One-dimensional proximity superconductivity in the quantum Hall regime.

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 states1-6. This interest has been motivated by prospects of finding new physics, including topologically protected quasiparticles7-9, but also extends into metrology and device applications10-13. So far it has proven challenging to achieve detectable supercurrents through quantum Hall conductors2,3,6. Here we show that domain walls in minimally twisted bilayer graphene14-18 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.

Origin of dielectric polarization suppression in confined water from first principles.

It has long been known that the dielectric constant of confined water should be different from that in bulk. Recent experiments have shown that it is vanishingly small, however the origin of the phenomenon remains unclear. Here we used ab initio molecular dynamics simulations (AIMD) and AIMD-trained machine-learning potentials to understand water's structure and electronic properties underpinning this effect. For the graphene and hexagonal boron-nitride substrates considered, we find that it originates in the spontaneous anti-parallel alignment of the water dipoles in the first two water layers near the solid interface. The interfacial layers exhibit net ferroelectric ordering, resulting in an overall anti-ferroelectric arrangement of confined water. Together with constrained hydrogen-bonding orientations, this leads to much reduced out-of-plane polarization. Furthermore, we directly contrast AIMD and simple classical force-field simulations, revealing important differences. This work offers insight into a property of water that is critical in modulating surface forces, the electric-double-layer formation and molecular solvation, and shows a way to compute it.

Proton and molecular permeation through the basal plane of monolayer graphene oxide.

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.

Proton transport through nanoscale corrugations in two-dimensional crystals.

Defect-free graphene is impermeable to all atoms1-5 and ions6,7 under 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 atom2,5. Such membranes were also shown to be impermeable to all ions, including the smallest one, lithium6,7. By contrast, graphene was reported to be highly permeable to protons, nuclei of hydrogen atoms8,9. There is no consensus, however, either on the mechanism behind the unexpectedly high proton permeability10-14 or even on whether it requires defects in graphene's crystal lattice6,8,15-17. Here, using high-resolution scanning electrochemical cell microscopy, 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 two-dimensional membranes greatly facilitates proton transport. The spatial distribution of proton currents visualized by scanning electrochemical cell microscopy 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 two-dimensional crystals, mostly considered and modelled as flat, and indicate that strain and curvature can be used as additional degrees of freedom to control the proton permeability of two-dimensional materials.

Mixing of moiré-surface and bulk states in graphite.

Van der Waals assembly enables the design of electronic states in two-dimensional (2D) materials, often by superimposing a long-wavelength periodic potential on a crystal lattice using moiré superlattices1-9. This twistronics approach has resulted in numerous previously undescribed physics, including strong correlations and superconductivity in twisted bilayer graphene10-12, resonant excitons, charge ordering and Wigner crystallization in transition-metal chalcogenide moiré structures13-18 and Hofstadter's butterfly spectra and Brown-Zak quantum oscillations in graphene superlattices19-22. Moreover, twistronics has been used to modify near-surface states at the interface between van der Waals crystals23,24. Here we show that electronic states in three-dimensional (3D) crystals such as graphite can be tuned by a superlattice potential occurring at the interface with another crystal-namely, crystallographically aligned hexagonal boron nitride. This alignment results in several Lifshitz transitions and Brown-Zak oscillations arising from near-surface states, whereas, in high magnetic fields, fractal states of Hofstadter's butterfly draw deep into the bulk of graphite. Our work shows a way in which 3D spectra can be controlled using the approach of 2D twistronics.

Giant magnetoresistance of Dirac plasma in high-mobility graphene.

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 behaviour in this regime is often obscured by charge inhomogeneity1,2 but thermal excitations can overcome the disorder at elevated temperatures and create an electron-hole plasma of Dirac fermions. The Dirac plasma has been found to exhibit unusual properties, including quantum-critical scattering3-5 and hydrodynamic flow6-8. However, little is known about the plasma's behaviour in magnetic fields. Here we report magnetotransport in this quantum-critical regime. In low fields, the plasma exhibits giant parabolic magnetoresistivity reaching more than 100 per cent in a magnetic field of 0.1 tesla at room temperature. This is orders-of-magnitude higher than magnetoresistivity found in any other system at such temperatures. We show that this behaviour is unique to monolayer graphene, being underpinned by its massless spectrum and ultrahigh mobility, despite frequent (Planckian limit) scattering3-5,9-14. With the onset of Landau quantization in a magnetic field of a few tesla, 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 screening15, indicating a many-body origin. Clear parallels with magnetotransport in strange metals12-14 and so-called quantum linear magnetoresistance predicted for Weyl metals16 offer an interesting opportunity to further explore relevant physics using this well defined quantum-critical two-dimensional system.

Unexpected catalytic activity of nanorippled graphene.

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 (2D) materials in general.

Long-term memory and synapse-like dynamics in two-dimensional nanofluidic channels.

Fine-tuned ion transport across nanoscale pores is key to many biological processes, including neurotransmission. Recent advances have enabled the confinement of water and ions to two dimensions, unveiling transport properties inaccessible at larger scales and triggering hopes of reproducing 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 unveil two types of nanofluidic memristors depending on channel material and confinement, with memory ranging from minutes to hours. We explain how large time scales could emerge from interfacial processes such as ionic self-assembly or surface adsorption. Such behavior allowed us to implement Hebbian learning with nanofluidic systems. This result lays the foundation for biomimetic computations on aqueous electrolytic chips.

Wien effect in interfacial water dissociation through proton-permeable graphene electrodes.

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 107 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 [Formula: see text] 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 108 V m-1. The use of graphene electrodes allows 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.

Imaging hydrodynamic electrons flowing without Landauer-Sharvin resistance.

Electrical resistance usually originates from lattice imperfections. However, even a perfect lattice has a fundamental resistance limit, given by the Landauer1 conductance caused by a finite number of propagating electron modes. This resistance, shown by Sharvin2 to appear at the contacts of electronic devices, sets the ultimate conduction limit of non-interacting electrons. Recent years have seen growing evidence of hydrodynamic electronic phenomena3-18, prompting recent theories19,20 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 show the details of the purely hydrodynamic flow. Strikingly, we find that electron hydrodynamics eliminates the bulk Landauer-Sharvin resistance. Finally, by imaging spiralling magneto-hydrodynamic Corbino flows, we show 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.

Highly efficient and selective extraction of gold by reduced graphene oxide.

Materials capable of extracting gold from complex sources, especially electronic waste (e-waste), are needed for gold resource sustainability and effective e-waste recycling. However, it remains challenging to achieve high extraction capacity and precise selectivity if only a trace amount of gold is present along with other metallic elements . Here we report an approach based on reduced graphene oxide (rGO) which provides an ultrahigh capacity and selective extraction of gold ions present in ppm concentrations (>1000 mg of gold per gram of rGO at 1 ppm). The excellent gold extraction performance 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 allow good dispersibility of the rGO material so that efficient adsorption and reduction of gold ions at the graphene areas can be realized. By controlling the protonation of the oxidized regions of rGO, gold can be extracted exclusively, without contamination by the other 14 co-existing elements typically present in e-waste. These findings are further exploited to demonstrate recycling gold from real-world e-waste with good scalability and economic viability, as exemplified by using rGO membranes in a continuous flow-through process.

Interfacial ferroelectricity in marginally twisted 2D semiconductors.

Twisted heterostructures of two-dimensional crystals offer almost unlimited scope for the design of new 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 polarization arranged into a twist-controlled network. The last can be moved by applying out-of-plane electrical fields, as visualized in situ using channelling contrast electron microscopy. The observed interfacial charge transfer, movement of domain walls and their bending rigidity agree well with theoretical calculations. 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 avenue towards room temperature electronic and optoelectronic semiconductor devices with built-in ferroelectric memory functions.

Out-of-equilibrium criticalities in graphene superlattices.

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 that resemble 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 to all graphene-based superlattices.

Exponentially selective molecular sieving through angstrom pores.

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.

Graphene's non-equilibrium fermions reveal Doppler-shifted magnetophonon resonances accompanied by Mach supersonic and Landau velocity effects.

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.

Long-range nontopological edge currents in charge-neutral graphene.

Van der Waals heterostructures display numerous unique electronic properties. Nonlocal measurements, wherein a voltage is measured at contacts placed far away from the expected classical flow of charge carriers, have been widely used in the search for novel transport mechanisms, including dissipationless spin and valley transport1-9, topological charge-neutral currents10-12, hydrodynamic flows13 and helical edge modes14-16. Monolayer1-5,10,15-19, bilayer9,11,14,20 and few-layer21 graphene, transition-metal dichalcogenides6,7 and moiré superlattices8,10,12 have been found to display pronounced nonlocal effects. However, the origin of these effects is hotly debated3,11,17,22-24. Graphene, in particular, exhibits giant nonlocality at charge neutrality1,15-19, a striking behaviour that has attracted competing explanations. Using a superconducting quantum interference device on a tip (SQUID-on-tip) for nanoscale thermal and scanning gate imaging25, here we demonstrate that the commonly occurring charge accumulation at graphene edges23,26-31 leads to giant nonlocality, producing narrow conductive channels that support long-range currents. Unexpectedly, although the edge conductance has little effect 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 at charge neutrality and away from it produces exotic flow patterns that are sensitive to edge disorder, in which charges can flow against the global electric field. The observed one-dimensional edge transport is generic and nontopological and is expected to support nonlocal transport in many electronic systems, offering insight into the numerous controversies and linking them to long-range guided electronic states at system edges.

Charge-polarized interfacial superlattices in marginally twisted hexagonal boron nitride.

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.

Tunnel field-effect transistors for sensitive terahertz detection.

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/[Formula: see text]) 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 under atomic-scale confinement.

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 used by microelectronics, pharmaceutical, food and other industries1-4. The century-old Kelvin equation5 is frequently used to describe condensation phenomena and has been shown to hold well for liquid menisci with diameters as small as several nanometres1-4,6-14. For even smaller capillaries that are involved in condensation under ambient humidity and so of particular practical interest, the Kelvin equation is expected to break down because the required confinement becomes comparable to the size of water molecules1-22. Here we use van der Waals assembly of two-dimensional crystals to create atomic-scale capillaries and study condensation within them. Our smallest capillaries are less than four ångströms in height and can accommodate just a monolayer of water. Surprisingly, even at this scale, we find that the macroscopic Kelvin equation using the characteristics of bulk water describes the condensation transition accurately in strongly hydrophilic (mica) capillaries and remains qualitatively valid for weakly hydrophilic (graphite) ones. We show that this agreement is fortuitous and can be attributed to elastic deformation of capillary walls23-25, which suppresses the giant oscillatory behaviour expected from the commensurability between the atomic-scale capillaries and water molecules20,21. Our work provides a basis for an improved understanding of capillary effects at the smallest scale possible, which is important in many realistic situations.

Long-range ballistic transport of Brown-Zak fermions in graphene superlattices.

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 106 cm2 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 1 K. 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.