Topological analysis of electron density and the electrostatic properties of isoniazid: an experimental and theoretical study

Isoniazid (isonicotinohydrazide) is an important first-line antitubercular drug that targets the InhA enzyme which synthesizes the critical component of the mycobacterial cell wall. An experimental charge-density analysis of isoniazid has been performed to understand its structural and electronic properties in the solid state. A high-resolution single-crystal X-ray intensity data has been collected at 90 K. An aspherical multipole refinement was carried out to explore the topological and electrostatic properties of the isoniazid molecule. The experimental results were compared with the theoretical charge-density calculations performed using CRYSTAL09 with the B3LYP/6-31G** method. A topological analysis of the electron density reveals that the Laplacian of electron density of the N-N bond is significantly less negative, which indicates that the charges at the b.c.p. (bond-critical point) of the bond are least accumulated, and so the bond is considered to be weak. As expected, a strong negative electrostatic potential region is present in the vicinity of the O1, N1 and N3 atoms, which are the reactive locations of the molecule. The C-H center dot center dot center dot N, C-H center dot center dot center dot O and N-H center dot center dot center dot N types of intermolecular hydrogen-bonding interactions stabilize the crystal structure. The topological analysis of the electron density on hydrogen bonding shows the strength of intermolecular interactions.

Topological blocking in quantum quench dynamics

We study the nonequilibrium dynamics of quenching through a quantum critical point in topological systems, focusing on one of their defining features: ground-state degeneracies and associated topological sectors. We present the notion of ``topological blocking,'' experienced by the dynamics due to a mismatch in degeneracies between two phases, and we argue that the dynamic evolution of the quench depends strongly on the topological sector being probed. We demonstrate this interplay between quench and topology in models stemming from two extensively studied systems, the transverse Ising chain and the Kitaev honeycomb model. Through nonlocal maps of each of these systems, we effectively study spinless fermionic p-wave paired topological superconductors. Confining the systems to ring and toroidal geometries, respectively, enables us to cleanly address degeneracies, subtle issues of fermion occupation and parity, and mismatches between topological sectors. We show that various features of the quench, which are related to Kibble-Zurek physics, are sensitive to the topological sector being probed, in particular, the overlap between the time-evolved initial ground state and an appropriate low-energy state of the final Hamiltonian. While most of our study is confined to translationally invariant systems, where momentum is a convenient quantum number, we briefly consider the effect of disorder and illustrate how this can influence the quench in a qualitatively different way depending on the topological sector considered.

Confining Dirac electrons on a topological insulator surface using potentials and a magnetic field

We study the effects of extended and localized potentials and a magnetic field on the Dirac electrons residing at the surface of a three-dimensional topological insulator like Bi2Se3. We use a lattice model to numerically study the various states; we show how the potentials can be chosen in a way which effectively avoids the problem of fermion doubling on a lattice. We show that extended potentials of different shapes can give rise to states which propagate freely along the potential but decay exponentially away from it. For an infinitely long potential barrier, the dispersion and spin structure of these states are unusual and these can be varied continuously by changing the barrier strength. In the presence of a magnetic field applied perpendicular to the surface, these states become separated from the gapless surface states by a gap, thereby giving rise to a quasi-one-dimensional system. Similarly, a magnetic field along with a localized potential can give rise to exponentially localized states which are separated from the surface states by a gap and thereby form a zero-dimensional system. Finally, we show that a long barrier and an impurity potential can produce bound states which are localized at the impurity, and an ``L''-shaped potential can have both bound states at the corner of the L and extended states which travel along the arms of the potential. Our work opens the way to constructing wave guides for Dirac electrons.

Edge states of a three-dimensional topological insulator

We use the bulk Hamiltonian for a three-dimensional topological insulator such as Bi-2 Se-3 to study the states which appear on its various surfaces and along the edge between two surfaces. We use both analytical methods based on the surface Hamiltonians (which are derived from the bulk Hamiltonian) and numerical methods based on a lattice discretization of the bulk Hamiltonian. We find that the application of a potential barrier along an edge can give rise to states localized at that edge. These states have an unusual energy-momentum dispersion which can be controlled by applying a potential along the edge; in particular, the velocity of these states can be tuned to zero. The scattering and conductance across the edge is studied as a function of the edge potential. We show that a magnetic field in a particular direction can also give rise to zero energy states on certain edges. We point out possible experimental ways of looking for the various edge states.

Robust local and nonlocal transport in the topological Kondo insulator SmB6 in the presence of a high magnetic field

SmB6 has been predicted to be a Kondo topological insulator with topologically protected conducting surface states. We have studied quantitatively the electrical transport through surface states in high-quality single crystals of SmB6. We observe a large nonlocal surface signal at temperatures lower than the bulk Kondo gap scale. Measurements and finite-element simulations allow us to distinguish unambiguously between the contributions from different transport channels. In contrast to general expectations, the electrical transport properties of the surface channels were found to be insensitive to high magnetic fields. We propose possible scenarios that might explain this unexpected finding. Local and nonlocal magnetoresistance measurements allowed us to identify possible signatures of helical spin states and strong interband scattering at the surface.

Nonlinear Differential Games-Based Impact-Angle-Constrained Guidance Law

The problem of intercepting a maneuvering target at a prespecified impact angle is posed in nonlinear zero-sum differential games framework. A feedback form solution is proposed by extending state-dependent Riccati equation method to nonlinear zero-sum differential games. An analytic solution is obtained for the state-dependent Riccati equation corresponding to the impact-angle-constrained guidance problem. The impact-angle-constrained guidance law is derived using the states line-of-sight rate and projected terminal impact angle error. Local asymptotic stability conditions for the closed-loop system corresponding to these states are studied. Time-to-go estimation is not explicitly required to derive and implement the proposed guidance law. Performance of the proposed guidance law is validated using two-dimensional simulation of the relative nonlinear kinematics as well as a thrust-driven realistic interceptor model.

Necessary and sufficient conditions for optimality in constrained general sum stochastic games

In this paper we first derive a necessary and sufficient condition for a stationary strategy to be the Nash equilibrium of discounted constrained stochastic game under certain assumptions. In this process we also develop a nonlinear (non-convex) optimization problem for a discounted constrained stochastic game. We use the linear best response functions of every player and complementary slackness theorem for linear programs to derive both the optimization problem and the equivalent condition. We then extend this result to average reward constrained stochastic games. Finally, we present a heuristic algorithm motivated by our necessary and sufficient conditions for a discounted cost constrained stochastic game. We numerically observe the convergence of this algorithm to Nash equilibrium. (C) 2015 Elsevier B.V. All rights reserved.

Bulk-Induced 1/f Noise at the Surface of Three-Dimensional Topological Insulators

Slow intrinsic fluctuations of resistance, also known as the flicker noise or 1/f-noise, in the surface transport of strong topological insulators (TIs) is a poorly understood phenomenon. Here, we have systematically explored the 1/f-noise in field-effect transistors (FET) of mechanically exfoliated Bi1.6Sb0.4Te2Se TI films when transport occurs predominantly via the surface states. We find that the slow kinetics of the charge disorder within the bulk of the TI induces mobility fluctuations at the surface, providing a new source of intrinsic 1/f-noise that is unique to bulk TI systems. At small channel thickness, the noise magnitude can be extremely small, corresponding to the phenomenological Hooge parameter gamma(H) as low as approximate to 10(-4), but it increases rapidly when channel thickness exceeds similar to 1 mu m. From the temperature (T)-dependence of noise, which displayed sharp peaks at characteristic values of T, we identified generation-recombination processes from interband transitions within the TI bulk as the dominant source of the mobility fluctuations in surface transport. Our experiment not only establishes an intrinsic microscopic origin of noise in TI surface channels, but also reveals a unique spectroscopic information on the impurity bands that can be useful in bulk TI systems in general.

Tailoring of Electronic Structure and Thermoelectric Properties of a Topological Crystalline Insulator by Chemical Doping

Topological crystalline insulators (TCIs) are a new quantum state of matter in which linearly dispersed metallic surface states are protected by crystal mirror symmetry. Owing to its vanishingly small bulk band gap, a TCI like Pb0.6Sn0.4Te has poor thermoelectric properties. Breaking of crystal symmetry can widen the band gap of TCI. While breaking of mirror symmetry in a TCI has been mostly explored by various physical perturbation techniques, chemical doping, which may also alter the electronic structure of TCI by perturbing the local mirror symmetry, has not yet been explored. Herein, we demonstrate that Na doping in Pb0.6Sn0.4Te locally breaks the crystal symmetry and opens up a bulk electronic band gap, which is confirmed by direct electronic absorption spectroscopy and electronic structure calculations. Na doping in Pb0.6Sn0.4Te increases p-type carrier concentration and suppresses the bipolar conduction (by widening the band gap), which collectively gives rise to a promising zT of 1 at 856 K for Pb0.58Sn0.40Na0.02Te. Breaking of crystal symmetry by chemical doping widens the bulk band gap in TCI, which uncovers a route to improve TCI for thermoelectric applications.

Pressure-induced phase transition in Bi2Se3 at 3 GPa: electronic topological transition or not?

In recent years, a low pressure transition around P similar to 3 GPa exhibited by the A(2)B(3)-type 3D topological insulators is attributed to an electronic topological transition (ETT) for which there is no direct evidence either from theory or experiments. We address this phase transition and other transitions at higher pressure in bismuth selenide (Bi2Se3) using Raman spectroscopy at pressure up to 26.2 GPa. We see clear Raman signatures of an isostructural phase transition at P similar to 2.4 GPa followed by structural transitions at similar to 10 GPa and 16 GPa. First-principles calculations reveal anomalously sharp changes in the structural parameters like the internal angle of the rhombohedral unit cell with a minimum in the c/a ratio near P similar to 3 GPa. While our calculations reveal the associated anomalies in vibrational frequencies and electronic bandgap, the calculated Z(2) invariant and Dirac conical surface electronic structure remain unchanged, showing that there is no change in the electronic topology at the lowest pressure transition.

Efficient topological localization using orientation adjacency coherence histograms

This paper describes an efficient vision-based global topological localization approach that uses a coarse-to-fine strategy. Orientation Adjacency Coherence Histogram (OACH), a novel image feature, is proposed to improve the coarse localization. The coarse localization results are taken as inputs for the fine localization which is carried out by matching Harris-Laplace interest points characterized by the SIFT descriptor. Computation of OACHs and interest points is efficient due to the fact that these features are computed in an integrated process. We have implemented and tested the localization system in real environments. The experimental results demonstrate that our approach is efficient and reliable in both indoor and outdoor environments. © 2006 IEEE.

On the topological bifurcation of flows around a rotating circular cylinder

Flow fields around a rotating circular cylinder in a uniform stream are computed using a low dimensional Galerkin method. Results show that the formation of a Fopple vortex pair behind a stationary circular cylinder is caused by the structural instability in the vicinity of the saddle located at the rear of the cylinder. For rotating cylinder a bifurcation diagram with the consideration of two parameters, Reynolds number Re and rotation parameter a, is built by a kinematic analysis of the steady flow fields.