Abstract: Within the framework of the nonlinear Ginzburg-Landau theory, we calculated the full phase diagram for a superconducting disk with radius R = 4 (T = 0) and we studied the behavior of the penetration and expulsion fields as a function of temperature for multivortex and giant vortex states.

Abstract: X-ray diffraction and energy dispersive x-ray spectroscopic analyses showed a natural galena (PbS) crystal from Freiberg in Saxony (Germany) to be a single phase specimen [rock salt (NaCl) structure type, space group Fm3m, a = 5.932(1) angstrom] with stoichiometric composition and an enhanced dislocation density (8 approximate to 1011 cm-2). The latter parameter leads to an increase of the electrical resistivity in the high-temperature regime, as well as to the appearance of phonon resonance with a characteristic frequency coPR = 3.8(1) THz. Being in the same range (i.e., 3-5.5 THz) with the sulfur optical modes of highest group velocities, it results in a drastic reduction (by similar to 75%) of thermal conductivity (K) at lower temperatures (i.e., < 100 K), as well as in the appearance of a characteristic minimum in K at T approximate to 30 K. Furthermore, the studied galena is characterized by phonon-drag behavior and by temperature dependent switch of the charge carrier scattering mechanism regime (i.e., scattering on dislocations for T < 100 K, on acoustic phonons for 100 K < T < 170 K and on both acoustic and optical phonons for 170 K < T < 300 K). The combined theoretical calculation and optical spectroscopic study confirm this mineral to be a direct gap degenerate semiconductor. The possible origins of the second-order Raman spectrum are discussed.