Phonon analogue of topological nodal semimetals

TL;DR

This paper introduces a mechanical analog of topological semimetals, demonstrating how gapless bulk modes in mechanical systems can be topologically protected and tunable, expanding the understanding of topological phenomena in bosonic systems.

Contribution

It generalizes the Kane-Lubensky mapping to gapless systems, constructing mechanical counterparts of topological semimetals with protected zero-frequency phonon modes.

Findings

Mechanical topological semimetals exhibit gapless bulk modes.

Zero-frequency phonon modes are topologically protected.

Modes have adjustable momenta and are robust to lattice changes.

Abstract

Topological band structures in electronic systems like topological insulators and semimetals give rise to highly unusual physical properties. Analogous topological effects have also been discussed in bosonic systems, but the novel phenomena typically occur only when the system is excited by finite-frequency probes. A mapping recently proposed by Kane and Lubensky [Nat. Phys. 10, 39 (2014)], however, establishes a closer correspondence. It relates the zero-frequency excitations of mechanical systems to topological zero modes of fermions that appear at the edges of an otherwise gapped system. Here we generalize the mapping to systems with an intrinsically gapless bulk. In particular, we construct mechanical counterparts of topological semimetals. The resulting gapless bulk modes are physically distinct from the usual acoustic Goldstone phonons, and appear even in the absence of continuous translation invariance. Moreover, the zero-frequency phonon modes feature adjustable momenta and are topologically protected as long as the lattice coordination is unchanged. Such protected soft modes with tunable wavevector may be useful in designing mechanical structures with fault-tolerant properties.