Chirality in Condensed Matter: Symmetry, Waves, and Quasiparticles

RESUMO

Chirality has become a recurring concept throughout condensed-matter physics, appearing in contexts ranging from optical activity and chiral phonons to magnetic excitations and hybrid quasiparticles. As its use has expanded, however, the concept has often become intertwined with related notions such as angular momentum, polarization, helicity, and nonreciprocity, obscuring its precise symmetry-based meaning. Although chirality is universally associated with broken spatial-inversion ($\mathcal{P}$) symmetry and preserved time-reversal ($\mathcal{T}$) symmetry, its physical manifestation and quantitative characterization strongly depend on the system and phenomenon under consideration. In this review, we examine chirality across photons, phonons, magnons, and hybrid excitations. We show that, while no universal measure of chirality exists, different physical systems admit different $\mathcal{P}$-odd and $\mathcal{T}$-even quantities that characterize specific chiral phenomena. We further argue that chirality is often best understood through chirality-selective interactions between waves, matter, and quasiparticles rather than as an intrinsic property of isolated excitations. From this perspective, hybridization provides a particularly promising setting for the emergence, transfer, and control of chirality in condensed-matter systems.