Unconventional superconductors have specific signatures in their magnetic properties, such as intrinsic magnetization at interfaces and around defects and fractional and multiquanta vortices, with much attention focused on heavy fermion and high- T c superconductors. Here, we report the observation of highly anomalous magnetization in β- PdB i 2 , a layered superconductor previously shown to exhibit a magnetic-field-induced transition from s -wave to nodal p -wave superconductivity at a transition field H * ∼ 0.1 T ( H C 1 < H * < H C 2 ) . This transition is driven by the coupling between spin-polarized electronic bands and the in-plane magnetic field. In the unconventional phase (above H * ) we observe three striking features: strictly linear and nonhysteretic dc magnetization, a sharp drop in the ac susceptibility when the field is applied parallel to the ab plane, and a pronounced anisotropy in the magnetic response between parallel and perpendicular field orientations. We show that these features are directly correlated with the expected transition to the nodal p -wave state and propose that the unusual magnetization behavior can be explained by a transition from a conventional vortex lattice in the low-field s -wave phase to a domain structure corresponding to spatial phase separation into superconducting ( p -wave) and normal domains above H * . Our work identifies experimental signatures of unconventional multiphase superconductivity, offering an insight into the magnetic-field response of nodal states.

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

Unconventional superconductivity, where electron pairing does not involve electron-phonon interactions, is often attributed to magnetic correlations in a material. Well known examples include high-Tc cuprates and uranium-based heavy fermion superconductors. Less explored are unconventional superconductors with strong spin-orbit coupling, where interactions between spin-polarised electrons and external magnetic field can result in multiple superconducting phases and field-induced transitions between them, a rare phenomenon in the superconducting state. Here we report a magnetic-field driven phase transition in β-PdBi2, a layered non-magnetic superconductor. Our tunnelling spectroscopy on thin PdBi2 monocrystals incorporated in planar superconductor-insulator-normal metal junctions reveals a marked discontinuity in the superconducting properties with increasing in-plane field, which is consistent with a transition from conventional (s-wave) to nodal pairing. Our theoretical analysis suggests that this phase transition may arise from spin polarisation and spin-momentum locking caused by locally broken inversion symmetry, with p-wave pairing becoming energetically favourable in high fields. Our findings also reconcile earlier predictions of unconventional multigap superconductivity in β-PdBi2 with previous experiments where only a single s-wave gap could be detected.

The electronic quality of two-dimensional systems is crucial when exploring quantum transport phenomena. In semiconductor heterostructures, decades of optimization have yielded record-quality two-dimensional gases with transport and quantum mobilities reaching close to 108 and 106 cm2 V-1 s-1, respectively1-10. Although the quality of graphene devices has also been improving, it remains comparatively lower11-17. Here we report a transformative improvement in the electronic quality of graphene by employing graphite gates placed in its immediate proximity, at 1 nm separation. The resulting screening reduces charge inhomogeneity by two orders of magnitude, bringing it down to a few 107 cm-2 and limiting potential fluctuations to less than 1 meV. Quantum mobilities reach 107 cm2 V-1 s-1, surpassing those in the highest-quality semiconductor heterostructures by an order of magnitude, and the transport mobilities match their record9,10. This quality enables Shubnikov-de Haas oscillations in fields as low as 1 mT and quantum Hall plateaux below 5 mT. Although proximity screening predictably suppresses electron-electron interactions, fractional quantum Hall states remain observable with their energy gaps reduced only by a factor of 3-5 compared with unscreened devices, demonstrating that many-body phenomena at spatial scales shorter than 10 nm remain robust. Our results offer a reliable route to improving electronic quality in graphene and other two-dimensional systems, which should facilitate the exploration of new physics previously obscured by disorder.

The origin of superconductivity in magic-angle twisted bilayer graphene has been a subject of intense debate. While some experimental evidence indicated an unconventional pairing mechanism, efforts to tune the critical temperature by screening the Coulomb interactions have been unsuccessful, possibly indicating a conventional phonon-mediated pairing. Here we study a double-layer electronic system consisting of two twisted graphene bilayers in immediate proximity of each other but remaining electronically decoupled. By increasing the carrier density in one bilayer, we completely suppressed both the superconductivity and the correlated-insulator state in the adjacent magic-angle graphene. The observation of such a screening effect offers strong support for an unconventional mechanism of Cooper pairing in magic-angle twisted bilayer graphene, shedding new light on the underlying physics governing their properties.

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

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

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.

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. We show that domain walls in minimally twisted bilayer graphene support exceptionally robust proximity superconductivity in the quantum Hall regime.

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.

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

AbstractThe ongoing efforts to optimize rechargeable Li-ion batteries led to the interest in intercalation of nanoscale layered compounds, including bilayer graphene. Its lithium intercalation has been demonstrated recently but the mechanisms underpinning the storage capacity remain poorly understood. Here, using magnetotransport measurements, we report in-operando intercalation dynamics of bilayer graphene. Unexpectedly, we find four distinct intercalation stages that correspond to well-defined Li-ion densities. Transitions between the stages occur rapidly (within 1 sec) over the entire device area. We refer to these stages as ‘in-plane’, with no in-plane analogues in bulk graphite. The fully intercalated bilayers represent a stoichiometric compound C14LiC14 with a Li density of ∼2.7·1014 cm−2, notably lower than fully intercalated graphite. Combining the experimental findings and DFT calculations, we show that the critical step in bilayer intercalation is a transition from AB to AA stacking which occurs at a density of ∼0.9·1014 cm−2. Our findings reveal the mechanism and limits for electrochemical intercalation of bilayer graphene and suggest possible avenues for increasing the Li storage capacity.

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.

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

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.

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 inhomogeneity(1,2) 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 scattering(3-5) and hydrodynamic flow(6-8). 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) scattering(3-5,9-14). 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 screening(15), indicating a many-body origin. Clear parallels with magnetotransport in strange metals(12-14) and so-called quantum linear magnetoresistance predicted for Weyl metals(16) offer an interesting opportunity to further explore relevant physics using this well defined quantum-critical two-dimensional system.

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.

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.

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.