Kramer-Pesch Approximation for Analyzing Field-Angle-Resolved Measurements Made in Unconventional Superconductors: A Calculation of the Zero-Energy Density of States

By measuring the angular-oscillations behavior of the heat capacity with respect to the applied field direction, one can detect the details of the gap structure. We introduce the Kramer-Pesch approximation as a new method to analyze the field-angle-dependent experiments, which improves the previous Doppler-shift technique. We show that the Fermi-surface anisotropy is an indispensable factor for identifying the superconducting gap symmetry.

Figure 1

Angular dependence of the ZEDOS calculated by the KPA in a $d_{x^2-y^2}$-wave SC with the spherical FS. The magnetic field tilts from the $c$ axis by polar angle ${\theta }_{\mathrm{M}}$. The smearing factor $\eta =0.05{\Delta }_0$ and the cutoff length $r_a=7{\xi }_0$.

Figure 2

Angular dependence of the ZEDOS obtained by (a) the KPA and (b) the direct numerical and KPA calculations in the $d_{x^2-y^2}$-wave SC with the cylindrical FS. (a) $\eta =0.05{\Delta }_0$ and $r_a=7{\xi }_0$. (b) $\eta =0.001{\Delta }_0$ and $r_a=5{\xi }_0$.

Figure 3

Angular dependence of the ZEDOS calculated by the KPA in SCs with a point-node gap on (a) the cylindrical and (b) the spherical FS. $\eta =0.05{\Delta }_0$ and $r_a=7{\xi }_0$.

Figure 4

Schematic figures of (a) the spherical and (b) the cylindrical FS in the $d$-wave case. The left and right panel denote a top and a side view, respectively. The hatched regions indicate the low-energy QPs around gap nodes.