Room-temperature ballistic transport in narrow graphene strips

We investigate electron-phonon couplings, scattering rates, and mean free paths in zigzag-edge graphene strips with widths of the order of 10 nm. Our calculations for these graphene nanostrips show both the expected similarity with single-wall carbon nanotubes (SWNTs) and the suppression of the electron-phonon scattering due to a Dirichlet boundary condition that prohibits one major backscattering channel present in SWNTs. Low-energy acoustic phonon scattering is exponentially small at room temperature due to the large phonon wave vector required for backscattering. We find within our model that the electron-phonon mean free path is proportional to the width of the nanostrip and is approximately 70 $\mu$m for an 11-nm-wide nanostrip.Comment: 5 pages and 5 figure

Electronic structure of the cuprate superconducting and pseudogap phases from spectroscopic imaging STM

We survey the use of spectroscopic imaging scanning tunneling microscopy (SI-STM) to probe the electronic structure of underdoped cuprates. Two distinct classes of electronic states are observed in both the d-wave superconducting (dSC) and the pseudogap (PG) phases. The first class consists of the dispersive Bogoliubov quasiparticle excitations of a homogeneous d-wave superconductor, existing below a lower energy scale E = Delta(0). We find that the Bogoliubov quasiparticle interference (QPI) signatures of delocalized Cooper pairing are restricted to a k-space arc, which terminates near the lines connecting k = +/-(pi/a(0), 0) to k = +/-(0, pi/a(0)). This arc shrinks continuously with decreasing hole density such that Luttinger's theorem could be satisfied if it represents the front side of a hole-pocket that is bounded behind by the lines between k = +/-(pi/a(0), 0) and k = +/-(0, pi/a(0)). In both phases, the only broken symmetries detected for the vertical bar E vertical bar < Delta(0) states are those of a d-wave superconductor. The second class of states occurs proximate to the PG energy scale E = Delta(1). Here the non-dispersive electronic structure breaks the expected 90 degrees-rotational symmetry of electronic structure within each unit cell, at least down to 180 degrees-rotational symmetry. This electronic symmetry breaking was first detected as an electronic inequivalence at the two oxygen sites within each unit cell by using a measure of nematic (C-2) symmetry. Incommensurate non-dispersive conductance modulations, locally breaking both rotational and translational symmetries, coexist with this intra-unit-cell electronic symmetry breaking at E = Delta(1). Their characteristic wavevector Q is determined by the k-space points where Bogoliubov QPI terminates and therefore changes continuously with doping. The distinct broken electronic symmetry states (intra-unit-cell and finite Q) coexisting at E similar to Delta(1) are found to be indistinguishable in the dSC and PG phases. The next challenge for SI-STM studies is to determine the relationship of the E similar to Delta(1) broken symmetry electronic states with the PG phase, and with the E < Delta(0) states associated with Cooper pairing.Publisher PDFPeer reviewe

Commensurate 4a04a_0 period Charge Density Modulations throughout the Bi2Sr2CaCu2O8+xBi_2Sr_2CaCu_2O_{8+x} Pseudogap Regime

Theories based upon strong real space (r-space) electron electron interactions have long predicted that unidirectional charge density modulations (CDM) with four unit cell (4$a_0$) periodicity should occur in the hole doped cuprate Mott insulator (MI). Experimentally, however, increasing the hole density p is reported to cause the conventionally defined wavevector $Q_A$ of the CDM to evolve continuously as if driven primarily by momentum space (k-space) effects. Here we introduce phase resolved electronic structure visualization for determination of the cuprate CDM wavevector. Remarkably, this new technique reveals a virtually doping independent locking of the local CDM wavevector at $|Q_0|=2\pi/4a_0$ throughout the underdoped phase diagram of the canonical cuprate $Bi_2Sr_2CaCu_2O_8$. These observations have significant fundamental consequences because they are orthogonal to a k-space (Fermi surface) based picture of the cuprate CDM but are consistent with strong coupling r-space based theories. Our findings imply that it is the latter that provide the intrinsic organizational principle for the cuprate CDM state

Probability distribution of the sizes of largest erased-loops in loop-erased random walks

We have studied the probability distribution of the perimeter and the area of the k-th largest erased-loop in loop-erased random walks in two-dimensions for k = 1 to 3. For a random walk of N steps, for large N, the average value of the k-th largest perimeter and area scales as N^{5/8} and N respectively. The behavior of the scaled distribution functions is determined for very large and very small arguments. We have used exact enumeration for N <= 20 to determine the probability that no loop of size greater than l (ell) is erased. We show that correlations between loops have to be taken into account to describe the average size of the k-th largest erased-loops. We propose a one-dimensional Levy walk model which takes care of these correlations. The simulations of this simpler model compare very well with the simulations of the original problem.Comment: 11 pages, 1 table, 10 included figures, revte

Topological Defects Coupling Smectic Modulations to Intra-unit-cell Nematicity in Cuprate

We study the coexisting smectic modulations and intra-unit-cell nematicity in the pseudogap states of underdoped Bi2Sr2CaCu2O8+{\delta}. By visualizing their spatial components separately, we identified 2\pi topological defects throughout the phase-fluctuating smectic states. Imaging the locations of large numbers of these topological defects simultaneously with the fluctuations in the intra-unit-cell nematicity revealed strong empirical evidence for a coupling between them. From these observations, we propose a Ginzburg-Landau functional describing this coupling and demonstrate how it can explain the coexistence of the smectic and intra-unit-cell broken symmetries and also correctly predict their interplay at the atomic scale. This theoretical perspective can lead to unraveling the complexities of the phase diagram of cuprate high-critical-temperature superconductors

Throughput Maximization in Multiprocessor Speed-Scaling

We are given a set of $n$ jobs that have to be executed on a set of $m$ speed-scalable machines that can vary their speeds dynamically using the energy model introduced in [Yao et al., FOCS'95]. Every job $j$ is characterized by its release date $r_j$, its deadline $d_j$, its processing volume $p_{i,j}$ if $j$ is executed on machine $i$ and its weight $w_j$. We are also given a budget of energy $E$ and our objective is to maximize the weighted throughput, i.e. the total weight of jobs that are completed between their respective release dates and deadlines. We propose a polynomial-time approximation algorithm where the preemption of the jobs is allowed but not their migration. Our algorithm uses a primal-dual approach on a linearized version of a convex program with linear constraints. Furthermore, we present two optimal algorithms for the non-preemptive case where the number of machines is bounded by a fixed constant. More specifically, we consider: {\em (a)} the case of identical processing volumes, i.e. $p_{i,j}=p$ for every $i$ and $j$, for which we present a polynomial-time algorithm for the unweighted version, which becomes a pseudopolynomial-time algorithm for the weighted throughput version, and {\em (b)} the case of agreeable instances, i.e. for which $r_i \le r_j$ if and only if $d_i \le d_j$, for which we present a pseudopolynomial-time algorithm. Both algorithms are based on a discretization of the problem and the use of dynamic programming

Proposal for a CFT interpretation of Watts' differential equation for percolation

G. M. T. Watts derived that in two dimensional critical percolation the crossing probability Pi_hv satisfies a fifth order differential equation which includes another one of third order whose independent solutions describe the physically relevant quantities 1, Pi_h, Pi_hv. We will show that this differential equation can be derived from a level three null vector condition of a rational c=-24 CFT and motivate how this solution may be fitted into known properties of percolation.Comment: LaTeX, 20p, added references, corrected typos and additional content

OSSOS: XXVII. Population Estimates for Theoretically Stable Centaurs Between Uranus and Neptune

We calculate the upper bounds of the population of theoretically stable Centaur orbits between Uranus and Neptune. These small bodies are on low-eccentricity, low-inclination orbits in two specific bands of semi-major axis, centred at $\sim$24.6 au and $\sim$25.6 au. They exhibit unusually long Gyr-stable lifetimes in previously published numerical integrations, orders of magnitude longer than that of a typical Centaur. Despite the increased breadth and depth of recent solar system surveys, no such objects have been found. Using the Outer Solar System Origins Survey (OSSOS) survey simulator to calculate the detection efficiency for these objects in an ensemble of fully characterised surveys, we determine that a population of 72 stable Centaurs with absolute magnitude $H_{r}\leq10$ ($95\%$ confidence upper limit) could remain undetected. The upcoming Legacy Survey of Space and Time (LSST) will be able to detect this entire intrinsic population due to its complete coverage of the ecliptic plane. If detected, these objects will be interesting dynamically-accessible mission targets -- especially as comparison of the stable Centaur orbital phase space to the outcomes of several modern planetary migration simulations suggests that these objects could be close to primordial in nature.Comment: Accepted to PSJ. 8 pages, 3 figures. Comments welcom

Fermi surface instabilities at finite Temperature

We present a new method to detect Fermi surface instabilities for interacting systems at finite temperature. We first apply it to a list of cases studied previously, recovering already known results in a very economic way, and obtaining most of the information on the phase diagram analytically. As an example, in the continuum limit we obtain the critical temperature as an implicit function of the magnetic field and the chemical potential $T_c(\mu,h)$. By applying the method to a model proposed to describe reentrant behavior in $Sr_3Ru_2O_7$, we reproduce the phase diagram obtained experimentally and show the presence of a non-Fermi Liquid region at temperatures above the nematic phase.Comment: 10 pages, 10 figure

Families of Vicious Walkers

We consider a generalisation of the vicious walker problem in which N random walkers in R^d are grouped into p families. Using field-theoretic renormalisation group methods we calculate the asymptotic behaviour of the probability that no pairs of walkers from different families have met up to time t. For d>2, this is constant, but for d<2 it decays as a power t^(-alpha), which we compute to O(epsilon^2) in an expansion in epsilon=2-d. The second order term depends on the ratios of the diffusivities of the different families. In two dimensions, we find a logarithmic decay (ln t)^(-alpha'), and compute alpha' exactly.Comment: 20 pages, 5 figures. v.2: minor additions and correction