Dicarboxylate assisted synthesis of the monoclinic heterometallic tetrathiocyanato bridged copper(II) and mercury(II) coordination polymer {Cu[Hg(SCN)4]}n: Synthesis, structural, vibration, luminescence, EPR studies and DFT calculations

The synthesis of the monoclinic polymorph of {Cu[Hg(SCN)₄]}_n is reported. The compound, as determined by X-ray diffraction of a twinned crystal, consists of mercury and copper atoms linked by μ_1,3-SCN bridges. The crystal packing shows a highly porous infinite 3D structure. Diagnostic resonances for the SCN^- ligand and metal-ligand bonds in the IR, far-IR and Raman spectra are assigned and discussed. The electronic band structure along with density of states (DOS) calculated by the DFT method indicates that the compound is an indirect band gap semiconductor. The DFT calculations show that the observed luminescence of the compound arises mainly from an excited LLCT state with small MLCT contributions (from the copper to unoccupied π^? orbital of the thiocyanate groups). The X-band EPR spectrum of the powdered sample at room temperature reveals an axial signal with anisotropic g factors consistent with the unpaired electron of Cu(II) ion in the d_x²−y² orbital.     

Double-resonance plasmon and polarization effects in a SERS fiber sensor with a grid nanostructure

We presented a systematic study of surface enhanced Raman scattering (SERS) fiber sensor with a grid nanostructure. The plasmonic resonance peak is stable when measuring gas and double-resonance plasmon can be effectively excited; meanwhile local electric field can be strongly enhanced with the metal coated nanostructured fiber facet. Studies on the influence of polarization effects, the plasmon resonance wavelength shift is relatively small in our structure.     

Numerical renormalization group at marginal spectral density: application to tunneling in Luttinger liquids

Many quantum mechanical problems (such as dissipative phase fluctuations in metallic and superconducting nanocircuits or impurity scattering in Luttinger liquids) involve a continuum of bosonic modes with a marginal spectral density diverging as the inverse of energy. We construct a numerical renormalization group in this singular case, with a manageable violation of scale separation at high energy, capturing reliably the low energy physics. The method is demonstrated by a nonperturbative solution over several energy decades for the dynamical conductance of a Luttinger liquid with a single static defect.     

Terahertz near-field imaging using subwavelength plasmonic apertures and a quantum cascade laser source

The first demonstration, to our knowledge, of near-field imaging using subwavelength plasmonic apertures with a terahertz quantum cascade laser source is presented. "Bull's-eye" apertures, featuring subwavelength circular apertures flanked by periodic annular corrugations were created using a novel fabrication method. A fivefold increase in intensity was observed for plasmonic apertures over plain apertures of the same diameter. Detailed studies of the transmitted beam profiles were undertaken for apertures with both planarized and corrugated exit facets, with the former producing spatially uniform intensity profiles and subwavelength spatial resolution. Finally, a proof-of-concept imaging experiment is presented, where an inhomogeneous pharmaceutical drug coating is investigated.     

Modified Darboux transformations with foreign auxiliary equations

We construct a new type of first-order Darboux transformations for the stationary Schrödinger equation. In contrast to the conventional case, our Darboux transformations support arbitrary (foreign) auxiliary equations. We show that among other applications, our formalism can be used to systematically construct Darboux transformations for Schrödinger equations with energy-dependent potentials, including a recent result (Lin et al., 2007) [16] as a special case.     

A simple method for analyzing 51V solid-state NMR spectra of complex systems

Five vanadium complexes as models for biological systems were investigated using ⁵¹V-MAS–NMR spectroscopy. All spectra show an uncommon line shape, which can be attributed to a shorter relaxation time of the satellite transition in contrast to the central one. A method for the reliable analysis of such kind of spectra is presented for the first time and the most important NMR parameters of the investigated complexes (quadrupolar coupling constant C_Q, asymmetry of the EFG tensor η_Q, isotropic chemical shift δ_iso, chemical shift anisotropy δ_σ and asymmetry of the CSA tensor η_σ) are presented. These results are of particular importance with respect to the analysis of the ⁵¹V-MAS–NMR spectra of vanadium moieties in biological matrices such as vanadium chloroperoxidase, which show hitherto unexplained low intensity of the satellite sideband pattern.     

Temperature dependence of metal-organic heteroepitaxy

The nucleation and growth of 2D layers of tetraphenyl porphyrin molecules on Ag(111) are studied with variable-temperature scanning tunneling microscopy. The organic/metal heteroepitaxy occurs by strict analogy to established principles for metal heteroepitaxy. A hierarchy of energy barriers for diffusion on terraces and along edges and around corners of adislands is established. The temperature is key to activating these barriers selectively, thus determining the shape of the organic aggregates, from a fractal shape at lower temperatures to a compact shape at higher temperatures. The energy barriers for the terrace diffusion of porpyrins and the molecule-molecule binding energy were determined to be 30 meV < E(terrace) < 60 and 130 meV < E(diss) < 160 meV, respectively, from measurements of island sizes as a function of temperature. This study provides an experimental verification of the validity of current models of epitaxy for the heteroepitaxy of organics and is thus expected to help establish design principles for complex metal-organic hybrid structures.     

An Explicit Computation of a Family of Trivializing Étale Covers

We explicitly compute étale covers of the smooth Fermat curves Y _p+1 = Proj k[u, v, w]/(u ^p+1 + v ^p+1 ? w ^p+1) which trivialize the vector bundles Syz(u ², v ², w ²)(3), where k is a field of characteristic p ≥ 3.     

Aspects of a Phase Transition in High-Dimensional Random Geometry

A phase transition in high-dimensional random geometry is analyzed as it arises in a variety of problems. A prominent example is the feasibility of a minimax problem that represents the extremal case of a class of financial risk measures, among them the current regulatory market risk measure Expected Shortfall. Others include portfolio optimization with a ban on short-selling, the storage capacity of the perceptron, the solvability of a set of linear equations with random coefficients, and competition for resources in an ecological system. These examples shed light on various aspects of the underlying geometric phase transition, create links between problems belonging to seemingly distant fields, and offer the possibility for further ramifications.