Topological phases in acoustic and mechanical systems
The study of classical wave physics has been reinvigorated by incorporating the concept of the geometric phase, which has its roots in optics, and topological notions that were previously explored in condensed matter physics. Recently, sound waves and a variety of mechanical systems have emerged as excellent platforms that exemplify the universality and diversity of topological phases. In this Review, we introduce the essential physical concepts that underpin various classes of topological phenomena realized in acoustic and mechanical systems: Dirac points, the quantum Hall, quantum spin Hall and valley Hall effects, Floquet topological phases, 3D gapless states and Weyl crystals.This Review describes topological phenomena that can be realized in acoustic and mechanical systems. Methods of symmetry breaking are described, along with the consequences and rich phenomena that emerge.Key pointsAcoustic and mechanical systems are versatile platforms to study a wide range of topological phases that were first investigated in condensed matter physics.Topological phenomena that can be observed include Dirac points and analogues of the quantum Hall effect, quantum spin Hall effect, valley Hall effect, Floquet topological phases, gapless states and Weyl systems.Because classical acoustic systems are different from condensed matter systems (for example, they lack Kramers degeneracy) new approaches are needed to realize topological phases.Schemes of symmetry breaking in phononic crystals play a key role in the realization of these topological phases, and their consequences and limitations are discussed.
Nature Reviews Physics