equation using the characteristics of bulk water is found to describe accurately the condensation transition in strongly hydrophilic (mica) capillaries and remains qualitatively valid for weakly hydrophilic (graphene) ones. We show that this agreement is somewhat fortuitous and can be attributed to elastic deformation of capillary walls, which suppresses giant oscillatory behavior expected due to commensurability between atomic-scale confinement and water molecules. Our work provides a much-needed basis for understanding of capillary effects at the smallest possible scale important in many realistic situations.

One of the long sought-after goals in manipulation of light through light-matter interactions is the realization of magnetic-field-tuneable colouration, so-called magneto-chromatic effect, which holds great promise for optical, biochemical and medical applications due to its contactless and non-invasive nature. This goal can be achieved by magnetic-field controlled birefringence, where colours are produced by the interference between phase-retarded components of transmitted polarised light. Thus far birefringence-tuneable coloration has been demonstrated using electric field, material chirality and mechanical strain but magnetic field control remained elusive due to either weak magneto-optical response of transparent media or low transmittance to visible light of magnetically responsive media, such as ferrofluids. Here we demonstrate magnetically tuneable colouration of aqueous suspensions of two-dimensional cobalt-doped titanium oxide which exhibit an anomalously large magneto-birefringence effect. The colour of the suspensions can be tuned over more than two wavelength cycles in the visible range by moderate magnetic fields below 0.8 T. We show that such giant magneto-chromatic response is due to particularly large phase retardation (>3 pi) of the polarised light, which in its turn is a combined result of a large Cotton-Mouton coefficient (three orders of magnitude larger than for known liquid crystals), relatively high saturation birefringence (delta n = 2 x 10^-4) and high transparency of our suspensions to visible light. The work opens a new avenue to achieve tuneable colouration through engineered magnetic birefringence and can readily be extended to other magnetic 2D nanocrystals. The demonstrated effect can be used in a variety of magneto-optical applications, including magnetic field sensors, wavelength-tuneable optical filters and see-through printing., Comment: 10 pages, 4 figures. Nature Communications, 2020, Accepted

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., Comment: 16 pages, 13 figures

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., Comment: 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 ~1,000 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 8-carbon-atom rings. The latter pose approximately twice lower energy barriers for incoming protons compared to the 6-atom rings of graphene and a relatively low barrier of ~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.

Understanding and tuning correlated states is of great interest and significance to modern condensed matter physics. The recent discovery of unconventional superconductivity and Mott-like insulating states in magic-angle twisted bilayer graphene (tBLG) presents a unique platform to study correlation phenomena, in which the Coulomb energy dominates over the quenched kinetic energy as a result of hybridized flat bands. Extending this approach to the case of twisted multilayer graphene would allow even higher control over the band structure because of the reduced symmetry of the system. Here, we study electronic transport properties in twisted trilayer graphene (tTLG, bilayer on top of monolayer graphene heterostructure). We observed the formation of van Hove singularities which are highly tunable by twist angle and displacement field and can cause strong correlation effects under optimum conditions, including superconducting states. We provide basic theoretical interpretation of the observed electronic structure., Comment: 16 pages, 9 figures

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

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

Despite being only one-atom thick, defect-free graphene is considered to be completely impermeable to all gases and liquids. This conclusion is based on theory and supported by experiments that could not detect gas permeation through micrometre-size membranes within a detection limit of 10^5 to 10^6 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 could discern permeation of just a few helium atoms per hour, and this detection limit is also valid for all other tested gases (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. The 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 transport. 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.

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., Comment: 16 pages, 7 figures

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., Comment: 18 pages, 12 figures

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 narrow bands in graphene bilayers twisted at 2 degrees. 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 valley splitting and allows selective focusing for different valleys, which is of interest for using this degree of freedom in frequently-discussed valleytronics.

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 high-temperature 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 visualise 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.

The field of nanofluidics has shown considerable progress over the past decade thanks to key instrumental advances, leading to the discovery of a number of exotic transport phenomena for fluids and ions under extreme confinement. Recently, van der Waals assembly of 2D materials allowed fabrication of artificial channels with angstr\"om-scale precision. This ultimate confinement to the true molecular scale revealed unforeseen behaviour for both mass and ionic transport. In this work, we explore pressure-driven streaming in such molecular-size slits and report a new electro-hydrodynamic effect under coupled pressure and electric force. It takes the form of a transistor-like response of the pressure induced ionic streaming: an applied bias of a fraction of a volt results in an enhancement of the streaming mobility by up to 20 times. The gating effect is observed with both graphite and boron nitride channels but exhibits marked material-dependent features. Our observations are rationalized by a theoretical framework for the flow dynamics, including the frictional interaction of water, ions and the confining surfaces as a key ingredient. The material dependence of the voltage modulation can be traced back to a contrasting molecular friction on graphene and boron nitride. The highly nonlinear transport under molecular-scale confinement offers new routes to actively control molecular and ion transport and design elementary building blocks for artificial ionic machinery, such as ion pumps. Furthermore, it provides a versatile platform to explore electro-mechanical couplings potentially at play in recently discovered mechanosensitive ionic channels.