宇田川 将文

We have studied the field-orientational dependence of zero-energy density of<br /> states (FODOS) for a series of systems with different Fermi surface and<br /> superconducting gap structures. Instead of phenomenological Doppler-shift<br /> method, we use an approximate analytical solution of Eilenberger equation<br /> together with self-consistent determination of order parameter and a<br /> variational treatment of vortex lattice. First, we compare zero-energy density<br /> of states (ZEDOS) when a magnetic field is applied in the nodal direction<br /> ($\nu_{node}(0)$) and in the antinodal direction ($\nu_{anti}(0)$), by taking<br /> account of the field-angle dependence of order parameter. As a result, we found<br /> that there exists a crossover magnetic field $H^*$ so that $\nu_{anti}(0) &gt;<br /> \nu_{node}(0)$ for $H &lt; H^*$, while $\nu_{node}(0) &gt; \nu_{anti}(0)$ for $H &gt;<br /> H^*$, consistent with our previous analyses. Next, we showed that $H^*$ and the<br /> shape of FODOS are determined by contribution from the small part of Fermi<br /> surface where Fermi velocity is parallel to field-rotational plane. In<br /> particular, we found that $H^*$ is lowered and FODOS has broader minima, when a<br /> superconducting gap has point nodes, in contrast to the result of the<br /> Doppler-shift method. We also studied the effects of in-plane anisotropy of<br /> Fermi surface. We found that in-plane anisotropy of quasi-two dimensional Fermi<br /> surface sometimes becomes larger than the effects of Doppler-shift and can<br /> destroy the Doppler-shift predominant region. In particular, this tendency is<br /> strong in a multi-band system where superconducting coherence lengths are<br /> isotropic. Finally, we addressed the problem of cusp-like singularity in<br /> YNi$_2$B$_2$C and present a possible explanation of this phenomenon.

We study the vortex state of a layered superconductor with vertical line<br /> nodes on its Fermi surface when a magnetic field is applied in the ab-plane<br /> direction. We rotate the magnetic field within the plane, and analyze the<br /> change of low-energy excitation spectrum. Our analysis is based on the<br /> microscopic<br /> Bogoliubov-de Gennes equation and a convenient approximate analytical method<br /> developped by Pesch and Dahm. Both methods give a consistent result. Near the<br /> upper critical field H$_{c2}$, we observe a larger zero-energy density of<br /> states(ZEDOS) when the magnetic field is applied in the nodal direction, while<br /> much below H$_{c2}$, larger ZEDOS is observed under a field in the anti-nodal<br /> direction. We give a natural interpretation to this crossover behavior in terms<br /> of momentum distribution of low-energy quasiparticles. We examine the recent<br /> field angle variation experiments of thermal conductivity and specific heat.<br /> Comparison with our results suggest that special care should be taken to derive<br /> the position of line nodes from the experimental data. Combining the<br /> experimental data of the specific heat and our analyses, we conclude that<br /> Sr$_2$RuO$_4$ has vertical line nodes in the direction of the a-axis and the<br /> b-axis.