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.

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.

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.

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.

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.

Optical imaging of electrical carrier injection into individual InAs quantum dots.

We image the micro-electroluminescence (EL) spectra of self-assembled InAs quantum dots (QDs) embedded in the intrinsic region of a GaAs p-i-n diode and demonstrate optical detection of carrier injection into a single QD. Tunneling of electrons and holes into the QDs at bias voltages below the flat-band condition leads to a spectrum of sharp EL lines from a small number of bright spots on the diode surface, characteristic of emission from individual QDs. We explain this behavior in terms of Coulomb interaction effects and the selective excitation of a small number of QDs within the ensemble due to preferential tunneling paths for carriers.

Manipulating and imaging the shape of an electronic wave function by magnetotunneling spectroscopy.

We measure the current due to electrons tunneling through the ground state of hydrogenic Si donors placed in a GaAs quantum well in the presence of a magnetic field tilted at an angle to the plane of the well. The component of B parallel to the direction of current compresses the donor wave function. By measuring the current as a function of the perpendicular component of B, we probe how the magnetocompression affects the spatial form of the wave function and observe directly the transition from Coulombic to magnetic confinement at high fields.

Microscopic analysis of the valence band and impurity band theories of (Ga,Mn)As.

We analyze microscopically the valence and impurity band models of ferromagnetic (Ga,Mn)As. We find that the tight-binding Anderson approach with conventional parametrization and the full potential local-density approximation+U calculations give a very similar band structure whose microscopic spectral character is consistent with the physical premise of the k·p kinetic-exchange model. On the other hand, the various models with a band structure comprising an impurity band detached from the valence band assume mutually incompatible microscopic spectral character. By adapting the tight-binding Anderson calculations individually to each of the impurity band pictures in the single Mn impurity limit and then by exploring the entire doping range, we find that a detached impurity band does not persist in any of these models in ferromagnetic (Ga,Mn)As.

Chaotic electron diffusion through stochastic webs enhances current flow in superlattices.

Understanding how complex systems respond to change is of fundamental importance in the natural sciences. There is particular interest in systems whose classical newtonian motion becomes chaotic as an applied perturbation grows. The transition to chaos usually occurs by the gradual destruction of stable orbits in parameter space, in accordance with the Kolmogorov-Arnold-Moser (KAM) theorem--a cornerstone of nonlinear dynamics that explains, for example, gaps in the asteroid belt. By contrast, 'non-KAM' chaos switches on and off abruptly at critical values of the perturbation frequency. This type of dynamics has wide-ranging implications in the theory of plasma physics, tokamak fusion, turbulence, ion traps, and quasicrystals. Here we realize non-KAM chaos experimentally by exploiting the quantum properties of electrons in the periodic potential of a semiconductor superlattice with an applied voltage and magnetic field. The onset of chaos at discrete voltages is observed as a large increase in the current flow due to the creation of unbound electron orbits, which propagate through intricate web patterns in phase space. Non-KAM chaos therefore provides a mechanism for controlling the electrical conductivity of a condensed matter device: its extreme sensitivity could find applications in quantum electronics and photonics.

Imaging the electron wave function in self-assembled quantum dots.

Magnetotunneling spectroscopy is used as a noninvasive and nondestructive probe to produce two-dimensional spatial images of the probability density of an electron confined in a self-assembled semiconductor quantum dot. The technique exploits the effect of the classical Lorentz force on the motion of a tunneling electron and can be regarded as the momentum (k) space analog of scanning tunneling microscopy imaging. The images reveal the elliptical symmetry of the ground state and the characteristic lobes of the higher energy states.

Tailoring the electrical conductivity of GaAs by nitrogen incorporation.

We investigate the electrical conductivity of the dilute nitride alloy GaAs(1-x)N(x), focusing on the range of concentrations of N over which this material system behaves as a good conductor. We report a large increase of the resistivity for x>0.2% and a strong reduction of the electron mobility, µ, at x∼0.1%. In the ultra-dilute regime (x∼0.1%) and at low electric fields (<1 kV cm(-1)), the electrical conductivity retains the characteristic features of electron transport through extended states, albeit with relatively low mobility (µâˆ¼0.1 m(2) V(-1) s(-1) at T = 293 K) due to scattering of electrons by N atoms. In contrast, at large electric fields (>1 kV cm(-1)), the conduction electrons gain sufficient energy to approach the energy of the resonant N level, where they become spatially localized. This resonant electron localization in an electric field (RELIEF) leads to negative differential velocity. The RELIEF effect could be observed in other III-N-V compounds, such as InAs(1-x)N(x) and InP(1-x)N(x), and has potential for applications in terahertz electronics.

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.

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.

Bifurcations and chaos in semiconductor superlattices with a tilted magnetic field.

We study the effects of dissipation on electron transport in a semiconductor superlattice with an applied bias voltage and a magnetic field that is tilted relative to the superlattice axis. In previous work, we showed that, although the applied fields are stationary, they act like a terahertz plane wave, which strongly couples the Bloch and cyclotron motion of electrons within the lowest miniband. As a consequence, the electrons exhibit a unique type of Hamiltonian chaos, which creates an intricate mesh of conduction channels (a stochastic web) in phase space, leading to a large resonant increase in the current flow at critical values of the applied voltage. This phase-space patterning provides a sensitive mechanism for controlling electrical resistance. In this paper, we investigate the effects of dissipation on the electron dynamics by modifying the semiclassical equations of motion to include a linear damping term. We demonstrate that, even in the presence of dissipation, deterministic chaos plays an important role in the electron transport process. We identify mechanisms for the onset of chaos and explore the associated sequence of bifurcations in the electron trajectories. When the Bloch and cyclotron frequencies are commensurate, complex multistability phenomena occur in the system. In particular, for fixed values of the control parameters several distinct stable regimes can coexist, each corresponding to different initial conditions. We show that this multistability has clear, experimentally observable, signatures in the electron transport characteristics.

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.

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.