Nodal structure of quasi-2D superconductors probed by magnetic field

We consider a quasi two-dimensional superconductor with line nodes in an in-plane magnetic field, and compute the dependence of the specific heat, $C$, and the in-plane heat conductivity, $\kappa$, on the angle between the field and the nodal direction in the vortex state. We use a variation of the microscopic Brandt-Pesch-Tewordt method that accounts for the scattering of quasiparticles off vortices, and analyze the signature of the nodes in $C$ and $\kappa$. At low to moderate fields the specific heat anisotropy changes sign with increasing temperature. Comparison with measurements of $C$ and $\kappa$ in CeCoIn${}_5$ resolves the contradiction between the two in favor of the $d_{x^2-y^2}$ gap.