Vortex structure in anisotropic and quantum-limit superconductors 異方的ならびに量子極限の超伝導体における渦構造

博士論文

Electronic structure of a single vortex (or vortex core structure) in type-II superconductors is theoretically discussed in the present thesis. Low-lying excited states in the superconductors due to the vortex, i.e., "vortex bound states," are examined in detail on the basis of numerical calculations. Two points are focused on: the effect of superconducting gap anisotropy on a vortex (Chapter 2) and the property of a vortex in quantum-limit situation (Chapter 3). The anisotropy of a superconducting energy gap has substantial effects on the structure of the vortex bound states. The local density of states around a vortex is calculated in a clean superconductor with the gap anisotropy within the framework of the quasiclassical theory of superconductivity. A characteristic structure of the local density of states, observed experimentally in the layered hexagonal superconductor 2H-NbSe(2) by scanning tunneling microscopy (STM), is well reproduced by assuming an anisotropic s-wave gap. The local density of states (or the bound states) around a vortex in superconductors with gap anisotropy is interpreted in terms of quasiparticle trajectories to facilitate an understanding of the rich electronic structure observed in STM experiments. This reveals not only a rich internal electronic structure associated with a vortex core, but also unique ability of the STM spectroscopy. The quantum limit means that the superconducting coherence length is small in the limit, i.e., it is comparable to the atomic length order. Focusing on quantum-limit behavior, fundamental structure of a vortex is studied by self-consistently solving the Bogoliubov-de Gennes equation. The discreteness of the energy levels of the vortex bound states is crucial for the vortex structure in the quantum limit. The following are revealed by the study of the quantum limit. The vortex core radius shrinks monotonically up to an atomic-scale length on lowering the temperature T, and the shrinkage stops to saturate at a lower T. The pair potential, supercurrent, and local density of states around the vortex exhibit Friedel-like oscillations. The local density of states inside a vortex core generally has particle-hole asymmetry induced by the existence of the vortex itself. Some essential properties of general vortices which are concealed within the conventional non-quantum-limit analysis can be extracted by the quantum-limit analysis. On the basis of the inherent particle-hole asymmetry inside vortex cores, it is discussed in this thesis that electric charging of a vortex core is originated from the Friedel oscillation of the Bogoliubov wave functions around the vortex (Chapter 4) . This mechanism of the vortex core charging is independent of the slope in the normal-state density of states at the Fermi level. The temperature dependence of the vortex core charge is also presented. It is expected that by using STM, information on the vortex core charging is extracted through a relation between the vortex core charge and the vortex bound states.