Topological $d$-wave Superconductivity and Nodal Line-Arc Intersections in Weyl Semimetals

Abstract

Superconducting Weyl semimetals present a novel and promising system to harbor new forms of unconventional topological superconductivity. Within the context of time-reversal symmetric Weyl semimetals with $d$-wave superconductivity, we demonstrate that the number of Majorana cones equates to the number of intersections between the $d$-wave nodal lines and the Fermi arcs. We illustrate the importance of nodal line-arc intersections by demonstrating the existence of locally stable surface Majorana cones that the winding number does not predict. The discrepancy between Majorana cones and the winding number necessitates an augmentation of the winding number formulation to account for each intersection. In addition, we show that imposing additional mirror symmetries globally protect the nodal line-arc intersections and the corresponding Majorana cones.