Advances in Phonons: From Band Topology to Phonon Chirality

Abstract

Phonons are ubiquitous quasiparticles in solid state systems describing the quantized vibrations of a crystal lattice. Phonons play a central role in a wide range of physical phenomena, from transport to symmetry-breaking orders, such as charge density waves and superconductivity. {Traditionally treated as spin-0 bosons that obey Bose-Einstein statistics,} phonons have recently emerged as a fertile ground for exploring topological physics, spurred by the rapid development of topological band theory initially formulated for fermionic systems. {It is now understood that the phonon eigenstates, characterized by their eigenvalues and eigenvectors, can carry nontrivial topological invariants, including the Berry phase and Chern number. This new understanding opens up avenues to investigate the interplay between lattice dynamics, topology, and chirality in bosonic systems. In this article, we review recent theoretical and experimental advances in the field of topological phonons and circularly polarized phonons. We introduce foundational concepts, including the classification of phononic band structures, symmetry-protected topological phases, and the definition of topological invariants in bosonic systems. We emphasize the concept of phonon angular momentum and its fundamental connection to Weyl phonons in $\mathcal{PT}$-breaking systems. Key experimental progresses on topological and circularly polarized phonons are discussed. We also outline outstanding challenges and promising directions for future research, such as the role of topology in phonon-mediated quasiparticle interactions and the manipulation of phonon angular momentum for potential applications in quantum technologies.}