Quasiparticle density of states in layered superconductors under a magnetic field parallel to theabplane: Determination of the gap structure ofSr2RuO4

Abstract

We study the vortex state of a layered superconductor with vertical line nodes on its Fermi surface when a magnetic field is applied in the $ab$-plane direction. We rotate the magnetic field within the plane, and analyze the change of low-energy excitation spectrum. Our analysis is based on the microscopic Bogoliubov-de Gennes equation and a convenient approximate analytical method invented by Pesch and developed by Dahm et al. Both methods give consistent results. Near the upper critical field ${H}_{c2}$, we observe a larger zero-energy density of states (ZEDOS) when the magnetic field is applied in the nodal direction, while much below ${H}_{c2}$, larger ZEDOS is observed under a field in the anti-nodal direction. We give a natural interpretation to this crossover behavior in terms of contributions of quasiparticles propagating parallel and perpendicular to the applied field in the plane. We examine the recent field angle variation experiments of thermal conductivity and specific heat. Comparisons with our results suggest that special care should be taken to derive the position of line nodes from the experimental data. Combining the experimental data of the specific heat and our analyses, we conclude that ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$ has a vertical-line-node-like structure in the direction of the $a$ axis and the $b$ axis.