Nodal Structure of Quasi-Two-Dimensional Superconductors Probed by a Magnetic Field

We consider a quasi-two-dimensional superconductor with line nodes in the presence of 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 ${\mathrm{CeCoIn}}_5$ resolves the contradiction between the two in favor of the $d_{x^2-y^2}$ gap.

Figure 1

(a) Low-energy DOS for $\mathit{H}\parallel \mathrm{\text{antinode}}$ and $\mathit{H}\parallel \mathrm{\text{node}}$ at $T=0.05T_c$. Arrows indicate $\epsilon (H)$, see text. (b)–(d) Angle-resolved DOS plotted at each position on the FS. Net DOS is proportional to the red shaded area, see text.

Figure 2

Specific heat anisotropy for different $T$ at two fields. Nodal direction ${\varphi }_0=45°$. Left panel: $H=0.26H_{c2}$, inversion of the anisotropy occurs at $T_0\sim 0.15T_c$. Right panel: $H=0.52H_{c2}$, no minimum for the field along the node at any $T$. Some curves are shifted by the amount indicated in parentheses.

Figure 3

Thermal conductivity anisotropy for different $T$ at a $H=0.26H_{c2}$ (left panel), and for different $H$ at $T=0.25T_c$ (right panel). Curves are shifted for clarity by the amount indicated. Left panel: notice the reversal of the 0°–90° anisotropy and the change from minimum to maximum at 45°. Right panel provides direct comparison with Ref. 6.