Showing papers by "Andre K. Geim published in 2020"

Limits on gas impermeability of graphene

Abstract: 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. Graphene is shown to be impermeable to helium and several other gases, except for hydrogen, which is attributed to the strong catalytic activity of ripples in the graphene sheet.

Evidence of flat bands and correlated states in buckled graphene superlattices

Abstract: Two-dimensional atomic crystals can radically change their properties in response to external influences, such as substrate orientation or strain, forming materials with novel electronic structure1–5. An example is the creation of weakly dispersive, ‘flat’ bands in bilayer graphene for certain ‘magic’ angles of twist between the orientations of the two layers6. 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 very accurate fine-tuning required to obtain the magic angle 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 tunnelling 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 transition7–9, resulting in a periodically modulated pseudo-magnetic field10–14, which in turn creates a ‘post-graphene’ material with flat electronic bands. When we introduce the Fermi level into these flat bands using electrostatic doping, we observe a pseudogap-like depletion in the density of states, which signals the emergence of a correlated state15–17. This buckling of two-dimensional crystals offers a strategy for creating other superlattice systems and, in particular, for exploring interaction phenomena characteristic of flat bands. Buckled monolayer graphene superlattices are found to provide an alternative to twisted bilayer graphene for the study of flat bands and correlated states in a carbon-based material.

Capillary condensation under atomic-scale confinement

Abstract: 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 angstroms 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. In the tiniest of capillaries, barely larger than a water molecule, condensation is surprisingly predictable from the macroscopic Kelvin condensation equation, a coincidence partially owing to elastic deformation of the capillary walls.

Electronic phase separation in multilayer rhombohedral graphite

Abstract: Of the two stable forms of graphite, hexagonal and rhombohedral, the former is more common and has been studied extensively. The latter is less stable, which has so far precluded its detailed investigation, despite many theoretical predictions about the abundance of exotic interaction-induced physics1–6. Advances in van der Waals heterostructure technology7 have now allowed us to make high-quality rhombohedral graphite films up to 50 graphene layers thick and study their transport properties. Here we show that the bulk electronic states in such rhombohedral graphite are gapped8 and, at low temperatures, electron transport is dominated by surface states. Because of their proposed topological nature, the surface states are of sufficiently high quality to observe the quantum Hall effect, whereby rhombohedral graphite exhibits phase transitions between a gapless semimetallic phase and a gapped quantum spin Hall phase with giant Berry curvature. We find that an energy gap can also be opened in the surface states by breaking their inversion symmetry by applying a perpendicular electric field. Moreover, in rhombohedral graphite thinner than four nanometres, 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. High-quality rhombohedral graphite films are found to offer an alternative to twisted bilayer graphene as a platform for studying correlated physics in carbon materials.

Charge-polarized interfacial superlattices in marginally twisted hexagonal boron nitride

Abstract: 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.

Viscous electron fluids

Abstract: Advances in materials science have made it possible for electrons in metals to exhibit exotic hydrodynamic effects.

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

Abstract: 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.

Proton and Li-Ion Permeation through Graphene with Eight-Atom-Ring Defects.

Abstract: 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 ∼1000 times higher than that of defect-free graphene. Lithium ions can also permeate through such disordered graphene. The enhanced proton and ion permeability is attributed to a high density of eight-carbon-atom rings. The latter pose approximately twice lower energy barriers for incoming protons compared to that of the six-atom rings of graphene and a relatively low barrier of ∼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.

Tunable van Hove Singularities and Correlated States in Twisted Trilayer Graphene

Abstract: 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.

Blue Energy Conversion from Holey-Graphene-like Membranes with a High Density of Subnanometer Pores.

Abstract: Blue energy converts the chemical potential difference from salinity gradients into electricity via reverse electrodialysis and provides a renewable source of clean energy. To achieve high energy c...

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

Abstract: 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.

In situ manipulation of van der Waals heterostructures for twistronics

Abstract: In van der Waals heterostructures, electronic bands of two-dimensional (2D) materials, their nontrivial topology, and electron-electron interactions can be markedly changed by a moire pattern induced by twist angles between different layers. This 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.

Tunnel field-effect transistors for sensitive terahertz detection

Abstract: 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.

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

Abstract: 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. Materials with tunable transmitted colours are sought after for a range of applications. The authors here present magnetic-field-controlled color tuning in a transparent suspension of 2D crystals with unusually large magneto-birefringence.

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

Abstract: 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

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

Abstract: 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. Here, the authors show that Brown-Zak fermions in graphene-on-boron-nitride superlattices exhibit mobilities above 106 cm2/V s and micrometer scale ballistic transport.

Electron Tunneling through Boron Nitride Confirms Marcus-Hush Theory Predictions for Ultramicroelectrodes.

Abstract: Marcus–Hush theory of electron transfer is one of the pillars of modern electrochemistry with a large body of supporting experimental evidence presented to date. However, some predictions, such as the electrochemical behavior at disk ultramicroelectrodes, remain unverified. Herein, we present a study of electron tunneling across a hexagonal boron nitride acting as a barrier between a graphite electrode and redox mediators in a liquid solution. This was achieved by the fabrication of disk ultramicroelectrodes with a typical diameter of 5 μm. Analysis of voltammetric measurements, using two common outer-sphere redox mediators, yielded several electrochemical parameters, including the electron transfer rate constant, limiting current, and transfer coefficient. They depart significantly from the Butler–Volmer kinetics and instead show behavior previously predicted by the Marcus–Hush theory of electron transfer. In addition, our system provides a noteworthy experimental platform, which could be applied to addr...

Minibands in twisted bilayer graphene probed by magnetic focusing.

Abstract: 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.

Giant magneto-birefringence effect and tuneable colouration of 2D crystals' suspensions

Abstract: 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.

Capillary condensation under atomic-scale confinement

Abstract: 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.

Evidence of Flat Bands and Correlated States in Buckled Graphene Superlattices

Abstract: 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.

Tunable van Hove Singularities and Correlated States in Twisted Trilayer Graphene

Abstract: 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.

Separation of water by pervaporation using a membrane

Abstract: This invention relates to uses of graphene oxide, and in particular graphene oxide on a porous support, and a membrane comprising these materials. This invention also relates to methods of dehydration, which include vapour phase separation and pervaporation. Pervaporation is a method of separating mixtures of liquids using a membrane. Pervaporation consists of two basic steps: permeation of the permeate through the membrane and evaporation of the permeate from the other side of the membrane. Pervaporation is a mild which can be used to separate components which would not survive the comparatively harsh conditions needed for distillation (high temp, and/or low pressure).