Control of proton transport and hydrogenation in double-gated graphene.

The basal plane of graphene can function as a selective barrier that is permeable to protons1,2 but impermeable to all ions3,4 and gases5,6, stimulating its use in applications such as membranes1,2,7,8, catalysis9,10 and isotope separation11,12. Protons can chemically adsorb on graphene and hydrogenate it13,14, inducing a conductor-insulator transition that has been explored intensively in graphene electronic devices13-17. However, both processes face energy barriers1,12,18 and various strategies have been proposed to accelerate proton transport, for example by introducing vacancies4,7,8, incorporating catalytic metals1,19 or chemically functionalizing the lattice18,20. But these techniques can compromise other properties, such as ion selectivity21,22 or mechanical stability23. Here we show that independent control of the electric field, E, at around 1 V nm-1, and charge-carrier density, n, at around 1 × 1014 cm-2, in double-gated graphene allows the decoupling of proton transport from lattice hydrogenation and can thereby accelerate proton transport such that it approaches the limiting electrolyte current for our devices. Proton transport and hydrogenation can be driven selectively with precision and robustness, enabling proton-based logic and memory graphene devices that have on-off ratios spanning orders of magnitude. Our results show that field effects can accelerate and decouple electrochemical processes in double-gated 2D crystals and demonstrate the possibility of mapping such processes as a function of E and n, which is a new technique for the study of 2D electrode-electrolyte interfaces.

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.

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.

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.

Hypoxia stimulates angiogenesis and a metabolic switch in human parathyroid adenoma cells.

Hypoxia, a primary stimulus for angiogenesis, is important for tumour proliferation and survival. The effects of hypoxia on parathyroid tumour cells, which may also be important for parathyroid autotransplantation in patients, are, however, unknown. We, therefore, assessed the effects of hypoxia on gene expression in parathyroid adenoma (PA) cells from patients with primary hyperparathyroidism. Cell suspensions from human PAs were cultured under normoxic or hypoxic conditions and then subjected to cDNA expression analysis. In total, 549 genes were significantly upregulated and 873 significantly downregulated. The most highly upregulated genes (carbonic anhydrase 9 (CA9), Solute carrier family 2A1 (SLC2A1) and hypoxia-inducible lipid droplet-associated protein (HIG2)) had known involvement in hypoxia responses. Dysregulation of oxidative phosphorylation and glycolysis pathway genes were also observed, consistent with data indicating that cells shift metabolic strategy of ATP production in hypoxic conditions and that tumour cells predominantly utilise anaerobic glycolysis for energy production. Proliferation- and angiogenesis-associated genes linked with growth factor signalling, such as mitogen-activated protein kinase kinase 1 (MAP2K1), Jun proto-oncogene (JUN) and ETS proto-oncogene 1 (ETS1), were increased, however, Ras association domain family member 1 (RASSF1), an inhibitor of proliferation was also upregulated, indicating these pathways are unlikely to be biased towards proliferation. Overall, there appeared to be a shift in growth factor signalling pathways from Jak-Stat and Ras signaling to extracellular signal-regulated kinases (ERKs) and hypoxia-inducible factor (HIF)-1α signalling. Thus, our data demonstrate that PAs, under hypoxic conditions, promote the expression of genes known to stimulate angiogenesis, as well as undergoing a metabolic switch.

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.

Giant magneto-birefringence effect and tuneable colouration of 2D crystal suspensions.

One of the long-sought-after goals in light manipulation is tuning of transmitted interference colours. Previous approaches toward this goal include material chirality, strain and electric-field controls. Alternatively, colour control by magnetic field offers contactless, non-invasive and energy-free advantages but has remained elusive due to feeble magneto-birefringence in conventional transparent media. Here we demonstrate an anomalously large magneto-birefringence effect in transparent suspensions of magnetic two-dimensional crystals, which arises from a combination of a large Cotton-Mouton coefficient and relatively high magnetic saturation birefringence. The effect is orders of magnitude stronger than those previously demonstrated for transparent materials. The transmitted colours of the suspension can be continuously tuned over two-wavelength cycles by moderate magnetic fields below 0.8 T. The work opens a new avenue to tune transmitted colours, and can be further extended to other systems with artificially engineered magnetic birefringence.

Publisher Correction: Control of electron-electron interaction in graphene by proximity screening.

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

Minibands in twisted bilayer graphene probed by magnetic focusing.

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.

Control of electron-electron interaction in graphene by proximity screenings.

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.

Limits on gas impermeability of graphene.

Despite being only one-atom thick, defect-free graphene is considered to be completely impermeable to all gases and liquids1-10. This conclusion is based on theory3-8 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.

Giant oscillations in a triangular network of one-dimensional states in marginally twisted graphene.

At very small twist angles of ∼0.1°, bilayer graphene exhibits a strain-accompanied lattice reconstruction that results in submicron-size triangular domains with the standard, Bernal stacking. If the interlayer bias is applied to open an energy gap inside the domain regions making them insulating, such marginally twisted bilayer graphene is expected to remain conductive due to a triangular network of chiral one-dimensional states hosted by domain boundaries. Here we study electron transport through this helical network and report giant Aharonov-Bohm oscillations that reach in amplitude up to 50% of resistivity and persist to temperatures above 100 K. At liquid helium temperatures, the network 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 narrow minibands formed by the network of one-dimensional states inside the gap.

Measuring Hall viscosity of graphene's electron fluid.

An electrical conductor subjected to a magnetic field exhibits the Hall effect in the presence of current flow. Here, we report a qualitative deviation from the standard behavior in electron systems with high viscosity. We found that the viscous electron fluid in graphene responds to nonquantizing magnetic fields by producing an electric field opposite to that generated by the ordinary Hall effect. The viscous contribution is substantial and identified by studying local voltages that arise in the vicinity of current-injecting contacts. We analyzed the anomaly over a wide range of temperatures and carrier densities and extracted the Hall viscosity, a dissipationless transport coefficient that was long identified theoretically but remained elusive in experiments.

Ballistic molecular transport through two-dimensional channels.

Gas permeation through nanoscale pores is ubiquitous in nature and has an important role in many technologies1,2. Because the pore size is typically smaller than the mean free path of gas molecules, the flow of the gas molecules is conventionally described by Knudsen theory, which assumes diffuse reflection (random-angle scattering) at confining walls3-7. This assumption holds surprisingly well in experiments, with only a few cases of partially specular (mirror-like) reflection known5,8-11. Here we report gas transport through ångström-scale channels with atomically flat walls12,13 and show that surface scattering can be either diffuse or specular, depending on the fine details of the atomic landscape of the surface, and that quantum effects contribute to the specularity at room temperature. The channels, made from graphene or boron nitride, allow helium gas flow that is orders of magnitude faster than expected from theory. This is explained by specular surface scattering, which leads to ballistic transport and frictionless gas flow. Similar channels, but with molybdenum disulfide walls, exhibit much slower permeation that remains well described by Knudsen diffusion. We attribute the difference to the larger atomic corrugations at molybdenum disulfide surfaces, which are similar in height to the size of the atoms being transported and their de Broglie wavelength. The importance of this matter-wave contribution is corroborated by the observation of a reversed isotope effect, whereby the mass flow of hydrogen is notably higher than that of deuterium, in contrast to the relation expected for classical flows. Our results provide insights into the atomistic details of molecular permeation, which previously could be accessed only in simulations10,14, and demonstrate the possibility of studying gas transport under controlled confinement comparable in size to the quantum-mechanical size of atoms.

Transport of hydrogen isotopes through interlayer spacing in van der Waals crystals.

Atoms start behaving as waves rather than classical particles if confined in spaces commensurate with their de Broglie wavelength. At room temperature this length is only about one ångström even for the lightest atom, hydrogen. This restricts quantum-confinement phenomena for atomic species to the realm of very low temperatures1-5. Here, we show that van der Waals gaps between atomic planes of layered crystals provide ångström-size channels that make quantum confinement of protons apparent even at room temperature. Our transport measurements show that thermal protons experience a notably higher barrier than deuterons when entering van der Waals gaps in hexagonal boron nitride and molybdenum disulfide. This is attributed to the difference in the de Broglie wavelengths of the isotopes. Once inside the crystals, transport of both isotopes can be described by classical diffusion, albeit with unexpectedly fast rates comparable to that of protons in water. The demonstrated ångström-size channels can be exploited for further studies of atomistic quantum confinement and, if the technology can be scaled up, for sieving hydrogen isotopes.

Unusual Suppression of the Superconducting Energy Gap and Critical Temperature in Atomically Thin NbSe2.

It is well-known that superconductivity in thin films is generally suppressed with decreasing thickness. This suppression is normally governed by either disorder-induced localization of Cooper pairs, weakening of Coulomb screening, or generation and unbinding of vortex-antivortex pairs as described by the Berezinskii-Kosterlitz-Thouless (BKT) theory. Defying general expectations, few-layer NbSe2, an archetypal example of ultrathin superconductors, has been found to remain superconducting down to monolayer thickness. Here, we report measurements of both the superconducting energy gap Δ and critical temperature TC in high-quality monocrystals of few-layer NbSe2, using planar-junction tunneling spectroscopy and lateral transport. We observe a fully developed gap that rapidly reduces for devices with the number of layers N ≤ 5, as does their TC. We show that the observed reduction cannot be explained by disorder, and the BKT mechanism is also excluded by measuring its transition temperature that for all N remains very close to TC. We attribute the observed behavior to changes in the electronic band structure predicted for mono- and bi- layer NbSe2 combined with inevitable suppression of the Cooper pair density at the superconductor-vacuum interface. Our experimental results for N > 2 are in good agreement with the dependences of Δ and TC expected in the latter case while the effect of band-structure reconstruction is evidenced by a stronger suppression of Δ and the disappearance of its anisotropy for N = 2. The spatial scale involved in the surface suppression of the density of states is only a few angstroms but cannot be ignored for atomically thin superconductors.

High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices.

Cyclotron motion of charge carriers in metals and semiconductors leads to Landau quantization and magneto-oscillatory behavior in their properties. Cryogenic temperatures are usually required to observe these oscillations. We show that graphene superlattices support a different type of quantum oscillation that does not rely on Landau quantization. The oscillations are extremely robust and persist well above room temperature in magnetic fields of only a few tesla. We attribute this phenomenon to repetitive changes in the electronic structure of superlattices such that charge carriers experience effectively no magnetic field at simple fractions of the flux quantum per superlattice unit cell. Our work hints at unexplored physics in Hofstadter butterfly systems at high temperatures.