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.

Kagome Quantum Oscillations in Graphene Superlattices

Electronic spectra of solids subjected to a magnetic field are often discussed in terms of Landau levels and Hofstadter-butterfly-style Brown-Zak minibands manifested by magneto-oscillations in two-dimensional electron systems. Here, we present the semiclassical precursors of these quantum magneto-oscillations which appear in graphene superlattices at low magnetic field near the Lifshitz transitions and persist at elevated temperatures. These oscillations originate from Aharonov-Bohm interference of electron waves following open trajectories that belong to a kagome-shaped network of paths characteristic for Lifshitz transitions in the moire superlattice minibands of twistronic graphenes.

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.

Elastocapillarity-driven 2D nano-switches enable zeptoliter-scale liquid encapsulation

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.

Angstrom-Scale Electrochemistry at Electrodes with Dimensions Commensurable and Smaller than Individual Reacting Species

In nature and technologies, many chemical reactions occur at interfaces with dimensions approaching that of a single reacting species in nano- and angstrom-scale. Mechanisms governing reactions at this ultimately small spatial regime remain poorly explored because of challenges to controllably fabricate required devices and assess their performance in experiment. Here we report how efficiency of electrochemical reactions evolves for electrodes that range from just one atom in thickness to sizes comparable with and exceeding hydration diameters of reactant species. The electrodes are made by encapsulating graphene and its multilayers within insulating crystals so that only graphene edges remain exposed and partake in reactions. We find that limiting current densities characterizing electrochemical reactions exhibit a pronounced size effect if reactant's hydration diameter becomes commensurable with electrodes' thickness. An unexpected blockade effect is further revealed from electrodes smaller than reactants, where incoming reactants are blocked by those adsorbed temporarily at the atomically narrow interfaces. The demonstrated angstrom-scale electrochemistry offers a venue for studies of interfacial behaviors at the true molecular scale.

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.

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.

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.

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.

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.

Photoaccelerated Water Dissociation Across One-Atom-Thick Electrodes

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 photoeffect is attributed to the combination of graphene's perfect selectivity with respect to protons, which prevents proton-hydroxide recombination, and to proton transport acceleration by the Wien effect, which occurs in synchrony with the water dissociation reaction. Our findings provide fundamental insights into ion dynamics near atomically thin proton-selective interfaces and suggest that strong interfacial fields can enhance and tune very fast ionic processes, which is of relevance for applications in photocatalysis and designing reconfigurable materials.

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 phenomena^3-18, prompting recent theories^19,20 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.

Alternating Superconducting and Charge Density Wave Monolayers within Bulk 6R-TaS2

Van der Waals (vdW) heterostructures continue to attract intense interest as a route of designing materials with novel properties that cannot be found in nature. 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 vdW material consisting of superconducting 1H TaS₂ monolayers interlayered with 1T TaS₂ monolayers displaying charge density waves (CDW). This bulk vdW heterostructure is created by phase transition of 1T-TaS₂ to 6R at 800 °C in an inert atmosphere. Its superconducting transition (T_c) is found at 2.6 K, exceeding the T_c of the bulk 2H phase. 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.

Gas permeation through graphdiyne-based nanoporous membranes

Nanoporous membranes based on two dimensional materials are predicted to provide highly selective gas transport in combination with extreme permeance. 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.

2D nanoporous membranes are predicted to provide highly selective gas transport in combination with extreme permeance. Here authors demonstrate gas separation performance and transport mechanisms through membranes of graphdiyne, a quasi 2D material with a graphene-like structure.

2D Functional Minerals as Sustainable Materials for Magneto-Optics

Liquid crystal devices using organic molecules are nowadays widely used to modulate transmitted light, but this technology still suffers from relatively weak response, high cost, toxicity and environmental concerns, and cannot fully meet the demand of future sustainable society. Here, an alternative approach to color-tunable optical devices, which is based on sustainable inorganic liquid crystals derived from 2D mineral materials abundant in nature, is described. The prototypical 2D mineral of vermiculite is massively produced by a green method, possessing size-to-thickness aspect ratios of >10³ , in-plane magnetization of >10 emu g^-1 , and an optical bandgap of >3 eV. These characteristics endow 2D vermiculite with sensitive magneto-birefringence response, been several orders of magnitude larger than organic counterparts, as well as capability of broad-spectrum modulation. The finding consequently permits the fabrication of various magnetochromic or mechanochromic devices with low or even zero-energy consumption during operation. This work creates opportunities for the application of sustainable materials in advanced optics.

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.

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.

Magneto-oscillations have revealed many interesting phenomena in graphene and quantum Hall systems, but they are typically measured at low currents and in equilibrium. Here, the authors report several non-equilibrium quantum effects observed in magneto-oscillations in graphene at high currents.

Magnetization Signature of Topological Surface States in a Non-Symmorphic Superconductor

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 the main characteristics of 2D topological superconductors. Yet, bulk materials known to combine inherent superconductivity with nontrivial topology remain scarce, largely because distinguishing their central characteristic-the topological surface states-has proved challenging due to a dominant contribution from the superconducting bulk. In this work, a highly anomalous behavior of surface superconductivity in topologically nontrivial 3D superconductor In₂ Bi, where the surface states result from its nontrivial band structure, itself a consequence of the non-symmorphic crystal symmetry and strong spin-orbit coupling, is reported. In contrast to smoothly decreasing diamagnetic susceptibility above the bulk critical field, H_c2 , as seen in conventional superconductors, a near-perfect, Meissner-like screening of low-frequency magnetic fields well above H_c2 is observed. The enhanced diamagnetism disappears at a new phase transition close to the critical field of surface superconductivity, H_c3 . Using theoretical modeling, the anomalous screening is shown to be consistent with modification of surface superconductivity by the topological surface states. The possibility of detecting signatures of the surface states using macroscopic magnetization provides a new tool for the discovery and identification of topological superconductors.

Out-of-Plane Dielectric Susceptibility of Graphene in Twistronic and Bernal Bilayers

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 α_exp = 10.8 ų and effective out-of-plane dielectric susceptibility ϵ_z = 2.5, including their on-layer electron density distribution at zero magnetic field and the interlayer Landau level pinning at quantizing magnetic fields.

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 transport^1-9, topological charge-neutral currents^10-12, hydrodynamic flows¹³ and helical edge modes^14-16. Monolayer^1-5,10,15-19, bilayer^9,11,14,20 and few-layer²¹ graphene, transition-metal dichalcogenides^6,7 and moiré superlattices^8,10,12 have been found to display pronounced nonlocal effects. However, the origin of these effects is hotly debated^{3,11,17,22-24}. Graphene, in particular, exhibits giant nonlocality at charge neutrality^1,15-19, 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 edges^23,26-31 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.

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.

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.

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

Blue energy converts the chemical potential difference from salinity gradients into electricity via reverse electrodialysis and provides a renewable source of clean energy. To achieve high energy conversion efficiency and power density, nanoporous membrane materials with both high ionic conductivity and ion selectivity are required. Here, we report ion transport through a network of holey-graphene-like sheets made by bottom-up polymerization. The resulting ultrathin membranes provide controlled pores of <10 Å in diameter with an estimated density of about 10¹² cm^-2. The pores' interior contains NH₂ groups that become electrically charged with varying pH and allow tunable ion selectivity. Using the holey-graphene-like membranes, we demonstrate power outputs reaching hundreds of watts per square meter. The work shows a viable route toward creating membranes with high-density angstrom-scale pores, which can be used for energy generation, ion separation, and related technologies.

In situ manipulation of van der Waals heterostructures for twistronics

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 moiré 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.

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.

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.

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.

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

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.

Indirect Excitons and Trions in MoSe2/WSe2 van der Waals Heterostructures

Indirect excitons (IX) in semiconductor heterostructures are bosons, which can cool below the temperature of quantum degeneracy and can be effectively controlled by voltage and light. IX quantum Bose gases and IX devices were explored in GaAs heterostructures where an IX range of existence is limited to low temperatures due to low IX binding energies. IXs in van der Waals transition-metal dichalcogenide (TMD) heterostructures are characterized by large binding energies giving the opportunity for exploring excitonic quantum gases and for creating excitonic devices at high temperatures. TMD heterostructures also offer a new platform for studying single-exciton phenomena and few-particle complexes. In this work, we present studies of IXs in MoSe₂/WSe₂ heterostructures and report on two IX luminescence lines whose energy splitting and temperature dependence identify them as neutral and charged IXs. The experimentally found binding energy of the indirect charged excitons, that is, indirect trions, is close to the calculated binding energy of 28 meV for negative indirect trions in TMD heterostructures [Deilmann, T.; Thygesen, K. S. Nano Lett. 2018, 18, 1460]. We also report on the realization of IXs with a luminescence line width reaching 4 meV at low temperatures. An enhancement of IX luminescence intensity and the narrow line width are observed in localized spots.

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

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 address a number of scientific problems such as identification of reaction mechanisms, surface modification, or long-range electron transfer.

Stacking Order in Graphite Films Controlled by van der Waals Technology

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 visualize the distribution of stacking domains in graphite films and then perform directional encapsulation of ABC-rich graphite crystallites with hexagonal boron nitride (hBN). We found that hBN encapsulation, which is introduced parallel to the graphite zigzag edges, preserves ABC stacking, while encapsulation along the armchair edges transforms the stacking to ABA. The technique presented here should facilitate new research on the important properties of ABC graphite.

Atomically thin micas as proton-conducting membranes

Monolayers of graphene and hexagonal boron nitride (hBN) are highly permeable to thermal protons^1,2. For thicker two-dimensional (2D) materials, proton conductivity diminishes exponentially, so that, for example, monolayer MoS₂ that is just three atoms thick is completely impermeable to protons¹. This seemed to suggest that only one-atom-thick crystals could be used as proton-conducting membranes. Here, we show that few-layer micas that are rather thick on the atomic scale become excellent proton conductors if native cations are ion-exchanged for protons. Their areal conductivity exceeds that of graphene and hBN by one to two orders of magnitude. Importantly, ion-exchanged 2D micas exhibit this high conductivity inside the infamous gap for proton-conducting materials³, which extends from ∼100 °C to 500 °C. Areal conductivity of proton-exchanged monolayer micas can reach above 100 S cm^-2 at 500 °C, well above the current requirements for the industry roadmap⁴. We attribute the fast proton permeation to ~5-Å-wide tubular channels that perforate micas' crystal structure, which, after ion exchange, contain only hydroxyl groups inside. Our work indicates that there could be other 2D crystals⁵ with similar nanometre-scale channels, which could help close the materials gap in proton-conducting applications.

Perfect proton selectivity in ion transport through two-dimensional crystals

Defect-free monolayers of graphene and hexagonal boron nitride are surprisingly permeable to thermal protons, despite being completely impenetrable to all gases. It remains untested whether small ions can permeate through the two-dimensional crystals. Here we show that mechanically exfoliated graphene and hexagonal boron nitride exhibit perfect Nernst selectivity such that only protons can permeate through, with no detectable flow of counterions. In the experiments, we use suspended monolayers that have few, if any, atomic-scale defects, as shown by gas permeation tests, and place them to separate reservoirs filled with hydrochloric acid solutions. Protons account for all the electrical current and chloride ions are blocked. This result corroborates the previous conclusion that thermal protons can pierce defect-free two-dimensional crystals. Besides the importance for theoretical developments, our results are also of interest for research on various separation technologies based on two-dimensional materials.

Defect-free monolayers of graphene and hexagonal boron nitride are highly permeable to thermal protons, but are impenetrable to gases. Here the authors show that mechanically exfoliated crystals exhibit perfect proton selectivity, corroborating proton transport through the bulk without atomic-scale defects.

Two-Dimensional Covalent Crystals by Chemical Conversion of Thin van der Waals Materials

Most of the studied two-dimensional (2D) materials have been obtained by exfoliation of van der Waals crystals. Recently, there has been growing interest in fabricating synthetic 2D crystals which have no layered bulk analogues. These efforts have been focused mainly on the surface growth of molecules in high vacuum. Here, we report an approach to making 2D crystals of covalent solids by chemical conversion of van der Waals layers. As an example, we used 2D indium selenide (InSe) obtained by exfoliation and converted it by direct fluorination into indium fluoride (InF₃), which has a nonlayered, rhombohedral structure and therefore cannot  possibly be obtained by exfoliation. The conversion of InSe into InF₃ is found to be feasible for thicknesses down to three layers of InSe, and the obtained stable InF₃ layers are doped with selenium. We study this new 2D material by optical, electron transport, and Raman measurements and show that it is a semiconductor with a direct bandgap of 2.2 eV, exhibiting high optical transparency across the visible and infrared spectral ranges. We also demonstrate the scalability of our approach by chemical conversion of large-area, thin InSe laminates obtained by liquid exfoliation, into InF₃ films. The concept of chemical conversion of cleavable thin van der Waals crystals into covalently bonded noncleavable ones opens exciting prospects for synthesizing a wide variety of novel atomically thin covalent crystals.

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.

The conductivity of marginally-twisted bilayer graphene is predicted to persist in presence of a bandgap-opening interlayer bias, owing to a network of 1D conductive states at domain boundaries. Here, the authors report Aharonov–Bohm oscillations up to 100 K, whereas at liquid helium temperatures another kind of oscillation appears, due to progressive population of the narrow minibands formed by the 2D network of 1D states inside the gap.

Colossal infrared and terahertz magneto-optical activity in a two-dimensional Dirac material

When two-dimensional electron gases (2DEGs) are exposed to a magnetic field, they resonantly absorb electromagnetic radiation via electronic transitions between Landau levels¹. In 2DEGs with a Dirac spectrum, such as graphene, theory predicts an exceptionally high infrared magneto-absorption, even at zero doping^2-5. However, the measured Landau-level magneto-optical effects in graphene have been much weaker than expected^2,6-12 because of imperfections in the samples available for such experiments. Here, we measure magneto-transmission and Faraday rotation in high-mobility encapsulated monolayer graphene using a custom-designed set-up for magneto-infrared microspectroscopy. Our results show strongly enhanced magneto-optical activity in the infrared and terahertz ranges, characterized by absorption of light near to the 50% maximum allowed, 100% magnetic circular dichroism and high Faraday rotation. Considering that sizeable effects have been already observed at routinely achievable magnetic fields, our findings demonstrate the potential of magnetic tuning in 2D Dirac materials for long-wavelength optoelectronics and plasmonics.

Simultaneous voltage and current density imaging of flowing electrons in two dimensions

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

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.

Author Correction: Planar and van der Waals heterostructures for vertical tunnelling single electron transistors

The original version of this Article contained an error in the spelling of the author Matthew Holwill, which was incorrectly given as Mathew Holwill. This has now been corrected in both the PDF and HTML versions of the Article.

Planar and van der Waals heterostructures for vertical tunnelling single electron transistors

Despite a rich choice of two-dimensional materials, which exists these days, heterostructures, both vertical (van der Waals) and in-plane, offer an unprecedented control over the properties and functionalities of the resulted structures. Thus, planar heterostructures allow p-n junctions between different two-dimensional semiconductors and graphene nanoribbons with well-defined edges; and vertical heterostructures resulted in the observation of superconductivity in purely carbon-based systems and realisation of vertical tunnelling transistors. Here we demonstrate simultaneous use of in-plane and van der Waals heterostructures to build vertical single electron tunnelling transistors. We grow graphene quantum dots inside the matrix of hexagonal boron nitride, which allows a dramatic reduction of the number of localised states along the perimeter of the quantum dots. The use of hexagonal boron nitride tunnel barriers as contacts to the graphene quantum dots make our transistors reproducible and not dependent on the localised states, opening even larger flexibility when designing future devices.

Failure of Conductance Quantization in Two-Dimensional Topological Insulators due to Nonmagnetic Impurities

Despite topological protection and the absence of magnetic impurities, two-dimensional topological insulators display quantized conductance only in surprisingly short channels, which can be as short as 100 nm for atomically thin materials. We show that the combined action of short-range nonmagnetic impurities located near the edges and on site electron-electron interactions effectively creates noncollinear magnetic scatterers, and, hence, results in strong backscattering. The mechanism causes deviations from quantization even at zero temperature and for a modest strength of electron-electron interactions. Our theory provides a straightforward conceptual framework to explain experimental results, especially those in atomically thin crystals, plagued with short-range edge disorder.

Resonant terahertz detection using graphene plasmons

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

Fluidity onset in graphene

Viscous electron fluids have emerged recently as a new paradigm of strongly-correlated electron transport in solids. Here we report on a direct observation of the transition to this long-sought-for state of matter in a high-mobility electron system in graphene. Unexpectedly, the electron flow is found to be interaction-dominated but non-hydrodynamic (quasiballistic) in a wide temperature range, showing signatures of viscous flows only at relatively high temperatures. The transition between the two regimes is characterized by a sharp maximum of negative resistance, probed in proximity to the current injector. The resistance decreases as the system goes deeper into the hydrodynamic regime. In a perfect darkness-before-daybreak manner, the interaction-dominated negative response is strongest at the transition to the quasiballistic regime. Our work provides the first demonstration of how the viscous fluid behavior emerges in an interacting electron system.

Anomalously low dielectric constant of confined water

The dielectric constant ε of interfacial water has been predicted to be smaller than that of bulk water (ε ≈ 80) because the rotational freedom of water dipoles is expected to decrease near surfaces, yet experimental evidence is lacking. We report local capacitance measurements for water confined between two atomically flat walls separated by various distances down to 1 nanometer. Our experiments reveal the presence of an interfacial layer with vanishingly small polarization such that its out-of-plane ε is only ~2. The electrically dead layer is found to be two to three molecules thick. These results provide much-needed feedback for theories describing water-mediated surface interactions and the behavior of interfacial water, and show a way to investigate the dielectric properties of other fluids and solids under extreme confinement.