The quantum twisting microscope.

The invention of scanning probe microscopy revolutionized the way electronic phenomena are visualized1. Whereas present-day probes can access a variety of electronic properties at a single location in space2, a scanning microscope that can directly probe the quantum mechanical existence of an electron at several locations would provide direct access to key quantum properties of electronic systems, so far unreachable. Here, we demonstrate a conceptually new type of scanning probe microscope-the quantum twisting microscope (QTM)-capable of performing local interference experiments at its tip. The QTM is based on a unique van der Waals tip, allowing the creation of pristine two-dimensional junctions, which provide a multitude of coherently interfering paths for an electron to tunnel into a sample. With the addition of a continuously scanned twist angle between the tip and sample, this microscope probes electrons along a line in momentum space similar to how a scanning tunnelling microscope probes electrons along a line in real space. Through a series of experiments, we demonstrate room-temperature quantum coherence at the tip, study the twist angle evolution of twisted bilayer graphene, directly image the energy bands of monolayer and twisted bilayer graphene and, finally, apply large local pressures while visualizing the gradual flattening of the low-energy band of twisted bilayer graphene. The QTM opens the way for new classes of experiments on quantum materials.

Imaging hydrodynamic electrons flowing without Landauer-Sharvin resistance.

Electrical resistance usually originates from lattice imperfections. However, even a perfect lattice has a fundamental resistance limit, given by the Landauer1 conductance caused by a finite number of propagating electron modes. This resistance, shown by Sharvin2 to appear at the contacts of electronic devices, sets the ultimate conduction limit of non-interacting electrons. Recent years have seen growing evidence of hydrodynamic electronic phenomena3-18, prompting recent theories19,20 to ask whether an electronic fluid can radically break the fundamental Landauer-Sharvin limit. Here, we use single-electron-transistor imaging of electronic flow in high-mobility graphene Corbino disk devices to answer this question. First, by imaging ballistic flows at liquid-helium temperatures, we observe a Landauer-Sharvin resistance that does not appear at the contacts but is instead distributed throughout the bulk. This underpins the phase-space origin of this resistance-as emerging from spatial gradients in the number of conduction modes. At elevated temperatures, by identifying and accounting for electron-phonon scattering, we show the details of the purely hydrodynamic flow. Strikingly, we find that electron hydrodynamics eliminates the bulk Landauer-Sharvin resistance. Finally, by imaging spiralling magneto-hydrodynamic Corbino flows, we show the key emergent length scale predicted by hydrodynamic theories-the Gurzhi length. These observations demonstrate that electronic fluids can dramatically transcend the fundamental limitations of ballistic electrons, with important implications for fundamental science and future technologies.

Imaging work and dissipation in the quantum Hall state in graphene.

Topology is a powerful recent concept asserting that quantum states could be globally protected against local perturbations1,2. Dissipationless topologically protected states are therefore of major fundamental interest as well as of practical importance in metrology and quantum information technology. Although topological protection can be robust theoretically, in realistic devices it is often susceptible to various dissipative mechanisms, which are difficult to study directly because of their microscopic origins. Here we use scanning nanothermometry3 to visualize and investigate the microscopic mechanisms that undermine dissipationless transport in the quantum Hall state in graphene. Simultaneous nanoscale thermal and scanning gate microscopy shows that the dissipation is governed by crosstalk between counterpropagating pairs of downstream and upstream channels that appear at graphene boundaries as a result of edge reconstruction. Instead of local Joule heating, however, the dissipation mechanism comprises two distinct and spatially separated processes. The work-generating process that we image directly, which involves elastic tunnelling of charge carriers between the quantum channels, determines the transport properties but does not generate local heat. By contrast, the heat and entropy generation process-which we visualize independently-occurs nonlocally upon resonant inelastic scattering from single atomic defects at graphene edges, and does not affect transport. Our findings provide an insight into the mechanisms that conceal the true topological protection, and suggest routes towards engineering more robust quantum states for device applications.

Publisher Correction: Imaging work and dissipation in the quantum Hall state in graphene.

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

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

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

Strong magnetophonon oscillations in extra-large graphene.

Van der Waals materials and their heterostructures offer a versatile platform for studying a variety of quantum transport phenomena due to their unique crystalline properties and the exceptional ability in tuning their electronic spectrum. However, most experiments are limited to devices that have lateral dimensions of only a few micrometres. Here, we perform magnetotransport measurements on graphene/hexagonal boron-nitride Hall bars and show that wider devices reveal additional quantum effects. In devices wider than ten micrometres we observe distinct magnetoresistance oscillations that are caused by resonant scattering of Landau-quantised Dirac electrons by acoustic phonons in graphene. The study allows us to accurately determine graphene's low energy phonon dispersion curves and shows that transverse acoustic modes cause most of phonon scattering. Our work highlights the crucial importance of device width when probing quantum effects and also demonstrates a precise, spectroscopic method for studying electron-phonon interactions in van der Waals heterostructures.

Composite super-moiré lattices in double-aligned graphene heterostructures.

When two-dimensional (2D) atomic crystals are brought into close proximity to form a van der Waals heterostructure, neighbouring crystals may influence each other's properties. Of particular interest is when the two crystals closely match and a moiré pattern forms, resulting in modified electronic and excitonic spectra, crystal reconstruction, and more. Thus, moiré patterns are a viable tool for controlling the properties of 2D materials. However, the difference in periodicity of the two crystals limits the reconstruction and, thus, is a barrier to the low-energy regime. Here, we present a route to spectrum reconstruction at all energies. By using graphene which is aligned to two hexagonal boron nitride layers, one can make electrons scatter in the differential moiré pattern which results in spectral changes at arbitrarily low energies. Further, we demonstrate that the strength of this potential relies crucially on the atomic reconstruction of graphene within the differential moiré super cell.

Edge currents shunt the insulating bulk in gapped graphene.

An energy gap can be opened in the spectrum of graphene reaching values as large as 0.2 eV in the case of bilayers. However, such gaps rarely lead to the highly insulating state expected at low temperatures. This long-standing puzzle is usually explained by charge inhomogeneity. Here we revisit the issue by investigating proximity-induced superconductivity in gapped graphene and comparing normal-state measurements in the Hall bar and Corbino geometries. We find that the supercurrent at the charge neutrality point in gapped graphene propagates along narrow channels near the edges. This observation is corroborated by using the edgeless Corbino geometry in which case resistivity at the neutrality point increases exponentially with increasing the gap, as expected for an ordinary semiconductor. In contrast, resistivity in the Hall bar geometry saturates to values of about a few resistance quanta. We attribute the metallic-like edge conductance to a nontrivial topology of gapped Dirac spectra.

Tea and coffee as sources of some minerals in the New Zealand diet.

Daily intakes of tea and coffee of a representative sample of adult New Zealanders (865 men and 1100 women) were calculated from 24-h dietary recalls. The mineral concentrations in tea and coffee samples were determined by atomic absorption spectrometry and used to estimate daily mineral intakes from these beverages. More than 80% consumed tea and about 60% consumed coffee on the day of the recall. The men drank significantly more tea than the women (p less than 0.001), but coffee intakes were similar. The results indicate that for New Zealand adults tea is a very good source of manganese and it also contains appreciable amounts of potassium. Coffee is a better source of potassium than tea, has appreciable amounts of magnesium, and may contribute significantly to manganese intakes in some instances. The amounts of copper, zinc, sodium, calcium, and iron extracted from tea leaves and coffee beans in the brewing processes are too low to be of any nutritional significance but minerals in the water used in their preparation may make a significant contribution to dietary intakes.

Weaning; a position statement.

1. Weaning is the process by which the milk fed infant is gradually accustomed to a varied diet. 2. The time at which weaning should commence should be signalled by the infant's being dissatisfied with a milk diet. While this tends to occur around five to six months of age, it may be later. 3. Appropriate foods to start weaning should be almost liquid in consistency, provide useful nutrients, and be of low allergenicity. 4. The aim is to achieve a diet based on family foods. These should conform to the criteria for a healthful diet, but should not be especially low in fat or rich in fibre. 5. In the earlier stages breast milk or formula remains the principal source of nutrition. Weaning foods should not be used in a way which discourages consumption of milks. 6. Water or diluted fruit juice may be used to assuage thirst, but should not supplant milk even in the later stages of weaning, since they contain no calcium or most other essential micronutrients. Tea and coffee are not suitable drinks for young children.

The role of dairy products in the New Zealand diet.

New Zealand is both a major producer and large consumer of dairy products. In 1976, for example, daily per capita consumption of liquid milk averaged 471 ml, cheese 13.7 g/d, and butter 38.4 g/d, the last apparently the highest in the world. Recent studies of the dietary habits of New Zealand adults, and of children of early school age in Dunedin (Birkbeck, Guthrie, Herbert, personal communication) have provided information on the role of dairy products as source of nutrients. National consumption figures or family market basket surveys provide no information about individual intakes, since they do not reflect age or sex differences between consumers.

Skeletal maturity in seven year old Dunedin children.

A study of 433 boys' and 403 girls' left hand/wrist radiographs taken within 0.1 years of the child's seventh birthday shows that the median equivalent skeletal maturity using the TW 2 20-bone score is identical to the English standards, and the RUS score is only slightly above the standards. It is thus valid to use Tanner's standards when assessing New Zealand white children. The wide range of values in a healthy population is stressed.

Blood pressure in a cohort of Dunedin seven year olds.

Blood pressure, pulse measurements, socio-economic status, and anthropometric data were recorded in 982 children within approximately one month of their seventh birthdays. The means, standard deviations, and 95th centiles are reported for systolic, diastolic phase IV, and diastolic phase V blood pressure. There was no significant difference between the socio-economic levels for any measure of blood pressure. Systolic blood pressure was slightly but significantly higher in boys than in girls; this difference disappeared after correction for height. There were small but significant correlations between blood pressure and pulse rate, weight, height, arm circumference, triceps skinfold thickness, and indices of obesity and body size. After adjustment for weight, the associations of systolic blood pressure with height, body mass index, and arm circumference were no longer significant.