Circumventing the no-go theorem: A single Weyl point surrounded by nodal walls

Abstract

Despite of 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. However, all the well-known conclusions from the no-go theorem are implicitly within the current framework of topological semimetals, and in this work, we shall go beyond it by exploring composites of topological metal and semimetal phases. Guided by crystal symmetry and T symmetry, we propose a new topological phase of T-invariant crystalline metal, where a single Weyl point resides 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. Meanwhile, the Fermi arc surface states, considered as a hallmark of Weyl semimetals, do not appear for this new composite topological phase. We show that this phase can be realized for space group 19 and 92, with and without spin-orbit coupling, respectively.