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

TL;DR

This paper introduces a spectroscopic method using polar angle-resolved density of states measurements to identify nodal gap structures in uniaxial superconductors, aiding in the detection of horizontal line and point nodes.

Contribution

It develops a theoretical framework for analyzing $N( heta)$ patterns to determine nodal structures, validated by comparison with experimental data.

Findings

Maxima of $N( heta)$ shift from anti-nodal to nodal directions with increasing magnetic field.

Local minima appear near the maxima in $N( heta)$, except for linear point nodes.

Features are robust and can be detected experimentally.

Abstract

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.