Abstract: We solve the linear GinzburgLandau (GL) equation in the presence of a uniform magnetic field with cylindrical symmetry and we find analytic expressions for the eigenfunctions in terms of the confluent hypergeometric functions. The discrete spectrum results from an implicit equation associated to the boundary conditions and it is resolved in analytic form using the continued fractions formalism. We study the dependence of the spectrum and the eigenfunctions on the sample size and the surface conditions for solid and hollow cylindrical superconductors. Finally, the solutions of the nonlinear GL formalism are constructed as expansions in the linear GL eigenfunction basis and selected by minimization of the free energy. We present examples of vortex states and their energies for different samples in enhancing/suppressing superconductivity surroundings.

Abstract: Aberration-corrected transmission electron microscopy, electron energy-loss spectroscopy, and density functional theory (DFT) calculations are used to solve several key questions about the surface structure, the particle morphology, and the distribution and nature of nitrogen impurities in detonation nanodiamond (DND) cleaned by a recently developed ozone treatment. All microscopy and spectroscopy measurements are performed at a lowered acceleration voltage (80/120kV), allowing prolonged and detailed experiments to be carried out while minimizing the risk of knock-on damage or surface graphitization of the nanodiamond. High-resolution TEM (HRTEM) demonstrates the stability of even the smallest nanodiamonds under electron illumination at low voltage and is used to image the surface structure of pristine DND. High resolution electron energy-loss spectroscopy (EELS) measurements on the fine structure of the carbon K-edge of nanodiamond demonstrate that the typical * pre-peak in fact consists of three sub-peaks that arise from the presence of, amongst others, minimal fullerene-like reconstructions at the nanoparticle surfaces and deviations from perfect sp(3) coordination at defects in the nanodiamonds. Spatially resolved EELS experiments evidence the presence of nitrogen within the core of DND particles. The nitrogen is present throughout the whole diamond core, and can be enriched at defect regions. By comparing the fine structure of the experimental nitrogen K-edge with calculated energy-loss near-edge structure (ELNES) spectra from DFT, the embedded nitrogen is most likely related to small amounts of single substitutional and/or A-center nitrogen, combined with larger nitrogen clusters.