Incommensurate Transverse Peierls Transition and Signature of Chiral Charge Density Wave in EuAl₄

In one-dimensional quantum materials, electrons and lattices can undergo a Peierls transition, a translational symmetry-breaking instability traditionally understood through electron coupling to longitudinal acoustic phonons. Recently, this paradigm has been revised in topological semimetals, where transverse acoustic phonons couple to p-orbital electrons, giving rise to a transverse Peierls transition. Importantly, transverse Peierls transition-induced distortions can further break mirror or inversion symmetries, producing nematic or chiral charge density waves. Here, we report the experimental identification of an incommensurate transverse Peierls transition in EuAl₄. Using meV-resolution inelastic x-ray scattering, we observe complete softening of a transverse acoustic phonon upon cooling, while the longitudinal acoustic mode remains unaffected. First-principles calculations reveal that the transverse Peierls transition wavevector coincides with a charge susceptibility peak connecting nested Dirac bands. Second harmonic generation confirms mirror symmetry breaking, supporting a chiral charge density wave stabilized by the transverse Peierls transition.