Multi‐Fold Fan‐Shape Surface State Induced by an Isolated Weyl Phonon Beyond No‐Go Theorem

Absence of any surface arc state has been regarded as the fundamental property of singular Weyl points, because they are circumvented from the Nielsen‐Ninomiya no‐go theorem. In this work, through systematic investigations on topological properties of isolated Weyl phonons (IWPs) surrounded by closed Weyl nodal walls (WNWs), which are located at the Brillouin zone (BZ) boundaries of bosonic systems, it uncovers that a new kind of phononic surface state, that is, the multi‐fold fan‐shape surface state named by us, is exhibited to connect the projections of IWP and WNWs. Importantly, the number of fan leaves in this surface state is associated with the Chern number of IWP. Moreover, the topological features of charge‐two IWP in K(2)Mg(2)O(3) (SG No. 96) and charge‐four IWP in Nb(3)Al(2)N (SG No. 213) confirm further the above fundamental properties of this kind of surface state. The theoretical work not only provides an effective way to seek for IWPs as well as to determine their Chern number in real materials, but also uncovers a new class of surface states in the topological Weyl complex composed of IWPs and WNWs.