Quantum Algorithm for Triangle Finding in Sparse Graphs

This paper presents a quantum algorithm for triangle finding over sparse graphs that improves over the previous best quantum algorithm for this task by Buhrman et al. [SIAM Journal on Computing, 2005]. Our algorithm is based on the recent $\tilde O(n^{5/4})$-query algorithm given by Le Gall [FOCS 2014] for triangle finding over dense graphs (here $n$ denotes the number of vertices in the graph). We show in particular that triangle finding can be solved with $O(n^{5/4-\epsilon})$ queries for some constant $\epsilon>0$ whenever the graph has at most $O(n^{2-c})$ edges for some constant $c>0$.Comment: 13 page

A dusty pinwheel nebula around the massive star WR 104

Wolf-Rayet (WR) stars are luminous massive blue stars thought to be immediate precursors to the supernova terminating their brief lives. The existence of dust shells around such stars has been enigmatic since their discovery some 30 years ago; the intense radiation field from the star should be inimical to dust survival. Although dust-creation models, including those involving interacting stellar winds from a companion star, have been put forward, high-resolution observations are required to understand this phenomena. Here we present resolved images of the dust outflow around Wolf-Rayet WR 104, obtained with novel imaging techniques, revealing detail on scales corresponding to about 40 AU at the star. Our maps show that the dust forms a spatially confined stream following precisely a linear (or Archimedian) spiral trajectory. Images taken at two separate epochs show a clear rotation with a period of 220 +/- 30 days. Taken together, these findings prove that a binary star is responsible for the creation of the circumstellar dust, while the spiral plume makes WR 104 the prototype of a new class of circumstellar nebulae unique to interacting wind systems.Comment: 7 pages, 2 figures, Appearing in Nature (1999 April 08

Gate-controlled Guiding of Electrons in Graphene

Ballistic semiconductor structures have allowed the realization of optics-like phenomena in electronics, including magnetic focusing and lensing. An extension that appears unique to graphene is to use both n and p carrier types to create electronic analogs of optical devices having both positive and negative indices of refraction. Here, we use gate-controlled density with both p and n carrier types to demonstrate the analog of the fiber-optic guiding in graphene. Two basic effects are investigated: (1) bipolar p-n junction guiding, based on the principle of angle-selective transmission though the graphene p-n interface, and (2) unipolar fiber-optic guiding, using total internal reflection controlled by carrier density. Modulation of guiding efficiency through gating is demonstrated and compared to numerical simulations, which indicates that interface roughness limits guiding performance, with few-nanometer effective roughness extracted. The development of p-n and fiber-optic guiding in graphene may lead to electrically reconfigurable wiring in high-mobility devices.Comment: supplementary materal at http://marcuslab.harvard.edu/papers/OG_SI.pd

Quantum interference and Klein tunneling in graphene heterojunctions

The observation of quantum conductance oscillations in mesoscopic systems has traditionally required the confinement of the carriers to a phase space of reduced dimensionality. While electron optics such as lensing and focusing have been demonstrated experimentally, building a collimated electron interferometer in two unconfined dimensions has remained a challenge due to the difficulty of creating electrostatic barriers that are sharp on the order of the electron wavelength. Here, we report the observation of conductance oscillations in extremely narrow graphene heterostructures where a resonant cavity is formed between two electrostatically created bipolar junctions. Analysis of the oscillations confirms that p-n junctions have a collimating effect on ballistically transmitted carriers. The phase shift observed in the conductance fringes at low magnetic fields is a signature of the perfect transmission of carriers normally incident on the junctions and thus constitutes a direct experimental observation of ``Klein Tunneling.''Comment: 13 pages and 6 figures including supplementary information. The paper has been modified in light of new theoretical results available at arXiv:0808.048

Tuning a Circular p-n Junction in Graphene from Quantum Confinement to Optical Guiding

The motion of massless Dirac-electrons in graphene mimics the propagation of photons. This makes it possible to control the charge-carriers with components based on geometrical-optics and has led to proposals for an all-graphene electron-optics platform. An open question arising from the possibility of reducing the component-size to the nanometer-scale is how to access and understand the transition from optical-transport to quantum-confinement. Here we report on the realization of a circular p-n junction that can be continuously tuned from the nanometer-scale, where quantum effects are dominant, to the micrometer scale where optical-guiding takes over. We find that in the nanometer-scale junction electrons are trapped in states that resemble atomic-collapse at a supercritical charge. As the junction-size increases, the transition to optical-guiding is signaled by the emergence of whispering-gallery modes and Fabry-Perot interference. The creation of tunable junctions that straddle the crossover between quantum-confinement and optical-guiding, paves the way to novel design-architectures for controlling electronic transport.Comment: 16 pages, 4 figure

Quantum and classical confinement of resonant states in a trilayer graphene Fabry-Pérot interferometer

The advent of few-layer graphene has given rise to a new family of two-dimensional systems with emergent electronic properties governed by relativistic quantum mechanics. The multiple carbon sublattices endow the electronic wavefunctions with pseudospin, a lattice analogue of the relativistic electron spin, whereas the multilayer structure leads to electric-field-effect tunable electronic bands. Here we use these properties to realize giant conductance oscillations in ballistic trilayer graphene Fabry-Pérot interferometers, which result from phase coherent transport through resonant bound states beneath an electrostatic barrier. We confine these states by selectively decoupling them from the leads, resulting in transport via non-resonant states and suppression of the giant oscillations. The confinement is achieved both classically, by manipulating quasiparticle momenta with a magnetic field, and quantum mechanically, by locally varying the pseudospin character of the carrier wavefunctions. Our results illustrate the unique potential of trilayer graphene as a versatile platform for electron optics and pseudospintronics.United States. Office of Naval Research (GATE MURI)National Science Foundation (U.S.) (Career Award DMR-0845287)Conselho Nacional de Pesquisas (Brazil

Wigner Crystallization in a Quasi-3D Electronic System

When a strong magnetic field is applied perpendicularly (along z) to a sheet confining electrons to two dimensions (x-y), highly correlated states emerge as a result of the interplay between electron-electron interactions, confinement and disorder. These so-called fractional quantum Hall (FQH) liquids form a series of states which ultimately give way to a periodic electron solid that crystallizes at high magnetic fields. This quantum phase of electrons has been identified previously as a disorder-pinned two-dimensional Wigner crystal with broken translational symmetry in the x-y plane. Here, we report our discovery of a new insulating quantum phase of electrons when a very high magnetic field, up to 45T, is applied in a geometry parallel (y-direction) to the two-dimensional electron sheet. Our data point towards this new quantum phase being an electron solid in a "quasi-3D" configuration induced by orbital coupling with the parallel field

Non-thermal emission processes in massive binaries

In this paper, I present a general discussion of several astrophysical processes likely to play a role in the production of non-thermal emission in massive stars, with emphasis on massive binaries. Even though the discussion will start in the radio domain where the non-thermal emission was first detected, the census of physical processes involved in the non-thermal emission from massive stars shows that many spectral domains are concerned, from the radio to the very high energies. First, the theoretical aspects of the non-thermal emission from early-type stars will be addressed. The main topics that will be discussed are respectively the physics of individual stellar winds and their interaction in binary systems, the acceleration of relativistic electrons, the magnetic field of massive stars, and finally the non-thermal emission processes relevant to the case of massive stars. Second, this general qualitative discussion will be followed by a more quantitative one, devoted to the most probable scenario where non-thermal radio emitters are massive binaries. I will show how several stellar, wind and orbital parameters can be combined in order to make some semi-quantitative predictions on the high-energy counterpart to the non-thermal emission detected in the radio domain. These theoretical considerations will be followed by a census of results obtained so far, and related to this topic... (see paper for full abstract)Comment: 47 pages, 5 postscript figures, accepted for publication in Astronomy and Astrophysics Review. Astronomy and Astrophysics Review, in pres

Application of Graphene within Optoelectronic Devices and Transistors

Scientists are always yearning for new and exciting ways to unlock graphene's true potential. However, recent reports suggest this two-dimensional material may harbor some unique properties, making it a viable candidate for use in optoelectronic and semiconducting devices. Whereas on one hand, graphene is highly transparent due to its atomic thickness, the material does exhibit a strong interaction with photons. This has clear advantages over existing materials used in photonic devices such as Indium-based compounds. Moreover, the material can be used to 'trap' light and alter the incident wavelength, forming the basis of the plasmonic devices. We also highlight upon graphene's nonlinear optical response to an applied electric field, and the phenomenon of saturable absorption. Within the context of logical devices, graphene has no discernible band-gap. Therefore, generating one will be of utmost importance. Amongst many others, some existing methods to open this band-gap include chemical doping, deformation of the honeycomb structure, or the use of carbon nanotubes (CNTs). We shall also discuss various designs of transistors, including those which incorporate CNTs, and others which exploit the idea of quantum tunneling. A key advantage of the CNT transistor is that ballistic transport occurs throughout the CNT channel, with short channel effects being minimized. We shall also discuss recent developments of the graphene tunneling transistor, with emphasis being placed upon its operational mechanism. Finally, we provide perspective for incorporating graphene within high frequency devices, which do not require a pre-defined band-gap.Comment: Due to be published in "Current Topics in Applied Spectroscopy and the Science of Nanomaterials" - Springer (Fall 2014). (17 pages, 19 figures

Galactic and Extragalactic Samples of Supernova Remnants: How They Are Identified and What They Tell Us

Supernova remnants (SNRs) arise from the interaction between the ejecta of a supernova (SN) explosion and the surrounding circumstellar and interstellar medium. Some SNRs, mostly nearby SNRs, can be studied in great detail. However, to understand SNRs as a whole, large samples of SNRs must be assembled and studied. Here, we describe the radio, optical, and X-ray techniques which have been used to identify and characterize almost 300 Galactic SNRs and more than 1200 extragalactic SNRs. We then discuss which types of SNRs are being found and which are not. We examine the degree to which the luminosity functions, surface-brightness distributions and multi-wavelength comparisons of the samples can be interpreted to determine the class properties of SNRs and describe efforts to establish the type of SN explosion associated with a SNR. We conclude that in order to better understand the class properties of SNRs, it is more important to study (and obtain additional data on) the SNRs in galaxies with extant samples at multiple wavelength bands than it is to obtain samples of SNRs in other galaxiesComment: Final 2016 draft of a chapter in "Handbook of Supernovae" edited by Athem W. Alsabti and Paul Murdin. Final version available at https://doi.org/10.1007/978-3-319-20794-0_90-