Probing phonon chirality and circular lattice motion with symmetry-selective nonlinear optical spectroscopy

Abstract: Truly chiral phonons are lattice eigenmodes that combine broken mirror symmetry with circular atomic motion. They can mediate angular-momentum-selective interactions in quantum materials, yet directly resolving both their chirality and underlying circular motion remains challenging, especially in high-symmetry crystals. Here we show that symmetry-selective terahertz difference-frequency spectroscopy provides a phase- and polarization-resolved route to identifying truly chiral phonons in a tabletop experiment. Using $α$-quartz as a benchmark, we validate this approach by resolving phonon chirality via chiral-sensitive $χ^{(2)}_{ijk}$ tensor elements ($i \neq j \neq k$), while vector-field detection directly reveals a time-dependent polarization rotation arising from circular ionic motion and thus nonzero angular momentum. Applying the same protocol to tetragonal $α$-TeO$_2$, we isolate chiral $E$-mode resonances below 5~THz and directly verify their circular lattice motion, thereby resolving a symmetry-imposed ambiguity in chiral-phonon identification in fourfold-symmetric crystals. Our results establish symmetry-selective nonlinear terahertz spectroscopy as a general route to identify truly chiral phonons in condensed matter systems.