Distribution of volumes and coordination number in jammed matter: mesoscopic ensemble

We investigate the distribution of the volume and coordination number associated to each particle in a jammed packing of monodisperse hard sphere using the mesoscopic ensemble developed in Nature 453, 606 (2008). Theory predicts an exponential distribution of the orientational volumes for random close packings and random loose packings. A comparison with computer generated packings reveals deviations from the theoretical prediction in the volume distribution, which can be better modeled by a compressed exponential function. On the other hand, the average of the volumes is well reproduced by the theory leading to good predictions of the limiting densities of RCP and RLP. We discuss a more exact theory to capture the volume distribution in its entire range. The available data suggests a plausible order/disorder transition defining random close packings. Finally, we consider an extended ensemble to calculate the coordination number distribution which is shown to be of an exponential and inverse exponential form for coordinations larger and smaller than the average, respectively, in reasonable agreement with the simulated data.Comment: 20 pages, 6 figures, accepted by JSTA

New Candidates for Topological Insulators : Pb-based chalcogenide series

Here, we theoretically predict that the series of Pb-based layered chalcogenides, Pb$_n$Bi$_2$Se$_{n+3}$ and Pb$_n$Sb$_2$Te$_{n+3}$, are possible new candidates for topological insulators. As $n$ increases, the phase transition from a topological insulator to a band insulator is found to occur between $n=2$ and 3 for both series. Significantly, among the new topological insulators, we found a bulk band gap of 0.40eV in PbBi$_2$Se$_4$ which is one of the largest gap topological insulators, and that Pb$_2$Sb$_2$Te$_5$ is located in the immediate vicinity of the topological phase boundary, making its topological phase easily tunable by changing external parameters such as lattice constants. Due to the three-dimensional Dirac cone at the phase boundary, massless Dirac fermions also may be easily accessible in Pb$_2$Sb$_2$Te$_5$

Formations and dynamics of two-dimensional spinning asymmetric quantum droplets controlled by a PT-symmetric potential

In this paper, vortex solitons are produced for a variety of 2D spinning quantum droplets (QDs) in a PT-symmetric potential, modeled by the amended Gross-Pitaevskii equation with Lee-Huang-Yang corrections. In particular, exact QD states are obtained under certain parameter constraints, providing a guide to finding the respective generic family. In a parameter region of the unbroken PT symmetry, different families of QDs originating from the linear modes are obtained in the form of multipolar and vortex droplets at low and high values of the norm, respectively, and their stability is investigated. In the spinning regime, QDs become asymmetric above a critical rotation frequency, most of them being stable. The effect of the PT -symmetric potential on the spinning and nonspinning QDs is explored by varying the strength of the gain-loss distribution. Generally, spinning QDs trapped in the PT -symmetric potential exhibit asymmetry due to the energy flow affected by the interplay of the gain-loss distribution and rotation. Finally, interactions between spinning or nonspinning QDs are explored, exhibiting elastic collisions under certain conditions.Comment: 18 pages, 10 figures (to be published in Chaos

Graded InGaN Buffers for Strain Relaxation in GaN/InGaN Epliayers Grown on Sapphire

Graded InGaN buffers are employed to relax the strain arising from the lattice and thermal mismatches between GaN/InGaN epilayers grown on sapphire. The formation of V-pits in linearly graded InGaN/GaN bulk epilayers is illustrated. The V-pits were sampled using Atomic Force Microscopy and Scanning Electron Microscopy to examine their variation from the theoretical geometry shape. We discovered that the size of the V-pit opening in linearly graded InGaN, with and without GaN cap layer, has a Gaussian distribution. As such, we deduce that the V-pits are produced at different rates, as the growth of the InGaN layer progresses. In Stage I, the V-pits form at a slow rate at the beginning and then accelerate in Stage II when a critical thickness is reached before decelerating in Stage III after arriving at a mean size. It is possible to fill the V-pits by growing a GaN cap layer. It turns out that the filling of the V-pits is more effective at lower growth temperature of the GaN cap layer and the size of the V-pits opening, which is continued in to GaN cap layer, is not dependent on the GaN cap layer thickness. Furthermore, graded InGaN/GaN layers display better strain relaxation as compared to conventionally grown bulk GaN. By employing a specially design configuration, the V-pits can be eliminated from the InGaN epilayer.Singapore-MIT Alliance (SMA

Graded InGaN Buffers for Strain Relaxation in GaN/InGaN Epilayers Grown on sapphire

Graded InGaN buffers were employed to relax the strain arising from the lattice and thermal mismatch in GaN/InGaN epilayers grown on sapphire. An enhanced strain relaxation was observed in GaN grown on a stack of five InGaN layers, each 200 nm thick with the In content increased in each layer, and with an intermediate thin GaN layer, 10 nm thick inserted between the InGaN layers, as compared to the conventional two-step growth of GaN epilayer on sapphire. The function of the intermediate layer is to progressively relax the strain and to annihilate the dislocations that build up in the InGaN layer. If the InGaN layers were graded too rapidly, more dislocations will be generated. This increases the probability of the dislocations getting entangled and thereby impeding the motion of the dislocations to relax the strain in the InGaN layer. The optimum growth conditions of the intermediate layer play a major role in promoting the suppression and filling of the V-pits in the GaN cap layer, and were empirically found to be a thin 10 nm GaN grown at 750 0°C and annealed at 1000 0°C.Singapore-MIT Alliance (SMA

Application of Edwards' statistical mechanics to high dimensional jammed sphere packings

The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song \emph{et al.}, Nature (London) {\bf 453}, 629 (2008)] is generalized to arbitrary dimension $d$ using a liquid-state description. The asymptotic high-dimensional behavior of the self-consistent relation is obtained by saddle-point evaluation and checked numerically. The resulting random close packing density scaling $\phi\sim d\,2^{-d}$ is consistent with that of other approaches, such as replica theory and density functional theory. The validity of various structural approximations is assessed by comparing with three- to six-dimensional isostatic packings obtained from simulations. These numerical results support a growing accuracy of the theoretical approach with dimension. The approach could thus serve as a starting point to obtain a geometrical understanding of the higher-order correlations present in jammed packings.Comment: 13 pages, 7 figure

High Indium Concentration InGaN/GaN Grown on Sapphire Substrate by MOCVD

The InGaN system provides the opportunity to fabricate light emitting devices over the whole visible and ultraviolet spectrum due to band-gap energies E[subscript g] varying between 3.42 eV for GaN and 1.89 eV for InN. However, high In content in InGaN layers will result in a significant degradation of the crystalline quality of the epitaxial layers. In addition, unlike other III-V compound semiconductors, the ratio of gallium to indium incorporated in InGaN is in general not a simple function of the metal atomic flux ratio, f[subscript Ga]/f[subscript In]. Instead, In incorporation is complicated by the tendency of gallium to incorporate preferentially and excess In to form metallic droplets on the growth surface. This phenomenon can definitely affect the In distribution in the InGaN system. Scanning electron microscopy, room temperature photoluminescence, and X-ray diffraction techniques have been used to characterize InGaN layer grown on InN and InGaN buffers. The growth was done on c-plane sapphire by MOCVD. Results showed that green emission was obtained which indicates a relatively high In incorporation.Singapore-MIT Alliance (SMA

Quark-Meson Coupling Model for a Nucleon

The quark-meson coupling model for a nucleon is considered. The model describes a nucleon as an MIT bag, in which quarks are coupled to scalar and vector mesons. A set of coupled equations for the quark and the meson fields are obtained and are solved in a self-consistent way. It is shown that the mass of a nucleon as a dressed MIT bag interacting with sigma- and omega-meson fields significantly differs from the mass of a free MIT bag. A few sets of model parameters are obtained so that the mass of a dressed MIT bag becomes the nucleon mass. The results of our calculations imply that the self-energy of the bag in the quark-meson coupling model is significant and needs to be considered in doing the nuclear matter calculations.Comment: 3 figure

Platinum composite nanowires for ultrasensitive mass detection

Platinum (Pt) composite nanowires were grown on the tip of tungsten (W) microprobes by focused-electron-beam induced chemical vapor deposition (FEB-CVD). An electrical field was used to drive a transversal mechanical vibration of the nanowires. Such nanowire vibrations were found to display the first and second harmonic resonances with frequencies in the range of tens of MHz. The Young's modulus of the nanowires was estimated to be in the range of (1.4 ± 0.1) × 102 GPa to (4.7 ± 0.2) × 102 GPa, dependent on the wire size. A mass responsivity of 2.1 × 1021 Hz/kg Hz/kg was demonstrated with the minimum detectable mass of about 0.4 attogram. Our results indicated the potentials of FEB-CVD for the fabrication of nano-balances on any surface for ultra-sensitive mechanical applications

Jamming II: Edwards' statistical mechanics of random packings of hard spheres

The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 60's. This problem finds applications spanning from the mathematician's pencil, the processing of granular materials, the jamming and glass transitions, all the way to fruit packing in every grocery. There are presently numerous experiments showing that the loosest way to pack spheres gives a density of ~55% (RLP) while filling all the loose voids results in a maximum density of ~63-64% (RCP). While those values seem robustly true, to this date there is no physical explanation or theoretical prediction for them. Here we show that random packings of monodisperse hard spheres in 3d can pack between the densities 4/(4 + 2 \sqrt 3) or 53.6% and 6/(6 + 2 \sqrt 3) or 63.4%, defining RLP and RCP, respectively. The reason for these limits arises from a statistical picture of jammed states in which the RCP can be interpreted as the ground state of the ensemble of jammed matter with zero compactivity, while the RLP arises in the infinite compactivity limit. We combine an extended statistical mechanics approach 'a la Edwards' (where the role traditionally played by the energy and temperature in thermal systems is substituted by the volume and compactivity) with a constraint on mechanical stability imposed by the isostatic condition. Ultimately, our results lead to a phase diagram that provides a unifying view of the disordered hard sphere packing problem.Comment: 55 pages, 19 figures, C. Song, P. Wang, H. A. Makse, A phase diagram for jammed matter, Nature 453, 629-632 (2008