Electric Field Effect in Atomically Thin Carbon Films

Diluted graphene antiferromagnet

We study RKKY interactions between local magnetic moments for both doped and undoped graphene. In the former case interactions for moments located on definite sublattices fall off as 1/R2, whereas for those placed at interstitial sites they decay as 1/R3. The interactions are primarily (anti)ferromagnetic for moments on (opposite) equivalent sublattices, suggesting that at low temperature dilute magnetic moments embedded in graphene can order into a state analogous to that of a dilute antiferromagnet. In the undoped case we find no net magnetic moment in the ground state, and demonstrate numerically this effect for ribbons, suggesting the possibility of an unusual spin-transfer device.

Phase-Coherent Transport in Graphene Quantum Billiards

As an emergent electronic material and model system for condensed-matter physics, graphene and its electrical transport properties have become a subject of intense focus. By performing low-temperature transport spectroscopy on single-layer and bilayer graphene, we observe ballistic propagation and quantum interference of multiply reflected waves of charges from normal electrodes and multiple Andreev reflections from superconducting electrodes, thereby realizing quantum billiards in which scattering only occurs at the boundaries. In contrast to the conductivity of conventional two-dimensional materials, graphene's conductivity at the Dirac point is geometry-dependent because of conduction via evanescent modes, approaching the theoretical value 4e(2)/pih (where e is the electron charge and h is Planck's constant) only for short and wide devices. These distinctive transport properties have important implications for understanding chaotic quantum systems and implementing nanoelectronic devices, such as ballistic transistors.

Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization

We discuss, for a two-dimensional Dirac Hamiltonian with a random scalar potential, the presence of a Z2 topological term in the nonlinear sigma model encoding the physics of Anderson localization in the symplectic symmetry class. The Z2 topological term realizes the sign of the Pfaffian of a family of Dirac operators. We compute the corresponding global anomaly, i.e., the change in the sign of the Pfaffian by studying a spectral flow numerically. This Z2 topological effect can be relevant to graphene when the impurity potential is long ranged and, also, to the two-dimensional boundaries of a three-dimensional lattice model of Z2 topological insulators in the symplectic symmetry class.

Rayleigh imaging of graphene and graphene layers

We investigate graphene and graphene layers on different substrates by monochromatic and white-light confocal Rayleigh scattering microscopy. The image contrast depends sensitively on the dielectric properties of the sample as well as the substrate geometry and can be described quantitatively using the complex refractive index of bulk graphite. For a few layers (<6), the monochromatic contrast increases linearly with thickness. The data can be adequately understood by considering the samples behaving as a superposition of single sheets that act as independent two-dimensional electron gases. Thus, Rayleigh imaging is a general, simple, and quick tool to identify graphene layers, which is readily combined with Raman scattering, that provides structural identification.

Graphene thickness determination using reflection and contrast spectroscopy

We have clearly discriminated the single-, bilayer-, and multiple-layer graphene (<10 layers) on Si substrate with a 285 nm SiO2 capping layer by using contrast spectra, which were generated from the reflection light of a white light source. Calculations based on Fresnel's law are in excellent agreement with the experimental results (deviation 2%). The contrast image shows the reliability and efficiency of this new technique. The contrast spectrum is a fast, nondestructive, easy to be carried out, and unambiguous way to identify the numbers of layers of graphene sheet. We provide two easy-to-use methods to determine the number of graphene layers based on contrast spectra: a graphic method and an analytical method. We also show that the refractive index of graphene is different from that of graphite. The results are compared with those obtained using Raman spectroscopy.

The optical visibility of graphene: interference colors of ultrathin graphite on SiO(2)

Monatomic layers of graphite are emerging as building blocks for novel optoelectronic devices. Experimental studies on a single graphite layer (graphene) are today possible since very thin graphite can be identified on a dielectric substrate using a normal optical microscope. We investigate the mechanism behind the strong visibility of graphite, and we discuss the importance of substrates and of the microscope objective used for the imaging.

Temperature dependence of the Raman spectra of graphene and graphene multilayers

We investigated the temperature dependence of the frequency of G peak in the Raman spectra of graphene on Si/SiO2 substrates. The micro-Raman spectroscopy was carried out under the 488 nm laser excitation over the temperature range from -190 to +100 degrees C. The extracted value of the temperature coefficient of G mode of graphene is chi = -0.016 cm-1/ degrees C for the single layer and chi = -0.015 cm-1/ degrees C for the bilayer. The obtained results shed light on the anharmonic properties of graphene.

Filling-factor-dependent magnetophonon resonance in graphene

We describe a peculiar fine structure acquired by the in-plane optical phonon at the Gamma point in graphene when it is brought into resonance with one of the inter-Landau-level transitions in this material. The effect is most pronounced when this lattice mode (associated with the G band in graphene Raman spectrum) is in resonance with inter-Landau-level transitions 0 --> +, 1 and -, 1 --> 0, at a magnetic field B{0} approximately 30 T. It can be used to measure the strength of the electron-phonon coupling directly, and its filling-factor dependence can be used experimentally to detect circularly polarized lattice vibrations.

Multiscale imaging and tip-scratch studies reveal insight into the plasma oxidation of graphite

The plasma oxidation process of highly oriented pyrolytic graphite (HOPG) has been investigated through a combination of multiscale (micrometric to atomic) imaging by atomic force and scanning tunneling microscopies (AFM/STM) and STM tip-scratching of the HOPG substrate. Complementary information was obtained by Raman spectroscopy and X-ray photoelectron spectroscopy (XPS). Repetitive imaging of the same HOPG location following a series of consecutive plasma treatments allowed an accurate determination of the plasma etch rates along both the a and c crystallographic directions of the graphite lattice. The etch rates were typically in the range of a few nm per min along the a axis, and the equivalent of 1-6 graphene layers per min along the c axis. The results pointed to the existence of two main plasma etching regimes, related to short (<20-30 min) and long (> or =30 min) treatment times. This was inferred not only from the measured plasma etch rates but also from the observation of fundamental differences in the atomic-scale surface structure of the plasma-treated HOPG samples, and from the general mechanical behavior of the materials under the action of the AFM tip. In particular, atomic-scale STM imaging suggested a change from a defected, but essentially graphitic, surface in the first regime to an amorphous carbon surface in the second regime. Together with AFM and STM, Raman spectroscopy and XPS provided a consistent picture of the surface structure and chemistry of the plasma-modified HOPG in the two regimes. The implications of these results as well as the possible mechanism that drives the plasma etching process in the two regimes are discussed.

Role of the trigonal warping on the minimal conductivity of bilayer graphene

Using a reformulated Kubo formula we calculate the zero-energy minimal conductivity of bilayer graphene taking into account the small but finite trigonal warping. We find that the conductivity is independent of the strength of the trigonal warping and it is 3 times as large as that without trigonal warping and 6 times larger than that in single layer graphene. Although the trigonal warping of the dispersion relation around the valleys in the Brillouin zone is effective only for low-energy excitations, our result shows that its role cannot be neglected in the zero-energy minimal conductivity.

Quantum Hall Effect in a Gate-Controlled p-n Junction of Graphene

The unique band structure of graphene allows reconfigurable electric-field control of carrier type and density, making graphene an ideal candidate for bipolar nanoelectronics. We report the realization of a single-layer graphene p-n junction in which carrier type and density in two adjacent regions are locally controlled by electrostatic gating. Transport measurements in the quantum Hall regime reveal new plateaus of two-terminal conductance across the junction at 1 and 32 times the quantum of conductance, e(2)/h, consistent with recent theory. Beyond enabling investigations in condensed-matter physics, the demonstrated local-gating technique sets the foundation for a future graphene-based bipolar technology.

Transverse field effect in graphene ribbons

It is shown that a graphene ribbon, a ballistic strip of carbon monolayer, may serve as a quantum wire whose electronic properties can be continuously and reversibly controlled by an externally applied transverse voltage. The electron bands of armchair-edge ribbons undergo dramatic transformations: The Fermi surface fractures, Fermi velocity and effective mass change sign, and excitation gaps are reduced by the transverse field. These effects are manifest in the conductance plateaus, van Hove singularities, thermopower, and activated transport. The control over one-dimensional bands may help enhance effects of electron correlations, and be utilized in device applications.

Surface transfer p-type doping of epitaxial graphene

Epitaxial graphene thermally grown on 6H-SiC(0001) can be p-type doped via a novel surface transfer doping scheme by modifying the surface with the electron acceptor, tetrafluoro-tetracyanoquinodimethane (F4-TCNQ). Synchrotron-based high-resolution photoemission spectroscopy reveals that electron transfer from graphene to adsorbed F4-TCNQ is responsible for the p-type doping of graphene. This novel surface transfer doping scheme by surface modification with appropriate molecular acceptors represents a simple and effective method to nondestructively dope epitaxial graphene for future nanoelectronics applications.

Enhanced half-metallicity in edge-oxidized zigzag graphene nanoribbons

We present a comprehensive theoretical study of the electronic properties and relative stabilities of edge-oxidized zigzag graphene nanoribbons. The oxidation schemes considered include hydroxyl, lactone, ketone, and ether groups. Using screened exchange density functional theory, we show that these oxidized ribbons are more stable than hydrogen-terminated nanoribbons except for the case of the etheric groups. The stable oxidized configurations maintain a spin-polarized ground state with antiferromagnetic ordering localized at the edges, similar to the fully hydrogenated counterparts. More important, edge oxidation is found to lower the onset electric field required to induce half-metallic behavior and extend the overall field range at which the systems remain half-metallic. Once the half-metallic state is reached, further increase of the external electric field intensity produces a rapid decrease in the spin magnetization up to a point where the magnetization is quenched completely. Finally, we find that oxygen-containing edge groups have a minor effect on the energy difference between the antiferromagnetic ground state and the above-lying ferromagnetic state.

Nonlocal exchange interaction removes half-metallicity in graphene nanoribbons

Band gap studies of zigzag-edge graphene ribbons are presented. While earlier calculations at LDA level show that zigzag-edge graphene ribbons become half-metallic when cross-ribbon electric fields are applied, our calculations with hybrid density functional demonstrate that finite graphene ribbons behave as half-semiconductors. The spin-dependent band gap can be changed in a wide range, making possible many applications in spintronics.

Perfectly conducting channel and universality crossover in disordered graphene nanoribbons

The band structure of graphene ribbons with zigzag edges have two valleys well separated in momentum space, related to the two Dirac points of the graphene spectrum. The propagating modes in each valley contain a single chiral mode originating from a partially flat band at the band center. This feature gives rise to a perfectly conducting channel in the disordered system, if the impurity scattering does not connect the two valleys, i.e., for long-range impurity potentials. Ribbons with short-range impurity potentials, however, through intervalley scattering display ordinary localization behavior. The two regimes belong to different universality classes: unitary for long-range impurities and orthogonal for short-range impurities.

Gate electrostatics and quantum capacitance of graphene nanoribbons

Capacitance-voltage (C-V) characteristics are important for understanding fundamental electronic structures and device applications of nanomaterials. The C-V characteristics of graphene nanoribbons (GNRs) are examined using self-consistent atomistic simulations. The results indicate strong dependence of the GNR C-V characteristics on the edge shape. For zigzag edge GNRs, highly nonuniform charge distribution in the transverse direction due to edge states lowers the gate capacitance considerably, and the self-consistent electrostatic potential significantly alters the band structure and carrier velocity. For an armchair edge GNR, the quantum capacitance is a factor of 2 smaller than its corresponding zigzag carbon nanotube, and a multiple gate geometry is less beneficial for transistor applications. Magnetic field results in pronounced oscillations on C-V characteristics.

Electromagnetic-field-induced suppression of transport through n-p junctions in graphene

We study electronic transport through an n-p junction in graphene irradiated by an electromagnetic field (EF). In the absence of EF one may expect the perfect transmission of quasiparticles flowing perpendicular to the junction. We show that the resonant interaction of propagating quasiparticles with the EF induces a dynamic gap between electron and hole bands in the quasiparticle spectrum of graphene. In this case the strongly suppressed quasiparticle transmission is only possible due to interband tunneling. The effect may be used to control transport properties of diverse structures in graphene, e.g., n-p-n transistors and quantum dots, by variation of the intensity and frequency of the external radiation.

Quantum criticality and minimal conductivity in graphene with long-range disorder

We consider the conductivity sigma of graphene with negligible intervalley scattering at half filling. We derive the effective field theory, which, for the case of a potential disorder, is a symplectic-class sigma model including a topological term with theta=pi. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of e(2)/h. When the effective time-reversal symmetry is broken, the symmetry class becomes unitary, and sigma acquires the value characteristic for the quantum Hall transition.

Soft materials with graphitic nanostructures

This review article focuses on our recent studies on novel soft materials consisting of carbon nanotubes. Single-walled carbon nanotubes, when suspended in imidazolium ion-based ionic liquids and ground in an agate mortar, form physical gels (bucky gels), where heavily entangled bundles of carbon nanotubes are exfoliated to give highly dispersed, much finer bundles. By using bucky gels, the first printable actuators that operate in air for a long time without any external electrolyte are developed. Furthermore, the use of polymerizable ionic liquids as the gelling media results in the formation of electroconductive polymer/nanotube composites with enhanced mechanical properties. The article also highlights a new family of nanotubular graphite, via self-assembly of amphiphilic hexabenzocoronene (HBC) derivatives. The nanotubes consist of a graphitic wall composed of a great number of pi-stacked HBC units and are electroconductive upon oxidation. The use of amphiphilic HBCs with functional groups results in the formation of nanotubes with various interesting properties.

Chirality and correlations in graphene

Graphene is described at low energy by a massless Dirac equation whose eigenstates have definite chirality. We show that the tendency of Coulomb interactions in lightly doped graphene to favor states with larger net chirality leads to suppressed spin and charge susceptibilities. Our conclusions are based on an evaluation of graphene's exchange and random-phase-approximation correlation energies. The suppression is a consequence of the quasiparticle chirality switch which enhances quasiparticle velocities near the Dirac point.

Transport measurements across a tunable potential barrier in graphene

The peculiar nature of electron scattering in graphene is among many exciting theoretical predictions for the physical properties of this material. To investigate electron scattering properties in a graphene plane, we have created a gate-tunable potential barrier within a single-layer graphene sheet. We report measurements of electrical transport across this structure as the tunable barrier potential is swept through a range of heights. When the barrier is sufficiently strong to form a bipolar junction (n-p-n or p-n-p) within the graphene sheet, the resistance across the barrier sharply increases. We compare these results to predictions for both diffusive and ballistic transport, as the barrier rises on a length scale comparable to the mean free path. Finally, we show how a magnetic field modifies transport across the barrier.

Atomic structure of graphene on SiO2

We employ scanning probe microscopy to reveal atomic structures and nanoscale morphology of graphene-based electronic devices (i.e., a graphene sheet supported by an insulating silicon dioxide substrate) for the first time. Atomic resolution scanning tunneling microscopy images reveal the presence of a strong spatially dependent perturbation, which breaks the hexagonal lattice symmetry of the graphitic lattice. Structural corrugations of the graphene sheet partially conform to the underlying silicon oxide substrate. These effects are obscured or modified on graphene devices processed with normal lithographic methods, as they are covered with a layer of photoresist residue. We enable our experiments by a novel cleaning process to produce atomically clean graphene sheets.

Intrinsic current-voltage characteristics of graphene nanoribbon transistors and effect of edge doping

We demonstrate that the electronic devices built on patterned graphene nanoribbons (GNRs) can be made with atomic-perfect-interface junctions and controlled doping via manipulation of edge terminations. Using first-principles transport calculations, we show that the GNR field effect transistors can achieve high performance levels similar to those made from single-walled carbon nanotubes, with ON/OFF ratios on the order of 10(3)-10(4), subthreshold swing of 60 meV per decade, and transconductance of 9.5 x 10(3) Sm-1.

Effect of electron-electron interactions on the conductivity of clean graphene

Minimal conductivity of a single undoped graphene layer is known to be of the order of the conductance quantum, independent of the electron velocity. We show that this universality does not survive electron-electron interaction, which results in nontrivial frequency dependence. We begin with analyzing the perturbation theory in the interaction parameter g for the electron self-energy and observe the failure of the random-phase approximation. The optical conductivity is then derived from the quantum kinetic equation, and the exact result is obtained in the limit when g<<1<< g|lnomega|.

High-resolution scanning tunneling microscopy imaging of mesoscopic graphene sheets on an insulating surface

We present scanning tunneling microscopy (STM) images of single-layer graphene crystals examined under ultrahigh vacuum conditions. The samples, with lateral dimensions on the micrometer scale, were prepared on a silicon dioxide surface by direct exfoliation of crystalline graphite. The single-layer films were identified by using Raman spectroscopy. Topographic images of single-layer samples display the honeycomb structure expected for the full hexagonal symmetry of an isolated graphene monolayer. The absence of observable defects in the STM images is indicative of the high quality of these films. Crystals composed of a few layers of graphene also were examined. They exhibited dramatically different STM topography, displaying the reduced threefold symmetry characteristic of the surface of bulk graphite.

Energy band-gap engineering of graphene nanoribbons

We investigate electronic transport in lithographically patterned graphene ribbon structures where the lateral confinement of charge carriers creates an energy gap near the charge neutrality point. Individual graphene layers are contacted with metal electrodes and patterned into ribbons of varying widths and different crystallographic orientations. The temperature dependent conductance measurements show larger energy gaps opening for narrower ribbons. The sizes of these energy gaps are investigated by measuring the conductance in the nonlinear response regime at low temperatures. We find that the energy gap scales inversely with the ribbon width, thus demonstrating the ability to engineer the band gap of graphene nanostructures by lithographic processes.

Interlayer interaction and electronic screening in multilayer graphene investigated with angle-resolved photoemission spectroscopy

The unusual transport properties of graphene are the direct consequence of a peculiar band structure near the Dirac point. We determine the shape of the pi bands and their characteristic splitting, and find the transition from two-dimensional to bulk character for 1 to 4 layers of graphene by angle-resolved photoemission. By detailed measurements of the pi bands we derive the stacking order, layer-dependent electron potential, screening length, and strength of interlayer interaction by comparison with tight binding calculations, yielding a comprehensive description of multilayer graphene's electronic structure.

Dissipative quantum hall effect in graphene near the Dirac point

We report on the unusual nature of the nu=0 state in the integer quantum Hall effect (QHE) in graphene and show that electron transport in this regime is dominated by counterpropagating edge states. Such states, intrinsic to massless Dirac quasiparticles, manifest themselves in a large longitudinal resistivity rho(xx) > or approximately h/e(2), in striking contrast to rho(xx) behavior in the standard QHE. The nu=0 state in graphene is also predicted to exhibit pronounced fluctuations in rho(xy) and rho(xx) and a smeared zero Hall plateau in sigma(xy), in agreement with experiment. The existence of gapless edge states puts stringent constraints on possible theoretical models of the nu=0 state.

Carrier transport in two-dimensional graphene layers

Carrier transport in gated 2D graphene monolayers is considered in the presence of scattering by random charged impurity centers with density n(i). Excellent quantitative agreement is obtained (for carrier density n>10(12) cm(-2)) with existing experimental data. The conductivity scales linearly with n/n(i) in the theory. We explain the experimentally observed asymmetry between electron and hole conductivities, and the high-density saturation of conductivity for the highest mobility samples. We argue that the experimentally observed saturation of conductivity at low density arises from the charged impurity induced inhomogeneity in the graphene carrier density which becomes severe for n less, similarn(i) approximately 10(12) cm(-2).

Weak localization in bilayer graphene

We have performed the first experimental investigation of quantum interference corrections to the conductivity of a bilayer graphene structure. A negative magnetoresistance--a signature of weak localization--is observed at different carrier densities, including the electroneutrality region. It is very different, however, from the weak localization in conventional two-dimensional systems. We show that it is controlled not only by the dephasing time, but also by different elastic processes that break the effective time-reversal symmetry and provide intervalley scattering.

Electric field effect tuning of electron-phonon coupling in graphene

Gate-modulated low-temperature Raman spectra reveal that the electric field effect (EFE), pervasive in contemporary electronics, has marked impacts on long-wavelength optical phonons of graphene. The EFE in this two-dimensional honeycomb lattice of carbon atoms creates large density modulations of carriers with linear dispersion (known as Dirac fermions). Our EFE Raman spectra display the interactions of lattice vibrations with these unusual carriers. The changes of phonon frequency and linewidth demonstrate optically the particle-hole symmetry about the charge-neutral Dirac point. The linear dependence of the phonon frequency on the EFE-modulated Fermi energy is explained as the electron-phonon coupling of massless Dirac fermions.

Randomness-induced XY ordering in a graphene quantum hall ferromagnet

Valley-polarized quantum Hall states in graphene are described by a Heisenberg O(3) ferromagnet model, with the ordering type controlled by the strength and the sign of the valley anisotropy. A mechanism resulting from electron coupling to the strain-induced gauge field, giving a leading contribution to the anisotropy, is described in terms of an effective random magnetic field aligned with the ferromagnet z axis. We argue that such a random field stabilizes the XY ferromagnet state, which is a coherent equal-weight mixture of the K and K' valley states. The implications such as the Berezinskii-Kosterlitz-Thouless ordering transition and topological defects with half-integer charge are discussed.

Anomalous absorption line in the magneto-optical response of graphene

The intensity as well as position in energy of the absorption lines in the infrared conductivity of graphene, both exhibit features that are directly related to the Dirac nature of its quasiparticles. We show that the evolution of the pattern of absorption lines as the chemical potential is varied encodes the information about the presence of the anomalous lowest Landau level. The first absorption line related to this level always appears with full intensity or is entirely missing, while all other lines disappear in two steps. We demonstrate that if a gap develops, the main absorption line splits into two provided that the chemical potential is greater than or equal to the gap.

Superconducting states of pure and doped graphene

We study the superconducting phases of the two-dimensional honeycomb lattice of graphene. We find two spin singlet pairing states; s wave and an exotic p+ip that is possible because of the special structure of the honeycomb lattice. At half filling, the p+ip phase is gapless and superconductivity is a hidden order. We discuss the possibility of a superconducting state in metal coated graphene.

Electrostatic deposition of graphene

Loose graphene sheets, one to a few atomic layers thick, are often observed on freshly cleaved HOPG surfaces. A straightforward technique using electrostatic attraction is demonstrated to transfer these graphene sheets to a selected substrate. Sheets from one to 22 layers thick have been transferred by this method. One sheet after initial deposition is measured by atomic force microscopy to be only an atomic layer thick (∼0.35 nm). A few weeks later, this height is seen to increase to ∼0.8 nm. Raman spectroscopy of a single layer sheet shows the emergence of an intense D band which dramatically decreases as the number of layers in the sheet increase. The intense D band in monolayer graphene is attributed to the graphene conforming to the roughness of the substrate. The disruption of the C-C bonds within the single graphene layer could also contribute to this intense D band as evidenced by the emergence of a new band at 1620 cm(-1).

Tunable quantum dots in bilayer graphene

We demonstrate theoretically that quantum dots in bilayers of graphene can be realized. A position-dependent doping breaks the equivalence between the upper and lower layer and lifts the degeneracy of the positive and negative momentum states of the dot. Numerical results show the simultaneous presence of electron and hole confined states for certain doping profiles and a remarkable angular momentum dependence of the quantum dot spectrum, which is in sharp contrast with that for conventional semiconductor quantum dots. We predict that the optical spectrum will consist of a series of nonequidistant peaks.

Impurities in a biased graphene bilayer

We study the problem of impurities and midgap states in a biased graphene bilayer. We show that the properties of the bound states, such as localization lengths and binding energies, can be controlled externally by an electric field effect. Moreover, the band gap is renormalized and impurity bands are created at finite impurity concentrations. Using the coherent potential approximation, we calculate the electronic density of states and its dependence on the applied bias voltage.

Novel electric field effects on Landau levels in graphene

A new effect in graphene in the presence of crossed uniform electric and magnetic fields is predicted. Landau levels are shown to be modified in an unexpected fashion by the electric field, leading to a collapse of the spectrum, when the value of electric to magnetic field ratio exceeds a certain critical value. Our theoretical results, strikingly different from the standard 2D electron gas, are explained using a "Lorentz boost," and as an "instability of a relativistic quantum field vacuum." It is a remarkable case of emergent relativistic type phenomena in nonrelativistic graphene. We also discuss few possible experimental consequence.

Quantum Hall Effect in Polar Oxide Heterostructures

We observed Shubnikov-de Haas oscillation and the quantum Hall effect in a high-mobility two-dimensional electron gas in polar ZnO/Mg(x)Zn(1-x)O heterostructures grown by laser molecular beam epitaxy. The electron density could be controlled in a range of 0.7 x 10(12) to 3.7 x 10(12) per square centimeter by tuning the magnesium content in the barriers and the growth polarity. From the temperature dependence of the oscillation amplitude, the effective mass of the two-dimensional electrons was derived as 0.32 +/- 0.03 times the free electron mass. Demonstration of the quantum Hall effect in an oxide heterostructure presents the possibility of combining quantum Hall physics with the versatile functionality of metal oxides in complex heterostructures.

Conical diffraction and gap solitons in honeycomb photonic lattices

We study wave dynamics in honeycomb photonic lattices, and demonstrate the unique phenomenon of conical diffraction around the singular diabolical (zero-effective-mass) points connecting the first and second bands. This constitutes the prediction and first experimental observation of conical diffraction arising solely from a periodic potential. It is also the first study on k space singularities in photonic lattices. In addition, we demonstrate "honeycomb gap solitons" residing in the gap between the second and the third bands, reflecting the special properties of these lattices.

The Focusing of Electron Flow and a Veselago Lens in Graphene p-n Junctions

The focusing of electric current by a single p-n junction in graphene is theoretically predicted. Precise focusing may be achieved by fine-tuning the densities of carriers on the n- and p-sides of the junction to equal values. This finding may be useful for the engineering of electronic lenses and focused beam splitters using gate-controlled n-p-n junctions in graphene-based transistors.