No abstract

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 K2Mg2O3 (SG No. 96) and charge‐four IWP in Nb3Al2N (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.

Weyl phonons have long been regarded as an important kind of topological bosonic quasiparticle states. Previous investigations in this field mainly focus on Weyl phonons located at high‐symmetry points (HSPs) in Brillouin zone (BZ), while those located at high‐symmetry lines (HSLs, not including HSPs) are still rarely studied. Considering that their symmetry‐protected conditions are much different, we name them conventional and unconventional Weyl phonons, respectively. In this work, taking charge‐two Weyl phonons (CTWPs) as examples, the complete classifications of all unconventional CTWPs is summarized by performing symmetry analysis in all 230 space groups (SGs). Moreover, due to their different phononic dispersions, the unconventional CTWPs can be classified as Type‐I, Type‐II, and Type‐III ones. Particularly, the k · p model of unconventional CTWPs shows a k‐type feature along the invariant lines while a k2‐type feature along other directions. Additionally, we uncover that a real chiral crystal material, that is, CsBe2F5 in SG 213, can exhibit well‐defined Type‐I and Type‐II unconventional CTWPs characterized by multiple double‐helicoid surface states. Our theoretical work not only puts forward an effective way for seeking for unconventional CTWPs, but also uncover the unique advantages of this kind of CTWPs toward realistic device applications.