Symmetry in Scalar Field Topology

Study of symmetric or repeating patterns in scalar fields is important in scientific data analysis because it gives deep insights into the properties of the underlying phenomenon. Though geometric symmetry has been well studied within areas like shape processing, identifying symmetry in scalar fields has remained largely unexplored due to the high computational cost of the associated algorithms. We propose a computationally efficient algorithm for detecting symmetric patterns in a scalar field distribution by analysing the topology of level sets of the scalar field. Our algorithm computes the contour tree of a given scalar field and identifies subtrees that are similar. We define a robust similarity measure for comparing subtrees of the contour tree and use it to group similar subtrees together. Regions of the domain corresponding to subtrees that belong to a common group are extracted and reported to be symmetric. Identifying symmetry in scalar fields finds applications in visualization, data exploration, and feature detection. We describe two applications in detail: symmetry-aware transfer function design and symmetry-aware isosurface extraction.

A density matrix renormalization group method study of optical properties of porphines and metalloporphines

The symmetrized density matrix renormalization group method is used to study linear and nonlinear optical properties of free base porphine and metalloporphine. Long-range interacting model, namely, Pariser-Parr-Pople model is employed to capture the quantum many-body effect in these systems. The nonlinear optical coefficients are computed within the correction vector method. The computed singlet and triplet low-lying excited state energies and their charge densities are in excellent agreement with experimental as well as many other theoretical results. The rearrangement of the charge density at carbon and nitrogen sites, on excitation, is discussed. From our bond order calculation, we conclude that porphine is well described by the 18-annulenic structure in the ground state and the molecule expands upon excitation. We have modeled the regular metalloporphine by taking an effective electric field due to the metal ion and computed the excitation spectrum. Metalloporphines have D(4h) symmetry and hence have more degenerate excited states. The ground state of metalloporphines shows 20-annulenic structure, as the charge on the metal ion increases. The linear polarizability seems to increase with the charge initially and then saturates. The same trend is observed in third order polarizability coefficients. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3671946]

Full spin and spatial symmetry adapted technique for correlated electronic hamiltonians: Application to an icosahedral cluster

One of the long standing problems in quantum chemistry had been the inability to exploit full spatial and spin symmetry of an electronic Hamiltonian belonging to a non-Abelian point group. Here, we present a general technique which can utilize all the symmetries of an electronic (magnetic) Hamiltonian to obtain its full eigenvalue spectrum. This is a hybrid method based on Valence Bond basis and the basis of constant z-component of the total spin. This technique is applicable to systems with any point group symmetry and is easy to implement on a computer. We illustrate the power of the method by applying it to a model icosahedral half-filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and in the largest non-Abelian point group. The C60 molecule has this symmetry and hence our calculation throw light on the higher energy excited states of the bucky ball. This method can also be utilized to study finite temperature properties of strongly correlated systems within an exact diagonalization approach. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Structural characterization, EPR and thermoluminescence properties of Cd-1 (-) xNixSiO3 nanocrystalline phosphors

Cd-1 - xNixSiO3 (x = 1-7 mol%) nanophosphors have been prepared for the first time by the combustion method using oxylyldihydrizide as a fuel. Powder X-ray diffraction results confirm the formation of monoclinic phase. Scanning electron micrographs show that Ni2+ influences the porosity of samples. The optical energy gap is widened with increase of Ni2+ ion dopant. The electron paramagnetic resonance spectrum of Ni2+ ions in CdSiO3 exhibits a symmetric absorption at g = 2.343 and the site symmetry around Ni2+ ions is predominantly octahedral. The number of spins participating in resonance (N) and the paramagnetic susceptibility (chi) has been evaluated. The thermoluminescence intensity is found to increase up to similar to 20 min ultra-violet exposure and thereafter, decrease with further increase of ultra-violet dose. The kinetic parameters such as activation energy (E), frequency factor (s)and order of kinetics was estimated using glow peak shape method and the results are discussed. (c) 2012 Elsevier Ltd. All rights reserved.

Optical Properties of 1P State Electron Bubbles in Liquid Helium-4

When an electron is injected into liquid helium, it forces open a cavity that is free of helium atoms (an electron bubble). If the electron is in the ground 1S state, this bubble is spherical. By optical pumping it is possible to excite a significant fraction of the electron bubbles to the 1P state; the bubbles then lose spherical symmetry. We present calculations of the energies of photons that are needed to excite these 1P bubbles to higher energy states (1D and 2S) and the matrix elements for these transitions. Measurement of these transition energies would provide detailed information about the shape of the 1P bubbles.

Crystal growth and nonlinear optical properties of sodium D-isoascorbate monohydrate

Optical quality single crystals of sodium D-isoascorbate monohydrate were grown by a slow cooling technique. The crystal possesses a bulky prismatic morphology. Thermal analyses indicate that the crystals are stable up to 125 degrees C. The optical transmission window ranges from 307 nm to 1450 nm. The principal refractive indices have been measured employing Brewster's angle method. The crystallographic and the principal dielectric axes coincide with each other such that a lies along Z, b along X and c along Y. The optic axis is oriented 58 degrees (at 532 nm) to the crystallographic a axis in the XZ plane and the crystal is negative biaxial. Type 1 and type 2 phase matching curves are generated and experimentally verified. No polarization dependence of the light absorption was observed confirming the validity of Kleinman's symmetry conjecture, leading to a single nonvanishing nonlinear tensor component. According to Hobden's classification the crystal belongs to class 3. The crystal also exhibits second order noncollinear conic sections. The single shot and multiple shot surface laser damage thresholds are determined to be 32.7 GW cm(-2) and 6.5 GW cm(-2) respectively for 1064 nm radiation.

Majorana fermions in superconducting wires: Effects of long-range hopping, broken time-reversal symmetry, and potential landscapes

We present a comprehensive study of two of the most experimentally relevant extensions of Kitaev's spinless model of a one-dimensional p-wave superconductor: those involving (i) longer-range hopping and superconductivity and (ii) inhomogeneous potentials. We commence with a pedagogical review of the spinless model and, as a means of characterizing topological phases exhibited by the systems studied here, we introduce bulk topological invariants as well as those derived from an explicit consideration of boundary modes. In time-reversal symmetric systems, we find that the longer range hopping leads to topological phases characterized by multiple Majorana modes. In particular, we investigate a spin model that respects a duality and maps to a fermionic model with multiple Majorana modes; we highlight the connection between these topological phases and the broken symmetry phases in the original spin model. In the presence of time-reversal symmetry breaking terms, we show that the topological phase diagram is characterized by an extended gapless regime. For the case of inhomogeneous potentials, we explore phase diagrams of periodic, quasiperiodic, and disordered systems. We present a detailed mapping between normal state localization properties of such systems and the topological phases of the corresponding superconducting systems. This powerful tool allows us to leverage the analyses of Hofstadter's butterfly and the vast literature on Anderson localization to the question of Majorana modes in superconducting quasiperiodic and disordered systems, respectively. We briefly touch upon the synergistic effects that can be expected in cases where long-range hopping and disorder are both present.

Low temperature combustion synthesis and magnetostructural properties of Co-Mn nanoferrites

In the present work, Co1-xMnxFe2O4 nanoparticles were synthesized by the low-temperature auto-combustion method. The thermal decomposition process was investigated by means of differential and thermal gravimetric analysis (TG-DTA) that showed the precursor yield the final product above 450 degrees C. The phase purity and crystal lattice symmetry were estimated from X-ray diffraction (XRD). Microstructural features observed by scanning electron microscopy (SEM) demonstrates that the fine clustered particles were formed with an increase in average grain size with Mn2+ content. Fourier transform infrared spectroscopy (FTIR) study confirms the formation of spinel ferrite. Room temperature magnetization measurements showed that the magnetization M-s increases from 29 to 60 emu/g and H-c increases from 13 to 28 Oe with increase in Mn2+ content, which implies that these materials may be applicable for magnetic data storage and recording media. (C) 2013 Elsevier B.V. All rights reserved.

Structural and thermodynamic properties of Fe1.12Te with multiple phase transitions

The parent compound of iron chalcogenide superconductors, Fe1+yTe, with a range of excess Fe concentrations exhibits intriguing structural and magnetic properties. Here, the interplay of magnetic and structural properties of Fe1.12Te single crystals have been probed by low-temperature synchrotron X-ray powder diffraction, magnetization, and specific heat measurements. Thermodynamic measurements reveal two distinct phase transitions, considered unique to samples possessing excess Fe content in the range of 0.11 <= y <= 0.13. On cooling, an antiferromagnetic transition, T-N approximate to 57K is observed. A closer examination of powder diffraction data suggests that the transition at TN is not purely magnetic, but accompanied by the commencement of a structural phase transition from tetragonal to orthorhombic symmetry. This is followed by a second prominent first-order structural transition at T-S with T-S < T-N, where an onset of monoclinic distortion is observed. The results point to a strong magneto-structural coupling in this material. (C) 2014 AIP Publishing LLC.

Phase transformation, improved ferroelectric and magnetic properties of (1-x) BiFeO3-xPb(Zr0.52Ti0.48)O-3 solid solutions

The authors prepared (1 - x) BiFeO3 - (x)Pb(Zr0.52Ti0.48)O-3 for x <= 0.30 by sol-gel method and investigated the material's structures, magnetic and electrical properties. Detailed Rietveld analysis of X-ray diffraction data revealed that the system retains distorted rhombohedral R3c structure for x <= 0.10 but transforms to monoclinic (Cc) structure for x > 0.10. Disappearance of some Raman modes corresponding to A1 modes and the decrease in the intensities of the remaining A1 modes with increasing x in the Raman spectra, which is a clear indication of structural modification and symmetry changes brought about by PZT doping. Enhanced magnetization with PZT doping content may be attributed to the gradual change and destruction in the spin cycloid structure of BiFeO3. The leakage current density at 3.5 kV/cm was reduced by approximately three orders of magnitude by doping PZT (x = 0.30), compared with BFO ceramics. (C) 2014 AIP Publishing LLC.

Photoluminescence properties of Eu3+-activated CaMoO4 phosphors for WLEDs applications and its Judd-Ofelt analysis

A series of scheelite-type Eu3+-activated CaMoO4 phosphors were synthesized by the nitrate-citrate gel combustion method. All the compounds crystallized in the tetragonal structure with space group I4(1)/a (No. 88). FESEM results reveal the spherical-like morphology. The CaMoO4 phosphor exhibited broad emission centered at 500 nm under the excitation of 298 nm wavelength, while Eu3+-activated CaMoO4 shows an intense characteristic red emission peak at 615 nm at different excitation wavelengths, due to D-5(0) -> F-7(2) transition of Eu3+ ions. The intensities of transitions between different J levels depend on the symmetry of the local environment of Eu3+ ions and were estimated using the Judd-Ofelt analysis. The high asymmetric ratio revealed that Eu3+ occupies sites with a low symmetry and without an inversion center. The CIE chromaticity co-ordinates (x, y) were calculated from emission spectra, and the values were close to the NTSC standard. Therefore, the present phosphor is highly useful for LEDs applications.

Synthesis of Eu3+-activated ZnO superstructures: Photoluminescence, Judd-Ofelt analysis and Sunlight photocatalytic properties

Photoluminescence and photocatalytic properties of Eu-doped ZnO nanoparticles (NPs) were synthesized by facile phyto route. XPS results demonstrated the existence of Eu3+ as dopant into ZnO. Morphologies of the NPs were mainly dependent on Eu3+ and Aloe vera gel. Red shift of energy band gap was due to the creation of intermediate energy states of Eu3+ and oxygen vacancies in the band gap. PL emission of ZnO:Eu3+ (1-11 mol%, 8 ml and 7 mol%, 2-12 ml) exhibit characteristic peaks of D-5(0) -> F-7(2) transitions. From the Judd-Ofelt analysis, intensities of transitions between different.' levels dependent on the symmetry of the local environment of Eu3+ ions. CIE chromaticity co-ordinates confirm reddish emission of the phosphor. Further, NPs exhibit excellent photocatalytic activity for the degradation of Rhodamine B (94%) under Sunlight was attributed to crystallite size, band gap, morphology and oxygen vacancies. In addition, photocatalyst reusability studies were conducted and found that Eu-doped catalyst could be reused several times with negligible decrease in catalytic activity. The present work directs new possibilities to provide some new insights into the design of new phyto synthesized nanophosphors for display devices, photocatalysts with high activity for environmental clean-up and solar energy conversion. (C) 2015 Elsevier B.V. All rights reserved.

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.

Lifshitz transition and modulation of electronic and transport properties of bilayer graphene by sliding and applied normal compressive strain

Using density functional theory (DFT) we investigate the changes in electronic and transport properties of graphene bilayer caused by sliding one of the layers. Change in stacking pattern breaks the lattice symmetry, which results in Lifshitz transition together with the modulation of the electronic structure. Going from AA to AB stacking by sliding along armchair direction leads to a drastic transition in electronic structure from linear to parabolic dispersion. Our transport calculations show a significant change in the overall transmission value for large sliding distances along zigzag direction. The increase in interlayer coupling with normal compressive strain increases the overlapping of conduction and valence band, which leads to further shift in the Dirac points and an enhancement in the Lifshitz transition. The ability to tune the topology of band structure by sliding and/or applying normal compressive strain will open doors for controlled tuning of many physical phenomenon such as Landau levels and quantum Hall effect in graphene. (C) 2015 Elsevier Ltd. All rights reserved.

Properties of the correlated electronic states of pyrene and hydrogenated pyrene

Approximate calculations are reported on pyrene within the PPP model Hamiltonian using a novel restricted CI scheme which employs both molecular orbital and valence bond techniques. Also reported are detailed full CI results of the PPP model on 2,7-dihydropyrene obtained using the valence bond method. Spectral studies, charge and spin density calculations in ground and excited states, and ring current calculations in the ground state of the molecules are presented. In pyrene, the calculated excitation energies are in good agreement with experiment. The closed structure pi-conjugated molecule pyrene appears to show smaller distortions from the ground state geometry compared with the open structure pi-conjugated molecule 2,7-dihydropyrene. The ground state equilibrium structure of 2,7-dihydropyrene can be viewed as two hexatriene molecules connected by a vinyl crosslink, as is evident from bond order and ring current calculations. This is consistent with the only Kekule resonant structure possible for this molecule.