Advances in Phonons: From Band Topology to Phonon Chirality

Phonons, the quantized collective vibrations of a crystal lattice, are among the most fundamental bosonic excitations in condensed matter systems. They govern thermal transport, mediate electron-phonon coupling, and drive symmetry-breaking orders such as charge density waves and conventional superconductivity. Long regarded as spin-0 bosons characterized only by their vibrational frequencies and linear or circular polarization, phonons have recently been revealed to host a much richer internal structure. Recent advances in topological band theory and quantum geometry have shown that phonon eigenstates, encoded in both their eigenvalues and eigenvectors, can exhibit nontrivial topological and geometric properties. These developments have established topological and circularly polarized phonons as two major frontiers in phonon physics, motivating this review of recent theoretical and experimental advances. We present a unified framework for classifying phonon modes in both reciprocal and real space, encompassing symmetry-protected topological phases, topological invariants, and phonon polarization. We then examine their coexistence in PT-broken systems through Weyl phonons, highlighting the simultaneous emergence of topological and rotational chirality. Finally, we discuss outstanding challenges and future research directions, including the role of topology and quantum geometry in phonon-mediated interactions and the controlled manipulation of phonon angular momentum for prospective quantum technologies.