Phonon analog of topological nodal semimetals

Topological band structures are ubiquitous in both fermionic and bosonic problems, but conventional wisdom holds that the topological features in a noninteracting bosonic system are only visible to finite-frequency probes. Utilizing a recently proposed boson-to-fermion mapping, the authors demonstrate that topological gapless phonon modes can in fact be brought all the way down to zero frequency. In particular, they construct spring-mass models that are analogs of two-dimensional Dirac semimetals, and hence feature topological zero-frequency phonon modes. These zero modes are physically distinct from the familiar Goldstone phonons, and are in fact present even in pinned disordered systems due to topological protection.