Circumventing the no-go theorem: A single Weyl point without surface Fermi arcs

Abstract

Despite a rapidly expanding inventory of possible crystalline Weyl semimetals, all of them are constrained by the Nielsen-Ninomiya no-go theorem, namely, that left- and right-handed Weyl points appear in pairs. With time-reversal (T) symmetry, an even stronger version holds for the semimetals, i.e., all eight time-reversal-invariant points in the Brillouin zone (BZ) simultaneously host Weyl points or not. Accompanying the no-go theorem, the surface of the system features Fermi arc states, which connect pairs of surface projected Weyl points. Here, we explicitly construct a topological phase of a T-invariant crystalline metal, which features a single Weyl point residing at the center of the BZ, surrounded by nodal walls spreading over the entire BZ boundary. In other words, a single Weyl point is realized with the no-go theorem being circumvented. Moreover, the surface Fermi arcs, considered as a hallmark of Weyl semimetals, do not appear for this composite topological phase. We show that this phase can be realized for space groups No. 19 and No. 92, with and without spin-orbit coupling, respectively.