Nodal gap detection through polar angle-resolved density of states measurements in uniaxial superconductors

We propose a spectroscopic method to identify the nodal gap structure in unconventional superconductors. This method best suits for locating the horizontal line node and for pinpointing the isolated point nodes by measuring polar angle ($\theta$) resolved zero energy density of states $N(\theta)$. This is measured by specific heat or thermal conductivity at low temperatures under a magnetic field. We examine a variety of uniaxially symmetric nodal structure, including point and/or line nodes with linear and quadratic dispersions, by solving Eilenberger equation in vortex states. It is found that (A) the maxima of $N(\theta)$ continuously shift from the anti-nodal to the nodal direction ($\theta_{\rm n}$) as a field increases accompanying the oscillation pattern reversal at low and high fields. Furthermore, (B) local minima emerge next to $\theta_{\rm n}$ on both sides except for the case of linear point node. These features are robust and detectable experimentally. Experimental results of $N(\theta)$ performed on several superconductors, UPd$_2$Al$_3$, URu$_2$Si$_2$, Cu$_x$Bi$_2$Se$_3$, and UPt$_3$, are examined and commented in light of the present theory.