Observation of Electron-Hole Puddles in Graphene Using a Scanning Single Electron Transistor

The electronic density of states of graphene is equivalent to that of relativistic electrons. In the absence of disorder or external doping the Fermi energy lies at the Dirac point where the density of states vanishes. Although transport measurements at high carrier densities indicate rather high mobilities, many questions pertaining to disorder remain unanswered. In particular, it has been argued theoretically, that when the average carrier density is zero, the inescapable presence of disorder will lead to electron and hole puddles with equal probability. In this work, we use a scanning single electron transistor to image the carrier density landscape of graphene in the vicinity of the neutrality point. Our results clearly show the electron-hole puddles expected theoretically. In addition, our measurement technique enables to determine locally the density of states in graphene. In contrast to previously studied massive two dimensional electron systems, the kinetic contribution to the density of states accounts quantitatively for the measured signal. Our results suggests that exchange and correlation effects are either weak or have canceling contributions.Comment: 13 pages, 5 figure

Valley filter and valley valve in graphene

It is known that the lowest propagating mode in a narrow ballistic ribbon of graphene may lack the twofold valley degeneracy of higher modes. Depending on the crystallographic orientation of the ribbon axis, the lowest mode mixes both valleys or lies predominantly in a single valley (chosen by the direction of propagation). We show, using a tight-binding model calculation, that a nonequilibrium valley polarization can be realized in a sheet of graphene, upon injection of current through a ballistic point contact with zigzag edges. The polarity can be inverted by local application of a gate voltage to the point contact region. Two valley filters in series may function as an electrostatically controlled ``valley valve'', representing a zero-magnetic-field counterpart to the familiar spin valve.Comment: RevTeX, 4 pages, 5 figure

Laser-induced etching of few-layer graphene synthesized by Rapid-Chemical Vapour Deposition on Cu thin films

The outstanding electrical and mechanical properties of graphene make it very attractive for several applications, Nanoelectronics above all. However a reproducible and non destructive way to produce high quality, large-scale area, single layer graphene sheets is still lacking. Chemical Vapour Deposition of graphene on Cu catalytic thin films represents a promising method to reach this goal, because of the low temperatures (T < 900 Celsius degrees) involved during the process and of the theoretically expected monolayer self-limiting growth. On the contrary such self-limiting growth is not commonly observed in experiments, thus making the development of techniques allowing for a better control of graphene growth highly desirable. Here we report about the local ablation effect, arising in Raman analysis, due to the heat transfer induced by the laser incident beam onto the graphene sample.Comment: v1:9 pages, 8 figures, submitted to SpringerPlus; v2: 11 pages, PDFLaTeX, 9 figures, revised peer-reviewed version resubmitted to SpringerPlus; 1 figure added, figure 1 and 4 replaced,typos corrected, "Results and discussion" section significantly extended to better explain etching mechanism and features of Raman spectra, references adde

Single to Double Hump Transition in the Equilibrium Distribution Function of Relativistic Particles

We unveil a transition from single peaked to bimodal velocity distribution in a relativistic fluid under increasing temperature, in contrast with a non-relativistic gas, where only a monotonic broadening of the bell-shaped distribution is observed. Such transition results from the interplay between the raise in thermal energy and the constraint of maximum velocity imposed by the speed of light. We study the Bose-Einstein, the Fermi-Dirac, and the Maxwell-J\"uttner distributions, all exhibiting the same qualitative behavior. We characterize the nature of the transition in the framework of critical phenomena and show that it is either continuous or discontinuous, depending on the group velocity. We analyze the transition in one, two, and three dimensions, with special emphasis on two-dimensions, for which a possible experiment in graphene, based on the measurement of the Johnson-Nyquist noise, is proposed.Comment: 5 pages, 5 figure

Observation of the Fractional Quantum Hall Effect in Graphene

When electrons are confined in two dimensions and subjected to strong magnetic fields, the Coulomb interactions between them become dominant and can lead to novel states of matter such as fractional quantum Hall liquids. In these liquids electrons linked to magnetic flux quanta form complex composite quasipartices, which are manifested in the quantization of the Hall conductivity as rational fractions of the conductance quantum. The recent experimental discovery of an anomalous integer quantum Hall effect in graphene has opened up a new avenue in the study of correlated 2D electronic systems, in which the interacting electron wavefunctions are those of massless chiral fermions. However, due to the prevailing disorder, graphene has thus far exhibited only weak signatures of correlated electron phenomena, despite concerted experimental efforts and intense theoretical interest. Here, we report the observation of the fractional quantum Hall effect in ultraclean suspended graphene, supporting the existence of strongly correlated electron states in the presence of a magnetic field. In addition, at low carrier density graphene becomes an insulator with an energy gap tunable by magnetic field. These newly discovered quantum states offer the opportunity to study a new state of matter of strongly correlated Dirac fermions in the presence of large magnetic fields

Bipolar supercurrent in graphene

Graphene -a recently discovered one-atom-thick layer of graphite- constitutes a new model system in condensed matter physics, because it is the first material in which charge carriers behave as massless chiral relativistic particles. The anomalous quantization of the Hall conductance, which is now understood theoretically, is one of the experimental signatures of the peculiar transport properties of relativistic electrons in graphene. Other unusual phenomena, like the finite conductivity of order 4e^2/h at the charge neutrality (or Dirac) point, have come as a surprise and remain to be explained. Here, we study the Josephson effect in graphene. Our experiments rely on mesoscopic superconducting junctions consisting of a graphene layer contacted by two closely spaced superconducting electrodes, where the charge density can be controlled by means of a gate electrode. We observe a supercurrent that, depending on the gate voltage, is carried by either electrons in the conduction band or by holes in the valence band. More importantly, we find that not only the normal state conductance of graphene is finite, but also a finite supercurrent can flow at zero charge density. Our observations shed light on the special role of time reversal symmetry in graphene and constitute the first demonstration of phase coherent electronic transport at the Dirac point.Comment: Under review, 12 pages, 4 Figs., suppl. info (v2 identical, resolved file problems

Room-temperature ferromagnetism in graphite driven by 2D networks of point defects

Ferromagnetism in carbon-based materials is appealing for both applications and fundamental science purposes because carbon is a light and bio-compatible material that contains only s and p electrons in contrast to traditional ferromagnets based on 3d or 4f electrons. Here we demonstrate direct evidence for ferromagnetic order locally at defect structures in highly oriented pyrolytic graphite (HOPG) with magnetic force microscopy and in bulk magnetization measurements at room temperature. Magnetic impurities have been excluded as the origin of the magnetic signal after careful analysis supporting an intrinsic magnetic behavior of carbon. The observed ferromagnetism has been attributed to originate from unpaired electron spins localized at grain boundaries of HOPG. Grain boundaries form two-dimensional arrays of point defects, where their spacing depends on the mutual orientation of two grains. Depending on the distance between these point defects, scanning tunneling spectroscopy of grain boundaries showed two intense split localized states for small distances between defects (< 4 nm) and one localized state at the Fermi level for large distances between defects (> 4 nm).Comment: 19 pages, 5 figure

First direct observation of Dirac fermions in graphite

Originating from relativistic quantum field theory, Dirac fermions have been recently applied to study various peculiar phenomena in condensed matter physics, including the novel quantum Hall effect in graphene, magnetic field driven metal-insulator-like transition in graphite, superfluid in 3He, and the exotic pseudogap phase of high temperature superconductors. Although Dirac fermions are proposed to play a key role in these systems, so far direct experimental evidence of Dirac fermions has been limited. Here we report the first direct observation of massless Dirac fermions with linear dispersion near the Brillouin zone (BZ) corner H in graphite, coexisting with quasiparticles with parabolic dispersion near another BZ corner K. In addition, we report a large electron pocket which we attribute to defect-induced localized states. Thus, graphite presents a novel system where massless Dirac fermions, quasiparticles with finite effective mass, and defect states all contribute to the low energy electronic dynamics.Comment: Nature Physics, in pres

Giant Faraday rotation in single- and multilayer graphene

Optical Faraday rotation is one of the most direct and practically important manifestations of magnetically broken time-reversal symmetry. The rotation angle is proportional to the distance traveled by the light, and up to now sizeable effects were observed only in macroscopically thick samples and in two-dimensional electron gases with effective thicknesses of several nanometers. Here we demonstrate that a single atomic layer of carbon - graphene - turns the polarization by several degrees in modest magnetic fields. The rotation is found to be strongly enhanced by resonances originating from the cyclotron effect in the classical regime and the inter-Landau-level transitions in the quantum regime. Combined with the possibility of ambipolar doping, this opens pathways to use graphene in fast tunable ultrathin infrared magneto-optical devices

Realization of a Tunable Artificial Atom at a Supercritically Charged Vacancy in Graphene

The remarkable electronic properties of graphene have fueled the vision of a graphene-based platform for lighter, faster and smarter electronics and computing applications. One of the challenges is to devise ways to tailor its electronic properties and to control its charge carriers. Here we show that a single atom vacancy in graphene can stably host a local charge and that this charge can be gradually built up by applying voltage pulses with the tip of a scanning tunneling microscope (STM). The response of the conduction electrons in graphene to the local charge is monitored with scanning tunneling and Landau level spectroscopy, and compared to numerical simulations. As the charge is increased, its interaction with the conduction electrons undergoes a transition into a supercritical regime 6-11 where itinerant electrons are trapped in a sequence of quasi-bound states which resemble an artificial atom. The quasi-bound electron states are detected by a strong enhancement of the density of states (DOS) within a disc centered on the vacancy site which is surrounded by halo of hole states. We further show that the quasi-bound states at the vacancy site are gate tunable and that the trapping mechanism can be turned on and off, providing a new mechanism to control and guide electrons in grapheneComment: 18 pages and 5 figures plus 14 pages and 15 figures of supplementary information. Nature Physics advance online publication, Feb 22 (2016