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.

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.

Direct band-gap crossover in epitaxial monolayer boron nitride.

Hexagonal boron nitride is a large band-gap insulating material which complements the electronic and optical properties of graphene and the transition metal dichalcogenides. However, the intrinsic optical properties of monolayer boron nitride remain largely unexplored. In particular, the theoretically expected crossover to a direct-gap in the limit of the single monolayer is presently not confirmed experimentally. Here, in contrast to the technique of exfoliating few-layer 2D hexagonal boron nitride, we exploit the scalable approach of high-temperature molecular beam epitaxy to grow high-quality monolayer boron nitride on graphite substrates. We combine deep-ultraviolet photoluminescence and reflectance spectroscopy with atomic force microscopy to reveal the presence of a direct gap of energy 6.1 eV in the single atomic layers, thus confirming a crossover to direct gap in the monolayer limit.

High-order fractal states in graphene superlattices.

Graphene superlattices were shown to exhibit high-temperature quantum oscillations due to periodic emergence of delocalized Bloch states in high magnetic fields such that unit fractions of the flux quantum pierce a superlattice unit cell. Under these conditions, semiclassical electron trajectories become straight again, similar to the case of zero magnetic field. Here, we report magnetotransport measurements that reveal second-, third-, and fourth-order magnetic Bloch states at high electron densities and temperatures above 100 K. The recurrence of these states creates a fractal pattern intimately related to the origin of Hofstadter butterflies. The hierarchy of the fractal states is determined by the width of magnetic minibands, in qualitative agreement with our band-structure calculations.

A direct test of the diathesis-stress model for depression.

The diathesis-stress theory for depression states that the effects of stress on the depression risk are dependent on the diathesis or vulnerability, implying multiplicative interactive effects on the liability scale. We used polygenic risk scores for major depressive disorder (MDD) calculated from the results of the most recent analysis from the Psychiatric Genomics Consortium as a direct measure of the vulnerability for depression in a sample of 5221 individuals from 3083 families. In the same we also had measures of stressful life events and social support and a depression symptom score, as well as DSM-IV MDD diagnoses for most individuals. In order to estimate the variance in depression explained by the genetic vulnerability, the stressors and their interactions, we fitted linear mixed models controlling for relatedness for the whole sample as well as stratified by sex. We show a significant interaction of the polygenic risk scores with personal life events (0.12% of variance explained, P-value=0.0076) contributing positively to the risk of depression. Additionally, our results suggest possible differences in the aetiology of depression between women and men. In conclusion, our findings point to an extra risk for individuals with combined vulnerability and high number of reported personal life events beyond what would be expected from the additive contributions of these factors to the liability for depression, supporting the multiplicative diathesis-stress model for this disease.

Giant Quantum Hall Plateau in Graphene Coupled to an InSe van der Waals Crystal.

We report on a "giant" quantum Hall effect plateau in a graphene-based field-effect transistor where graphene is capped by a layer of the van der Waals crystal InSe. The giant quantum Hall effect plateau arises from the close alignment of the conduction band edge of InSe with the Dirac point of graphene. This feature enables the magnetic-field- and electric-field-effect-induced transfer of charge carriers between InSe and the degenerate Landau level states of the adjacent graphene layer, which is coupled by a van der Waals heterointerface to the InSe.

An atomic carbon source for high temperature molecular beam epitaxy of graphene.

We report the use of a novel atomic carbon source for the molecular beam epitaxy (MBE) of graphene layers on hBN flakes and on sapphire wafers at substrate growth temperatures of ~1400 °C. The source produces a flux of predominantly atomic carbon, which diffuses through the walls of a Joule-heated tantalum tube filled with graphite powder. We demonstrate deposition of carbon on sapphire with carbon deposition rates up to 12 nm/h. Atomic force microscopy measurements reveal the formation of hexagonal moiré patterns when graphene monolayers are grown on hBN flakes. The Raman spectra of the graphene layers grown on hBN and sapphire with the sublimation carbon source and the atomic carbon source are similar, whilst the nature of the carbon aggregates is different - graphitic with the sublimation carbon source and amorphous with the atomic carbon source. At MBE growth temperatures we observe etching of the sapphire wafer surface by the flux from the atomic carbon source, which we have not observed in the MBE growth of graphene with the sublimation carbon source.

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

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

The direct-to-indirect band gap crossover in two-dimensional van der Waals Indium Selenide crystals.

The electronic band structure of van der Waals (vdW) layered crystals has properties that depend on the composition, thickness and stacking of the component layers. Here we use density functional theory and high field magneto-optics to investigate the metal chalcogenide InSe, a recent addition to the family of vdW layered crystals, which transforms from a direct to an indirect band gap semiconductor as the number of layers is reduced. We investigate this direct-to-indirect bandgap crossover, demonstrate a highly tuneable optical response from the near infrared to the visible spectrum with decreasing layer thickness down to 2 layers, and report quantum dot-like optical emissions distributed over a wide range of energy. Our analysis also indicates that electron and exciton effective masses are weakly dependent on the layer thickness and are significantly smaller than in other vdW crystals. These properties are unprecedented within the large family of vdW crystals and demonstrate the potential of InSe for electronic and photonic technologies.

Tuning the valley and chiral quantum state of Dirac electrons in van der Waals heterostructures.

Chirality is a fundamental property of electrons with the relativistic spectrum found in graphene and topological insulators. It plays a crucial role in relativistic phenomena, such as Klein tunneling, but it is difficult to visualize directly. Here, we report the direct observation and manipulation of chirality and pseudospin polarization in the tunneling of electrons between two almost perfectly aligned graphene crystals. We use a strong in-plane magnetic field as a tool to resolve the contributions of the chiral electronic states that have a phase difference between the two components of their vector wave function. Our experiments not only shed light on chirality, but also demonstrate a technique for preparing graphene's Dirac electrons in a particular quantum chiral state in a selected valley.

Resonant Zener tunnelling via zero-dimensional states in a narrow gap diode.

Interband tunnelling of carriers through a forbidden energy gap, known as Zener tunnelling, is a phenomenon of fundamental and technological interest. Its experimental observation in the Esaki p-n semiconductor diode has led to the first demonstration and exploitation of quantum tunnelling in a condensed matter system. Here we demonstrate a new type of Zener tunnelling that involves the resonant transmission of electrons through zero-dimensional (0D) states. In our devices, a narrow quantum well of the mid-infrared (MIR) alloy In(AsN) is placed in the intrinsic (i) layer of a p-i-n diode. The incorporation of nitrogen in the quantum well creates 0D states that are localized on nanometer lengthscales. These levels provide intermediate states that act as "stepping stones" for electrons tunnelling across the diode and give rise to a negative differential resistance (NDR) that is weakly dependent on temperature. These electron transport properties have potential for the development of nanometre-scale non-linear components for electronics and MIR photonics.

Phonon-Assisted Resonant Tunneling of Electrons in Graphene-Boron Nitride Transistors.

We observe a series of sharp resonant features in the differential conductance of graphene-hexagonal boron nitride-graphene tunnel transistors over a wide range of bias voltages between 10 and 200 mV. We attribute them to electron tunneling assisted by the emission of phonons of well-defined energy. The bias voltages at which they occur are insensitive to the applied gate voltage and hence independent of the carrier densities in the graphene electrodes, so plasmonic effects can be ruled out. The phonon energies corresponding to the resonances are compared with the lattice dispersion curves of graphene-boron nitride heterostructures and are close to peaks in the single phonon density of states.

Twist-controlled resonant tunnelling in graphene/boron nitride/graphene heterostructures.

Recent developments in the technology of van der Waals heterostructures made from two-dimensional atomic crystals have already led to the observation of new physical phenomena, such as the metal-insulator transition and Coulomb drag, and to the realization of functional devices, such as tunnel diodes, tunnel transistors and photovoltaic sensors. An unprecedented degree of control of the electronic properties is available not only by means of the selection of materials in the stack, but also through the additional fine-tuning achievable by adjusting the built-in strain and relative orientation of the component layers. Here we demonstrate how careful alignment of the crystallographic orientation of two graphene electrodes separated by a layer of hexagonal boron nitride in a transistor device can achieve resonant tunnelling with conservation of electron energy, momentum and, potentially, chirality. We show how the resonance peak and negative differential conductance in the device characteristics induce a tunable radiofrequency oscillatory current that has potential for future high-frequency technology.

Resonant tunnelling and negative differential conductance in graphene transistors.

The chemical stability of graphene and other free-standing two-dimensional crystals means that they can be stacked in different combinations to produce a new class of functional materials, designed for specific device applications. Here we report resonant tunnelling of Dirac fermions through a boron nitride barrier, a few atomic layers thick, sandwiched between two graphene electrodes. The resonance occurs when the electronic spectra of the two electrodes are aligned. The resulting negative differential conductance in the device characteristics persists up to room temperature and is gate voltage-tuneable due to graphene's unique Dirac-like spectrum. Although conventional resonant tunnelling devices comprising a quantum well sandwiched between two tunnel barriers are tens of nanometres thick, the tunnelling carriers in our devices cross only a few atomic layers, offering the prospect of ultra-fast transit times. This feature, combined with the multi-valued form of the device characteristics, has potential for applications in high-frequency and logic devices.

Linear magnetoresistance due to multiple-electron scattering by low-mobility islands in an inhomogeneous conductor.

Linear transverse magnetoresistance is commonly observed in many material systems including semimetals, narrow band-gap semiconductors, multi-layer graphene and topological insulators. It can originate in an inhomogeneous conductor from distortions in the current paths induced by macroscopic spatial fluctuations in the carrier mobility and it has been explained using a phenomenological semiclassical random resistor network model. However, the link between the linear magnetoresistance and the microscopic nature of the electron dynamics remains unknown. Here we demonstrate how the linear magnetoresistance arises from the stochastic behaviour of the electronic cycloidal trajectories around low-mobility islands in high-mobility inhomogeneous conductors and that this process is only weakly affected by the applied electric field strength. Also, we establish a quantitative link between the island morphology and the strength of linear magnetoresistance of relevance for future applications.

Subterahertz acoustical pumping of electronic charge in a resonant tunneling device.

We demonstrate that controlled subnanosecond bursts of electronic charge can be transferred through a resonant tunneling diode by successive picosecond acoustic pulses. The effect exploits the nonlinear current-voltage characteristics of the device and its asymmetric response to the compressive and tensile components of the strain pulse. This acoustoelectronic pump opens new possibilities for the control of quantum phenomena in nanostructures.

Laser location and manipulation of a single quantum tunneling channel in an InAs quantum dot.

We use a femtowatt focused laser beam to locate and manipulate a single quantum tunneling channel associated with an individual InAs quantum dot within an ensemble of dots. The intensity of the directed laser beam tunes the tunneling current through the targeted dot with an effective optical gain of 10(7) and modifies the curvature of the dot's confining potential and the spatial extent of its ground state electron eigenfunction. These observations are explained by the effect of photocreated hole charges which become bound close to the targeted dot, thus acting as an optically induced gate electrode.

Addendum to "Vibrations of a diamagnetically levitated water droplet".

We derive an analytical expression for the frequency of the shape oscillations of a diamagnetically levitated water droplet, in which the equilibrium shape is not spherical. We give the eigenfrequencies of all modes to first order in the oscillation amplitude and potential energy of the magnetogravitational trap confining the droplet. We compare the result with experimental measurements of the eigenfrequencies.

Field-effect tunneling transistor based on vertical graphene heterostructures.

An obstacle to the use of graphene as an alternative to silicon electronics has been the absence of an energy gap between its conduction and valence bands, which makes it difficult to achieve low power dissipation in the OFF state. We report a bipolar field-effect transistor that exploits the low density of states in graphene and its one-atomic-layer thickness. Our prototype devices are graphene heterostructures with atomically thin boron nitride or molybdenum disulfide acting as a vertical transport barrier. They exhibit room-temperature switching ratios of ≈50 and ≈10,000, respectively. Such devices have potential for high-frequency operation and large-scale integration.

Nanoscale potential fluctuations in (GaMn)As/GaAs heterostructures: from individual ions to charge clusters and electrostatic quantum dots.

During growth of the dilute p-type ferromagnetic semiconductor Ga1-xMnxAs, interstitial manganese, Mni(2+), is formed when x exceeds 2%. The double donor Mni(2+) compensates the free holes that mediate ferromagnetism. Annealing causes out-diffusion of these interstitials, thereby increasing the Curie temperature. Here, we use cross sectional scanning tunneling microscopy and spectroscopy to visualize the potential landscape which arises due to the clustering of Mni(2+) in annealed p-i-n (GaMn)As-GaAs double barrier heterostructures. We map the local minima in the potential landscape, link them to clusters of individual Mni(2+) ions, and show that the ions are doubly charged.