Planar Topological Defects in Unconventional Superconductors

In this work, we consider the properties of planar topological defects in unconventional superconductors. Specifically, we calculate microscopically the interaction energy of domain walls separating degenerate ground states in a chiral p-wave fermionic superfluid. The interaction is mediated by the quasiparticles experiencing Andreev scattering at the domain walls. As a by-product, we derive a useful general expression for the free energy of an arbitrary nonuniform texture of the order parameter in terms of the quasiparticle scattering matrix. The thesis is structured as follows. We begin with a historical review of the theories of superconductivity (Sec. 1.1), which led the way to the celebrated Bardeen-Cooper- Schrieffer (BCS) theory (Sec. 1.3). Then we proceed to the treatment of superconductors with so-called "unconventional pairing" in Sec. 1.4, and in Sec. 1.5 we introduce the specific case of chiral p-wave superconductivity. After introducing in Sec. 2 the domain wall (DW) model that will be considered throughout the work, we derive the Bogoliubov-de Gennes (BdG) equations in Sec. 3.1, which determine the quasiparticle excitation spectrum for a nonuniform superconductor. In this work, we use the semiclassical (Andreev) approximation, and solve the Andreev equations (which are a particular case of the BdG equations) in Sec. 4 to determine the quasiparticle spectrum for both the single- and two-DW textures. The Andreev equations are derived in Sec. 3.2, and the formal properties of the Andreev scattering coefficients are discussed in the following subsection. In Sec. 5, we use the transfer matrix method to relate the interaction energy of the DWs to the scattering matrix of the Bogoliubov quasiparticles. This facilitates the derivation of an analytical expression for the interaction energy between the two DWs in Sec. 5.3. Finally, to illustrate the general applicability our method, we apply it in Sec. 6 to the interaction between phase solitons in a two-band s-wave superconductor.

Polytypism and Silicon carbide : a solid state nuclear magnetic resonance study

A survey of predominantly industrial silicon carbide has been carried out using Magic Angle Spinning nuclear magnetic resonance (MAS nmr); a solid state technique. Three silicon carbide polytypes were studied; 3C, 6H, and 15R. The 13C and 29 Si MAS nmr spectra of the bulk SiC sample was identified on the basis of silicon (carbon) site type in the d iff ere n t pol Y t Y pes • Out to 5.00 A fro mac en t r a lsi 1 i con (0 r carbon) atom four types of sites were characterized using symmetry based calculations. This method of polytype analysis was also considered, in the prelminary stages, for applications with other polytypic material; CdBr 2 , CdI 2 , and PbI 2 " In an attempt to understand the minor components of silicon carbide, such as its surface, some samples were hydrofluoric acid washed and heated to extreme temperatures. Basically, an HF removable species which absorbs at -110 ppm (Si0 2 ) in the 29 Si MAS nmr spectrum is found in silicon carbide after heating. Other unidentified peaks observed at short recycle delays in some 29 Si MAS nmr spectra are considered to be impurities that may be within the lattice. These components comprise less than 5% of the observable silicon. A Tl study was carried out for 29 Si nuclei in a 3C ii polytype sample, using the Driven Equilibrium Single-Pulse Observation of T1 (DESPOT) technique. It appears as though there are a number of nuclei that have the same chemical shift but different T1 relaxation times. The T1 values range from 30 seconds to 11 minutes. Caution has to be kept when interpreting these results because this is the first time that DESPOT has been used for solid samples and it is not likely in full working order. MAS nmr indicates that the 13C and 29 Si ~sotropic chemical shifts of silicon carbide appear to have a reciprocal type of relationship_ Single crystal nmr analysis of a 6H sample is accordance with this finding when only the resultant isotropic shift is considered. However, single crystal nmr also shows that the actual response of the silicon and carbon nuclear environment to the applied magnetic field at various angles is not at all reciprocal. Such results show that much more single crystal nmr work is required to determine the actual behavior of the local magnetic environment of the SiC nuclei.

Effects of naringenin on glucose uptake in L6 skeletal muscle cells

Diabetes mellitus is a disorder of inadequate insulin action and consequent high blood glucose levels. Type 2 diabetes accounts for the majority of cases of the disease and is characterized by insulin resistance and relative insulin deficiency resulting in metabolic deregulation. It is a complex disorder to treat as its pathogenesis is not fully understood and involves a variety of defects including ~-cell failure, insulin resistance in the classic target tissues (adipose, muscle, liver), as well as defects in a-cells and kidney, brain, and gastrointestinal tissue. Present oral treatments, which aim at mimicking the effects of insulin, remain limited in their efficacy and therefore the study of the effects of novel compounds on insulin target tissues is an important area of research both for potentially finding more treatment options as well as for increasing our knowledge of metabolic regulation in health and disease. In recent years the extensively studied polyphenol, resveratrol, has been reported to have antidiabetic effects showing that it increases glucose uptake by skeletal muscle cells and prevents fatty acid-induced insulin resistance in vitro and in vivo. Naringenin, a citrus flavonoid with structural similarities to resveratrol, is reported to have antioxidan.t, antiproliferative, anticancer, and anti-inflammatory properties. Effects on glucose and lipid metabolism have also been reported including blood glucose and lipid lowering effects. However, whether naringenin has insulinlike effects is not clear. In the present study the effects of naringenin on glucose uptake in skeletal muscle cells are examined and compared with those of insulin. Naringenin treatment of L6 myotubes increased glucose uptake in a dose- and time dependent manner and independent of insulin. The effects of naringenin on glucose uptake achieved similar levels as seen with maximum insulin stimulation and its effect was additive with sub-maximal insulin treatment. Like insulin naringenin treatment did not increase glucose uptake in myoblasts. To elucidate the mechanism involved in naringenin action we looked at its effect on phosphatidylinositol 3-kinase (PI3K) and Akt, two signalling molecules that are involved in the insulin signalling cascade leading to glucose uptake. Naringenin did not stimulate basal or insulinstimulated Akt phosphorylation but inhibition of PI3K by wortmannin partially repressed the naringenin-induced glucose uptake. We also examined naringenin's effect on AMP-activated protein kinase (AMPK), a molecule that is involved in mediating glucose uptake by a variety of stimuli. Naringenin stimulated AMPK phosphorylation and this effect was not inhibited by wortmannin. To deduce the nature of the naringenin-stimulated AMPK phosphorylation and its impact on glucose uptake we examined the role of several molecules implicated in mod.ulating AMPK activity including SIRTl, LKB 1, and ca2+ Icalmodulin-dependent protein kinase kinase (CaMKK). Our results indicate that inhibition of SIRTI did not prevent the naringeninstimulated glucose uptake Of. AMPK phosphorylation; naringenin did not stimulate LKB 1 phosphorylation; and inhibition of CaMKK did not prevent naringeninstimulated glucose uptake. Inhibition of AMPK by compound C also did not prevent naringenin-stimulated glucose uptake but effectively inhibited the phosphorylation of AMPK suggesting that AMPK may not be required for the naringenin-stimulated glucose uptake.