Evidence of gate-tunable topological excitations in two-dimensional electron systems

We report experimental observations of a new mechanism of charge transport in two-dimensional electron systems (2DESs) in the presence of strong Coulomb interaction and disorder. We show that at low enough temperature the conductivity tends to zero at a nonzero carrier density, which represents the point of essential singularity in a Berezinskii-Kosterlitz-Thouless-like transition. Our experiments with many 2DESs in GaAs/AlGaAs heterostructures suggest that the charge transport at low carrier densities is due to the melting of an underlying ordered ground state through proliferation of topological defects. Independent measurement of low-frequency conductivity noise supports this scenario.

Quenching across quantum critical points: Role of topological patterns

We introduce a one-dimensional version of the Kitaev model consisting of spins on a two-legged ladder and characterized by Z(2) invariants on the plaquettes of the ladder. We map the model to a fermionic system and identify the topological sectors associated with different Z2 patterns in terms of fermion occupation numbers. Within these different sectors, we investigate the effect of a linear quench across a quantum critical point. We study the dominant behavior of the system by employing a Landau-Zener-type analysis of the effective Hamiltonian in the low-energy subspace for which the effective quenching can sometimes be non-linear. We show that the quenching leads to a residual energy which scales as a power of the quenching rate, and that the power depends on the topological sectors and their symmetry properties in a non-trivial way. This behavior is consistent with the general theory of quantum quenching, but with the correlation length exponent nu being different in different sectors. Copyright (C) EPLA, 2010

Interdiffusion study on Co(W) solid solution and topological close-packed mu phase in Co-W system

An interdiffusion study is conducted on the Co-W system by a diffusion couple technique. The interdiffusion coefficient of the Co(W) solid solution and the Co7W6 mu phase is determined. The activation energy is found to increase with the W content of the Co(W) solid solution. (C) 2010 Elsevier Ltd. All rights reserved.

Fluorescence and topological gap of conjugated phenylene polymers

We propose that strong fluorescence in conjugated polymers requires a dipole-allowed state to be the lowest singlet. Hückel theory for para-conjugated phenyl rings yields an extended, topologically one-dimensional ?-system with increased alternation, states localized on each ring, and charge-transfer excitations between them. Exact Pariser�Parr�Pople results and molecular spectra for oligomers support a topological contribution and a lowest dipole-allowed singlet in phenylene polymers.

Linear dynamics and active control of an elastically supported travelling string

In this paper, the linear dynamics and active control of a string travelling with uniform velocity is presented. Discrete elastic supports are introduced along the length of the string. Finite element formulation is adopted to obtain the governing equations of motion. The velocity of translation introduces gyroscopic terms in the system equations. The effect of translation and the discrete elastic supports on the free vibration solution is studied. The solution is utilized in actively controlling the string vibrations due to an initial disturbance. The control, affected in modal space, is optimal with respect to a quadratic performance index. Numerical results are presented to demonstrate the effectiveness of the control strategy in regulating the travelling string vibrations.

Studies in crystal engineering: Effect of fluorine substitution in crystal packing and topological photodimerization of styryl coumarins in the solid state

Styryl coumarins generally yield centrosymmetric (alpha-mode, anti-HT) photodimers when subjected to irradiation in the solid state, However, the substitution of fluorine dramatically alters the packing mode and steers the molecules 4-(4-fluorostyryl)coumarin 1 and 4-(2-fluorostyryl)coumarin 2 to form a stereospecific photodimer, beta-mode, syn-HH across the styrenic double bond (yield 78-85%). The stereochemistry of the photodimer 2a has been established by X-ray crystallography. There is no evidence for the presence of C-H ... F interactions. The true nature of the weak atom-atom interactions called into play when fluorine is substituted is not clear, It is observed that the fluoro substituted compounds have greater crystal density than the corresponding unsubstituted ones.

Violin string shape functions for finite element analysis of rotating Timoshenko beams

Violin strings are relatively short and stiff and are well modeled by Timoshenko beam theory. We use the static part of the homogeneous differential equation of violin strings to obtain new shape functions for the finite element analysis of rotating Timoshenko beams. For deriving the shape functions, the rotating beam is considered as a sequence of violin strings. The violin string shape functions depend on rotation speed and element position along the beam length and account for centrifugal stiffening effects as well as rotary inertia and shear deformation on dynamic characteristics of rotating Timoshenko beams. Numerical results show that the violin string basis functions perform much better than the conventional polynomials at high rotation speeds and are thus useful for turbo machine applications. (C) 2011 Elsevier B.V. All rights reserved.

Studies in crystal engineering: Crystal packing, topological photodimerization and structure-reactivity correlations in fluoro-substituted styrylcoumarins

In continuation of our studies on the influence of fluoro substitution on the solid state photobehaviour and packing pattern of styrylcoumarins, the results obtained for 4-(3-fluorostyryl)coumarin 1, 4-styryl-6-fluorocoumarin 2 and 4-styryl-7-fluorocoumarin 3 are presented. The configuration of the dimers was established on the basis of crystal packing of 1 and 2 (alpha-packed). A rationale for the significantly lower dimer yield in the crystal for 2 is proposed. In the observed centrosymmetric arrangement of the reactants the C=O ...pi (phenyl) contacts seem to provide additional attractive interactions. C-H ... O and C-H ... F hydrogen bonding seems to provide stability in these structures.

Topological phases, Majorana modes and quench dynamics in a spin ladder system

We explore the salient features of the `Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections between spin phases and topologically non-trivial phases of non-interacting fermionic systems, demonstrating the equivalence between the spontaneous breaking of global Z(2) symmetry in spin systems and the existence of isolated Majorana modes. In the Kitaev ladder, we investigate topological properties of the system in different sectors characterized by the presence or absence of a vortex in each plaquette of the ladder. We show that vortex patterns can yield a rich parameter space for tuning into topologically non-trivial phases. We introduce and employ a new topological invariant for explicitly determining the presence of zero energy Majorana modes at the boundaries of such phases. Finally, we discuss dynamic quenching between topologically non-trivial phases in the Kitaev ladder and, in particular, the post-quench dynamics governed by tuning through a quantum critical point.

Study of temperature distribution along an artificially polluted insulator string

Insulator becomes wet partially or completely, and the pollution layer on it becomes conductive, when collecting pollutants for an extended period during dew, light rain, mist, fog or snow melting. Heavy rain is a complicated factor that it may wash away the pollution layer without initiating other stages of breakdown or it may bridge the gaps between sheds to promote flashover. The insulator with a conducting pollution layer being energized, can cause a surface leakage current to flow (also temperature-rise). As the surface conductivity is non-uniform, the conducting pollution layer becomes broken by dry bands (at spots of high current density), interrupting the flow of leakage current. Voltage across insulator gets concentrated across dry bands, and causes high electric stress and breakdown (dry band arcing). If the resistance of the insulator surface is sufficiently low, the dry band arcs can be propagated to bridge the terminals causing flashover. The present paper concerns the evaluation of the temperature distribution along the surface of an energized artificially polluted insulator string.

String-like propagation of the 5-coordinated defect state in supercooled water: molecular origin of dynamic and thermodynamic anomalies

We find that at low temperature water, large amplitude (similar to 60 degrees) rotational jumps propagate like a string, with the length of propagation increasing with lowering temperature. The strings are formed by mobile 5-coordinated water molecules which move like a Glarum defect (J. Chem. Phys., 1960, 33, 1371), causing water molecules on the path to change from 4-coordinated to 5-coordinated and again back to 4-coordinated water, and in the process cause the tagged water molecule to jump, by following essentially the Laage-Hynes mechanism (Science, 2006, 311, 832-835). The effects on relaxation of the propagating defect causing large amplitude jumps are manifested most dramatically in the mean square displacement (MSD) and also in the rotational time correlation function of the O-H bond of the molecule that is visited by the defect (transient transition to the 5-coordinated state). The MSD and the decay of rotational time correlation function, both remain quenched in the absence of any visit by the defect, as postulated by Glarum long time ago. We establish a direct connection between these propagating events and the known thermodynamic and dynamic anomalies in supercooled water. These strings are found largely in the regions that surround the relatively rigid domains of 4-coordinated water molecules. The propagating strings give rise to a noticeable dynamical heterogeneity, quantified here by a sharp rise in the peak of the four-point density response function, chi(4)(t). This dynamics heterogeneity is also responsible for the breakdown of the Stokes-Einstein relation.

Faster Algorithms for Incremental Topological Ordering.Robert Tarjan

We present two online algorithms for maintaining a topological order of a directed acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm takes O(m 1/2) amortized time per arc and our second algorithm takes O(n 2.5/m) amortized time per arc, where n is the number of vertices and m is the total number of arcs. For sparse graphs, our O(m 1/2) bound improves the best previous bound by a factor of logn and is tight to within a constant factor for a natural class of algorithms that includes all the existing ones. Our main insight is that the two-way search method of previous algorithms does not require an ordered search, but can be more general, allowing us to avoid the use of heaps (priority queues). Instead, the deterministic version of our algorithm uses (approximate) median-finding; the randomized version of our algorithm uses uniform random sampling. For dense graphs, our O(n 2.5/m) bound improves the best previously published bound by a factor of n 1/4 and a recent bound obtained independently of our work by a factor of logn. Our main insight is that graph search is wasteful when the graph is dense and can be avoided by searching the topological order space instead. Our algorithms extend to the maintenance of strong components, in the same asymptotic time bounds.

Spin-polarized STM spectra of Dirac electrons on the surface of a topological insulator

We provide a theory for the tunneling conductance G(V) of Dirac electrons on the surface of a topological insulator as measured by a spin-polarized scanning tunneling microscope tip for low-bias voltages V. We show that if the in-plane rotational symmetry on the surface of the topological insulator is broken by an external field that does not couple to spin directly (such as an in-plane electric field), G(V) exhibits an unconventional dependence on the direction of the magnetization of the tip, i.e., it acquires a dependence on the azimuthal angle of the magnetization of the tip. We also show that G(V) can be used to measure the magnitude of the local out-of-plane spin orientation of the Dirac electrons on the surface. We explain the role of the Dirac electrons in this unconventional behavior and suggest experiments to test our theory.

Charge Density Analysis of a Pentaborate Ion in an Ammonium Borate: Toward the Understanding of Topological Features in Borate Minerals

Structural and charge density distribution studies have been carried out on a single crystal data of an ammonium borate, [C(10)H(26)N(4)][B(5)O(6)(OH)(4)](2), synthesized by solvothermal method. Further, the experimentally observed geometry is used for the theoretical charge density calculations using the B3LYP/6-31G** level of theory, and the results are compared with the experimental values. Topological analysis of charge density based on the Atoms in Molecules approach for B-O bonds exhibit mixed covalent/ionic character. Detailed analysis of the hydrogen bonds in the crystal structure in the ammonium borate provides insights into the understanding of the reaction pathways that net atomic charges and electrostatic potential isosurfaces also give additional such systems. could result in the formation of borate minerals. The input to evaluate chemical and physical properties in such systems.

Topological analysis of general linear networks

A new method of network analysis, a generalization in several different senses of existing methods and applicable to all networks for which a branch-admittance (or impedance) matrix can be formed, is presented. The treatment of network determinants is very general and essentially four terminal rather than three terminal, and leads to simple expressions based on trees of a simple graph associated with the network and matrix, and involving products of low-order, usually(2 times 2)determinants of tree-branch admittances, in addition to tree-branch products as in existing methods. By comparison with existing methods, the total number of trees and of tree pairs is usually considerably reduced, and this fact, together with an easy method of tree-pair sign determination which is also presented, makes the new method simpler in general. The method can be very easily adapted, by the use of infinite parameters, to accommodate ideal transformers, operational amplifiers, and other forms of network constraint; in fact, is thought to be applicable to all linear networks.