Derivation of the superconducting gap equation for the noncentrosymmetric superconductor Li2Pt3B

We present here the mathematical background of our approach, presented in Phys. Rev. B 86, 134526 (2012) regarding the gap function and symmetry for the noncentrosymmetric (NCS) superconductor $Li_2Pt_3B$. As revealed by the experiment, this NCS superconductor gives rise to line nodes in the superconducting order parameter, which is responsible for many of its experimental behaviors. Owing to the enhanced d-character of the relevant bands that cross the Fermi level,the system gets weakly correlated. The nature and symmetry of this nodal behavior is explained from a microscopic viewpoint. In this article starting with an Hubbard model relevant for this NCS system by considering the effect of the onsite Coulomb repulsion on the pairing potential perturbatively, we extract the superconducting gap equation. Further analysis of this equation predicts a $s_\pm$ wave gap function with line nodes as the most promising candidate in the superconducting state.Comment: 7 pages, Proceeding versio

Synthesis and Characterization of Trivalent Al Substituted Zinc Ferrite using Ethylene Diamine (EDA) as Ligand

Nano domain Al substituted Zinc ferrite was prepared by chemical route using Ethylene Diamine as ligand. High purity precursors nitrate salts of Zinc, Fe(3+), Al(3+) were utilized along with citric acid which acts as both fuel and complexing agent. Two different molar ratios of Zn(2+):(Fe3+):Al(3+) is 1:1.5:0.5 and 1:1.25:0.75. After ensuring proper mix of the solution Ethylene diamine was added dropwise to form a gel like mass with proper pH control. Before annealing, thermal analysis was carried to determine the crystallization/phase transition zone. Drying was carried in several stages. Initially, gel like mass was obtained after drying at 40°C while pH was about 7. Drying of gel was carried in oil bath at about 90°C and powdered mass obtained was grinded followed by auto combustion at 150°C for 60 minutes before annealing at 150°C, 350°C, 650°C, 950°C for 2 hours to ensure the phase formation. Crystallite size, lattice strain and lattice parameters were studied from XRD analysis

Ginzburg-Landau theory of noncentrosymmetric superconductors

The data of temperature dependent superfluid density $n_s(T)$ in Li$_2$Pd$_3$B and Li$_2$Pt$_3$B [Yuan {\it et al.}, \phrl97, 017006 (2006)] show that a sudden change of the slope of $n_s (T)$ occur at slightly lower than the critical temperature. Motivated by this observation, we microscopically derive the Ginzburg-Landau (GL) equations for noncentrosymmetric superconductors with Rashba type spin orbit interaction. Cooper pairing is assumed to occur between electrons only in the same spin split band and pair scattering is allowed to occur between two spin split bands. The GL theory of such a system predicts two transition temperatures, the higher of which is the conventional critical temperature $T_c$ while the lower one $T^*$ corresponds to the cross-over from a mixed singlet-triplet phase at lower temperatures to only spin-singlet or spin-triplet (depending on the sign of the interband scattering potential) phase at higher temperatures. As a consequence, $n_s (T)$ shows a kink at this cross-over temperature. We attribute the temperature at which sudden change of slope occurs in the observed $n_s (T)$ to the temperature $T^*$. This may also be associated with the observed kink in the penetration depth data of CePt$_3$Si. We have also estimated critical field near critical temperature.Comment: 7 pages, 1 figur

Development of Selenium-Silica Nanocomposites By Sol-Gel Process Utilizing Three Different Reducing Agents and Its Characterization

Nanocrystalline Selenium was synthesized within a silica matrix using a sol-gel method with high-purity SeO2, ethyl alcohol, distilled water, and TEOS (Tetraethyl orthosilicate). This process encapsulated the selenium dioxide in the silica matrix, which was then reduced at about 100°C using an oil bath. Three reducing agents were employed: acetone vapor, and sodium borohydride (NaBH4) and hydrazine (N2H4) in liquid form. DSC-TGA analyses of the precursor mixture determined the crystallization temperature for selenium nanoparticle formation within the matrix to be around 100°C. Post-heating phase analysis via XRD revealed hexagonal structures, with crystallite sizes between 33 and 43 nm determined using Debye-Scherrer's formula. Morphological studies showed irregular polygonal shapes with rough surfaces, with particulate sizes under 0.2µ for acetone vapor, around 0.1µ for hydrazine, and slightly over 0.1µ for sodium borohydride. Time variations were explored to observe phase and crystallite size changes. FTIR analysis was conducted for bonding assessment, revealing M-O coordination. The composite's absorbance was examined through UV-VIS spectroscopy, and its morphological attributes were investigated using FESEM analysis, complemented by EDX to determine elemental compositio