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It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature $\mathrm{\Xi }$ and the critical temperature $T_c$ is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions $d=1,2$ and give an exemplary proof in the weak coupling limit.

A discussion is made on the appearance of strong effective magnetic field with a new quantum state induced by the zero-point plasma oscillation in semi-localized half-filling electron system in the 2D network of circular molecular orbits. With the help of numerical calculation we study the appearance of superconductivity in the Cu and Ru oxide superconductor employing the field-induced quantum state and a gauge-field pairing model, and succeed in giving a unified explanation to the two apparently different types of oxide superconductivity. It is found that in the Cu oxide superconductor singlet pairing of d_x²-y² symmetry occurs in each CuO₂ layer at the decoupling of the zero-spin-sum singlet FQHE state by small carrier doping, while in the Ru oxide superconductor triplet electron pairing is caused by two neighboring RuO₂ layers at the decoupling of the spin-polarized FQHE Ψ_1,1,1 state where the pairs have d_3z²-r² symmetry with horizontal node on the Fermi surface. Numerical calculation gives critical temperature consistent with experimental observation.

We develop the invariant eigen-operator (IEO) theory proposed in the preceding study (Phys. Lett. A321 (2004) 75) to the pseudo-invariant eigen-operator (PIEO) method, with which we derive energy-level gap of two generalized Jaynes–Cummings models. The PIEO usually exists in some Hilbert space which is spanned by the eigenvectors of conservative quantities of the dynamic system.

We show that the recently proposed invariant eigen-operator method is particularly applicable to solving the energy levels for some Hamiltonians in molecular physics. These are tri-atom molecules, the identical d-dimensional coupled harmonic oscillators and the dissipative linear-chain molecular model etc. The calculation is more direct and simpler than the usual diagonalization method for dynamic Hamiltonians.

The report contains a brief history of the superconductor’s researches and their applications carried out in the Institute for Low Temperature Physics and Engineering (ILTPE) of the National Academy of Sciences of Ukraine since the ILTPE foundation in 1960. The most important results of the researches in the field of the low- and high-temperature superconductors (HTS) are stated more detailed. The experimental validation of an electromagnetic radiation of Josephson junctions; the electron pairing and existence of the distant order in the HTS; a creation of the superconducting quantum interference devices (SQUIDs) on the basis of the HTS; formation and moving of the local frozen magnetic field along the surface of the HTS; the transport properties of new Fe-based superconductors can be referred to such results.

We demonstrate that the nonrelativistic fermions open the energy gap when the SU($N$) gauge bosons, mediating the interaction between fermions, acquire the mass. Surprisingly, even though there is the SU($N$) gauge symmetry, there is always one fermionic energy gap which is not degenerate to the rest of the $N-1$ fermions for $N\ge 3$ in the fundamental representation.

CdGa₂S₄ was prepared in powder form by reacting CdS and Ga₂S₃. The powder had a tetragonal crystal structure with lattice parameters, a = 0.559 ± 0.005 nm, c = 1.008 ± 0.009 nm and c/a = 1.803. CdGa₂S₄ films deposited by thermal evaporation of the powder were noncrystalline. After annealing, the CdGa₂S₄ thin films contain crystals with the tetragonal crystal structure. The optical constants (the refractive index n, the absorption index k and the absorption coefficient α) were determined for CdGa₂S₄ thin films in the thickness range 170–452 nm. It was found that both n and k are independent of the film thickness and both are slightly different as deposited and annealed films. The refractive index shows anomalous dispersion in the spectral range 300–700 nm. The high frequency dielectric constant ε_∞ was determined for the as-deposited and after being annealed films. It was found that ε_∞ = 5.12 and 5.52 for the as-deposited and after being annealed films respectively. Graphical representations of (αhν)^r = f(hν) yield three linear parts, indicating the existence of two indirect and one direct allowed transitions. The values of , and for CdGa₂S₄ for the as-deposited and annealed films are presented.

Based upon the Slater–Koster tight-binding calculations, we investigated electronic properties of the "metallic" single-walled carbon nanotubes (SWNTs) in detail. Our results show that tube curvature may produce an energy gap at the Fermi level for zigzag and chiral "metallic" SWNTs, and this effect decreases with the increasing of either the radius or the chiral angle. Our calculated results are in good agreement with experiments.

Optical transmittance on ferroelectric BaTi_xO₅ (x=1.7, 2, 2.1)-based glasses prepared recently by a containerless synthesis technique is measured at room temperature in the wavelength range 190–800 nm. A sharp decrease in the transmittance observed in the ultraviolet (UV) region, which shifts toward longer wavelength region on increasing x is associated with fundamental absorption edge. From the linear region of the absorption coefficient calculated from the transmittance spectrum the optical band gap of 3.41 eV is estimated for x=1.7, which decreases on increasing x. The Urbach energy increases on increasing x demonstrating an increase of structural disorder in the ferroelectric BaTi_xO₅ glass on increasing Ti concentration.

Based on the invariant eigen-operator method³ we developed a general way to calculate the energy gaps of quadratic Boson or Fermion Hamiltonians. As an application, we calculated the energy gaps of an electron in uniform magnetic field (UMF) and a quadratic potential. We also checked the gauge invariance of electromagnetic field.

Well-dispersed undoped and copper-doped zinc oxide nanoparticles (Zn${}_{1-x}$Cu${}_x$O, $x$ = 0, 1, 5 and 10 wt.%) have been synthesized by precipitation method at room temperature. X-ray diffraction data revealed that the undoped and copper-doped zinc oxide nanoparticles are in phase pure wurtzite structure and the crystallite size increases from 24 nm to 36 nm with increase in dopant concentration. The optical band gap was found to decrease with increasing dopant concentration, which clearly indicates the blue shift. High-resolution scanning electron microscope image shows that the synthesized samples consist of an assembly of nanopetals. Transmission electron microscope image also confirmed the average particle size of 20–50 nm. Energy-dispersive X-ray spectrum shows that the prepared samples are free from impurities. Photoluminescence spectra exposed that copper ions are doped into the lattice positions of ZnO. A simultaneous differential scanning calorimeter/thermogravimetric analysis combination was used to study the phase variations.

We study the band structure of the lattice-matched graphene/$h$-BN bilayer system in the most stable configuration. An effective way to individually manipulate the edge state by the boundary potentials is proposed. It is shown that the boundary potential can not only shift and deform the edge bands, but also modify the energy gap. We also explore the transport properties of graphene/$h$-BN under a magnetic field. The boundary potential can change the distribution of the edge states, resulting in an interesting evolution of the quantized conductance.

Nickel-substituted copper oxide nanoparticles at various concentrations were synthesized by the microwave irradiation technique. The consequence of nickel doping on crystal structure, optical properties, and magnetic properties was examined by means of X-ray diffractometer, ultraviolet-visible spectrometer, Fourier transform infrared (FT-IR) spectrometer, transmission electron microscope, and vibrating sample magnetometer (VSM). X-ray diffraction analysis shows that the samples are monoclinic and their crystallite size varies from 25nm to 42nm, and lattice constant significantly increases with nickel concentration. Additional increase of nickel content (7%) decreases the lattice constant. TEM micrograph witnessed that the prepared nanoparticles were sphere-shaped and the particle distribution is in the range between 20 and 40nm. Bandgap measurement reveals that both undoped and nickel-doped copper oxides are direct bandgap semiconductor materials with bandgaps of 3.21 and 3.10eV, respectively, FT-IR spectra of the synthesized samples confirmed the nickel doping. VSM studies confirmed the ferromagnetic behavior of the synthesized samples at room temperature. The results revealed that the nickel-doped copper oxide nanoparticles synthesized via the microwave irradiation method exhibit better magnetic properties than the undoped copper oxide.

Polyvinyl alcohol (PVA) films doped with potassium iodide (KI) have been prepared by casting from their aqueous solutions. The structure of the doped samples was investigated using Fourier transform infrared spectroscopy. The addition of KI to PVA structure leads to form crosslinking as well as the increase of the amorphous ratio within the investigated sample. The optical measurements were recorded at room temperature in the range of 200–2500nm. It was found that the optical energy gap of the investigated sample increases with increasing KI ratio. The effect of the addition increment of KI on the optical parameters of PVA has been investigated. Dielectric spectra of PVA doped with KI were studied in the temperature and the frequency ranges of 303–373K and 100Hz–5MHz, respectively. The behavior of dielectric constant (${\epsilon }_1$) and dielectric loss index (${\epsilon }_2$) of PVA sample doped with KI exhibits good linearity with temperature. The obtained results suggest strongly the applicability of these materials in the temperature sensor applications.

This paper focuses on the synthesis and structural, optical, and magnetic characterization of Mn-doped CoFe₂O₄ nanoparticles synthesized by a simple chemical co-precipitation method. Synthesized magnetic nanoparticles were characterized by XRD, FTIR, UV-Vis, PL, TEM, VSM, and EPR spectroscopy. XRD analysis confirmed the significant reduction in the crystallite size from $\sim 17$nm to 10nm as the Mn content is increased from 0 to 1. UV-Vis spectra confirmed that the Co–Mn ferrite is a direct bandgap magnetic material that possesses an energy gap from 3.92eV to 4.33eV. FTIR vibrational frequency observed between 468 and 548 ${\text{cm}}^{-1}$confirmed the existence of metal–oxygen bond at tetrahedral and octahedral sites. Photoluminescence spectra confirmed the red emission of the samples from the peak at 680nm. TEM analysis suggests that the single domain of CoFe₂O₄ nanoparticles may vary between 38 and 72nm. Composition analysis confirmed the homogeneous mixing of Co, Mn Fe, and O atoms in the synthesized samples. The VSM study confirmed that Mn substitution favors transition from ferromagnetic to superparamagnetic. VSM analysis also confirmed the lessening in saturation magnetization and coercivity on Mn doping. The X-band electron paramagnetic resonance spectrum recorded at room temperature conveys that the superexchange interaction is increased with the increase in Mn concentration.

Nano-CdS samples are synthesized by precipitation method and are annealed at 50°C, 82°C and 110°C for 5 h in air. The particle size of these annealed samples is measured by photoacoustic technique and the influence of annealing on the thermal properties are measured and discussed.

A computational study on adsorption and dissociation mechanisms of H₂ molecule on ZnO cluster was analysed using Density Functional Theory (DFT) approach in Gaussian 09 software. The stable sites for hydrogen adsorption were inferred from the adsorption energy and bond length. Further investigations such as Mulliken charge, HOMO–LUMO energy gap and intrinsic reaction coordinate (IRC) were performed for the stable adsorption sites. It infers that the (ZnO)₆ cluster has the highest binding energy of 1.851eV (O-site) and the least binding energy of $-$3.865eV (O-site), showing most favorable size for both adsorption and dissociation of H₂ molecule. The IRC plot clearly shows the dissociation mechanism of hydrogen on the ZnO cluster.

Size-dependent optical properties of semiconductor cadmium tellurite (CdTe) quantum dots (QDs) were examined by UV–Visible absorption, photoluminescence, Transmission electron microscope (TEM) and $Z$-scan. Red shift in the wavelength was observed in absorption and photoluminescence as the size increased. The size of the CdTe QDs is in the range between 3nm and 6nm. Two-photon absorption with reverse saturable absorption varied with size in picosecond region due to exciton oscillator. CdTe QDs can be used as optical limiters in the region of visibility.

In this research, an attempt is made to prepare an organic–inorganic hybrid material that aims to improve some of the physical properties of polymeric mixtures composed of polyethelyne oxide (PEO) and polystyrene (PS) by adding copper oxide (CuO) nanoparticles to the single polymers as well as by adding them to the mixture whereby 5% of nanoparticles were added to the polymer. The effect of the addition was studied by SEM and UV–Visible spectrophotometer. The energy band gaps attained by Tauc equation proved that the energy bandgaps are (from 4.4, 3.1 and 3.1eV) for nanocomposites.

Chloroquine (CQ) has been a good treatment for antimalarial mainstay for several decades; additionally discovered, it has a significant therapeutic impact on some instances of fungal inhibition. This study focused on the effect of novel CQ compounds on the activity of two different species of fungi, Aspergillus niger and Aspergillus falves. The activity of each CQ derivative was monitored using Nuclear magnetic resonance spectroscopy (NMR), minimal inhibitory concentration and physical parameters such as optical microscopy, UV/visible absorbance and optical band gap. NMR indicated the conjugation between the substrate and amino acid. The optical microscopic images indicated homogeneously distributed and uniform density distribution of CQ-derivative particles on the glass substrates. The samples’ presented absorption peaks at 203, 207 and 220 nm wavelengths, suggesting the important electronic transition with reducing the indirect bandgap from 4.1 eV to 3.95 eV. These compounds have the best antifungal growth inhibitory properties and excellent features, indicating cosmetics use.