Effects of Fermi surface and superconducting gap structure in the field-rotational experiments: A possible explanation of the cusp-like singularity in YNi$_2$B$_2$C

Abstract

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