Flicker noise in degenerately doped Si single crystals near the metal-insulator transition

In this paper we report some of the important results of experimental investigations of the flicker noise near the metal-insulator (MI) transition in doped silicon single crystals. This is the first comprehensive work to study low-frequency noise in heavily doped Si over an extensive temperature range (2 K<T<500 K). The measurements of conductance fluctuations (flicker noise) were carried out in the frequency range 10⁻²<f<4 × 10¹ Hz in single crystalline Si across the MI transition by doping with phosphorous and boron. The magnitude of noise in heavily doped Si is much larger than that seen in lightly doped Si over the whole temperature range. The extensive temperature range covered allowed us to detect two distinct noise mechanisms. At low temperatures (T<100 K) universal conductance fluctuations (UCF) dominate and the spectral dependence of the noise is determined by dephasing the electron from defects with two-levels (TLS). At higher temperatures (T>200 K) the noise arises from activated defect dynamics. As the MI transition is approached, the 1/f spectral power, typical of the metallic regime, gets modified by the presence of discrete Lorentzians which arise from generation-recombination process which is the characteristic of a semiconductor.     

Two highly unsymmetrical tetradentate (N3O) Schiff base copper(II) complexes: Template synthesis,structural characterization,magnetic and computational studies

Two new copper(II) complexes, [Cu₂(L¹)₂](ClO₄)₂ (1) and [Cu(L²)(ClO₄)] (2), of the highly unsymmetrical tetradentate (N₃O) Schiff base ligands HL¹ and HL² (where HL¹ = N-(2-hydroxyacetophenone)-bis-3-aminopropylamine and HL² = N-(salicyldehydine)-bis-3-aminopropylamine) have been synthesised using a template method. Their single crystal X-ray structures show that in complex 1 two independent copper(II) centers are doubly bridged through phenoxo-O atoms (O1A and O1B) of the two ligands and each copper atom is five-coordinated with a distorted square pyramidal geometry. The asymmetric unit of complex 2 consists of two crystallographically independent N-(salicylidene)-bis(aminopropyl)amine-copper(II) molecules, A and B, with similar square pyramidal geometries. Cryomagnetic susceptibility measurements (5–300 K) on complex 1 reveal a distinct antiferromagnetic interaction with J = ?23.6 cm^?1, which is substantiated by a DFT calculation (J = ?27.6 cm^?1) using the B3LYP functional. Complex 1, immobilized over highly ordered hexagonal mesoporous silica, shows moderate catalytic activity for the epoxidation of cyclohexene and styrene in the presence of TBHP as an oxidant.     

Explicit subspace designs

A subspace design is a collection {H ₁, H ₂, ...,H _M } of subspaces of \(\mathbb{F}_q^m\) with the property that no low-dimensional subspace W of \(\mathbb{F}_q^m\) intersects too many subspaces of the collection. Subspace designs were introduced by Guruswami and Xing (STOC 2013) who used them to give a randomized construction of optimal rate list-decodable codes over constant-sized large alphabets and sub-logarithmic (and even smaller) list size. Subspace designs are the only non-explicit part of their construction. In this paper, we give explicit constructions of subspace designs with parameters close to the probabilistic construction, and this implies the first deterministic polynomial time construction of list-decodable codes achieving the above parameters.Our constructions of subspace designs are natural and easily described, and are based on univariate polynomials over finite fields. Curiously, the constructions are very closely related to certain good list-decodable codes (folded RS codes and univariate multiplicity codes). The proof of the subspace design property uses the polynomial method (with multiplicities): Given a target low-dimensional subspace W, we construct a nonzero low-degree polynomial P _W that has several roots for each H _i that non-trivially intersects W. The construction of P _W is based on the classical Wronskian determinant and the folded Wronskian determinant, the latter being a recently studied notion that we make explicit in this paper. Our analysis reveals some new phenomena about the zeroes of univariate polynomials, namely that polynomials with many structured roots or many high multiplicity roots tend to be linearly independent.     

Di­methyl 6‐methoxy‐4aβ‐methyl‐9‐oxo‐1,2,3,4,4a,9,10,10aβ‐octa­hydro­phenanthrene‐1,1‐di­carboxyl­ate

In the title tricyclic keto‐diester, C₂₀H₂₄O₆, a potential intermediate in the synthesis of bioactive podocarpic acid, the outer cyclo­hexane ring (in a chair conformation) is cis fused to the central cyclo­hexanone ring (in a half‐chair conformation). The conformational analysis of the compound, investigated by semi‐empirical quantum mechanical AM1 calculations, shows a good agreement with the X‐ray structure, except for the orientation of the methyl, methoxy­phenyl and methoxy­carbonyl substituents.     

Observation of non-Gaussian conductance fluctuations at low temperatures in Si:P(b) at the metal-insulator transition

We report investigations of conductance fluctuations (with 1/f(alpha) power spectra) in doped silicon at low temperatures (T<20 K) as it is tuned through the metal-insulator transition (MIT) by changing the carrier concentration n. The scaled magnitude of noise, gamma(H), increases with decreasing T following an approximate power law gamma(H) approximately T-beta. At low T, gamma(H) diverges as n decreases through the critical concentration n(c), accompanied by a growth of low-frequency spectral weight. The second spectrum and probability density of the fluctuations show strong non-Gaussian behavior below 20 K as n/n(c) decreases through 1. This is interpreted as the onset of a glassy freezing of the electronic system across the MIT.     

Cyanometallate incorporated supramolecular networks based on a nitroalkyl-substituted CuN4 precursor: Synthesis, crystal structure, thermal and electrochemical studies

Two new copper(II) complexes, viz. [Cu(nelin)(H₂O)₂]₂[Fe(CN)₆] · 6H₂O (2) and [{Cu(nelin)}₂Ni(CN)₄](ClO₄)₂ · 2H₂O (3), have been synthesized using [Cu(nelin)](ClO₄)₂ (1) (nelin = 1,9-diamino-5-methyl-5-nitro-3,7-diazanonane) as a nitroalkyl-substituted Cu^IIN₄ precursor, and their structures and supramolecular networks have been fully explored using the single crystal X-ray diffraction technique. The H-bonded 1D chains of 2 run along the a-axis, being generated from supramolecular synthons using cations and anions, and are further propagated into a 3D array to form irregular honeycomb-like channels which are divided into two halves, with each half accomodating a helical water chain running in opposite directions to each other. In complex 3, the trinuclear units are arranged in successive rows in a herringbone fashion and bifurcated hydrogen bonding through the uncoordinated terminals of the [Ni(CN)₄]²⁻ units give rise to a supramolecular (4,4) network. A comparison of the PXRD pattern of complex 2 and its dehydrated form indicate marked changes in the diffraction pattern with the development of a quasi glassy nature in the dehydrated form. The electrochemical properties of 1, 2 and 3 have been investigated in comparative ways using the cyclic voltammetric technique in aqueous and MeCN solutions with Ag/AgCl as a reference electrode. Electrochemical reduction generates the one-electron reduced nitro-radical anion. In water–alcohol glass at 77 K complex 2 exhibits a typical four-line hyperfine EPR spectra with g_|| = 2.11, g = 2.02, A_|| = 150 Oe and A = 5 Oe at ν = 9.45 MHz.     

The minimum rank problem: A counterexample

We provide a counterexample to a recent conjecture that the minimum rank over the reals of every sign pattern matrix can be realized by a rational matrix. We use one of the equivalences of the conjecture and some results from projective geometry. As a consequence of the counterexample we show that there is a graph for which the minimum rank of the graph over the reals is strictly smaller than the minimum rank of the graph over the rationals. We also make some comments on the minimum rank of sign pattern matrices over different subfields of R.