Vortex Charges And Vortex State Phase Transitions In Superconductors

The progress of nanofabrication technologies from the 1990s resulted in an increase of interest in the study of superconducting properties of mesoscopic samples. A mesoscopic sample is such that its size is comparable to the coherencelengthξand penetration depthλ. The properties of mesoscopic systems areconsiderably influenced by confinement effects. Therefore, the vortex state will depend on the size and the geometry of the sample. In addition, the vortex structure in high temperature superconductors (HTSCs) has attracted significant interest for many years. Since the parent compounds are antiferromagnetic Mott insulators, novel physical properties of HTSCs including those in the vortex state would be expected due to the competition between spin magnetism and superconductivity in these systems.The vortex charge distribution and vortex state phase transitions of HTSCs and thin mesoscopic rings are investigated theoretically in the framework of the Bogoliubov-de Gennes theory and the phenomenological Ginzburg-Landau theorywithin the de Gennes boundary condition (?) (b is thesurface extrapolation length). Main results are summarized as follows:(1) The effect of neat-nearest-neighbor (nnn) hopping on the antiferromagnetism and vortex charges for doped HTSCs is investigated by numerically solving the Bogoliubov-de Gennes equations based on a model Hamiltonian with competing antiferromagnetic (AFM) and d-wave superconductivity interactions. We find that the AFM order magnitude in the vortex core is first enhanced and then suppressed for an optimally doped sample, accompanied with vortex charge sign change from positive to negative when the relative nnn hopping strength (in units of nearest neighbor hopping strength) increases from 0 to 0.4. It is also found that positive vortex charges can be observed at a large nnn hopping strength even though the AFM order remains strong for an underdoped sample. In addition, the structure transitions between two-dimensional fourfold symmetry and one-dimensional stripe of vortex charge and spin-density wave orders may occur by tuning the nnn hopping strength.(2) The superconducting state of a thin mesoscopic superconducting ring surrounded by a medium which enhanced its superconductivity (of a negative surface extrapolation length b) near the boundary is investigated by the phenomenological Ginzburg-Landau theory. The free energy, the Cooper-pair density, and the current density as well as the H-T phase diagram are investigated for a ring with different surface enhancement or for different rings with the same surface enhancement. It is also found that the stable multivortex state can occur in the small ring that we studied if the enhanced surface superconductivity is stronger, and the stable (1: L₂) and (2: L₂) states can exist as the ground states with increasing the inner radius.(3) The superconducting phase transitions between different vortex states with the magnetic field for a thin mesoscopic superconducting ring surrounded by a medium that enhanced its superconductivity near the boundary are investigated by the phenomenological Ginzburg-Landau theory. The transitions between different giant vortex states and between the giant vortex and multivortex states withâ–³L > 1 (L is the vorticity of the vortex state) are found for a small ring with increasing surface enhancement. The influences of the surface enhancing superconducting effect and the inner radius as well as the temperature on phase transition are studied by examiningthe H-|ξ/b|, H-R_i and H-T phase diagrams, respectively. Further increasingthe effect of enhanced surface superconductivity, we find the reentrant transition with the same vorticity and the transitions between the stable multivortex states withâ–³L > 1 for different ring inner radii. We also investigate the vortex configurations for a relatively large ring, and the vortex state with two stable vortex shells can be found as the ground state due to the enhanced surface superconductivity.(4) The charge distribution in a thin mesoscopic superconducting ring with enhanced surface superconductivity is investigated by the phenomenological Ginzburg-Landau theory. The nature of charge distribution is considerably influenced by the extrapolation length b, the inner and outer radius, and the applied magnetic field. We find a complete negative charge distribution besides the conventional charge distributions of charging vortex states in the Meissner state and the giant vortex state. In addition, one type of charge distribution that only exists in a giant vortex state can also be found in the Meissner state for a ring with a small inner radius. For the multivortex state, we find that the stable multivortex state can exist in small mesoscopic superconducting rings that we studied. The charge distributions for different kinds of multivortex states are given.