Figure 4
From: Nexus fermions in topological symmorphic crystalline metals
Material realizations of the new topological metal in WC class of materials. (a) Crystal structure of WC with space group P-6m2 (#187), showing the W and C atoms as silver and bronze spheres. (b) The corresponding bulk Brillouin zone with the relevant high symmetry points (yellow dots), k z  = 0 mirror plane (turquoise), and three mirror planes (blue) that intersect along the C 3-axis. (c) Band structure calculation of WC without SOC. In the absence of SOC, the crossing along \(M-K-{\rm{\Gamma }}\) results in a nodal ring around the K point. (d) Same calculation as in (c) but with the inclusion of SOC. Enclosed in the red rectangular box are two observed crossings points along the \({\rm{\Gamma }}-A\) line. Furthermore, inclusion of SOC allows for the touching points along \(M-K-{\rm{\Gamma }}\) that are protected by the k z  = 0 mirror plane to remain and form two nodal rings around the K point. (e) In the left panel, a zoomed-in calculation of the region within the red rectangular box in (d) reveals that the doubly (blue) and singly (black) degenerate bands cross at two different energies. The triply-degenerate node above the Fermi level is type-I, and the one below the Fermi level is type-II. In the right panel, the type-II character of the triply-degenerate fermion is shown by cutting through the degeneracy point along the k a -direction. (f) Zoomed-in calculation of the observed type-II triply-degenerate crossing in (e) in the absence (left panel) and presence of a magnetic field along the k z -direction. The application of the field along this direction preserved C 3 symmetry, and results in the triply-degenerate fermion to split into a pair of Weyl fermions by splitting the doubly-degenerate band into two singly-degenerate bands. The resulting two Weyl fermions are labeled as W 1 and W 2, marking the crossing points between the black/yellow and red/yellow bands, respectively.
