Incommensurate Transverse Peierls Transition

TL;DR

This paper reports the experimental discovery of an incommensurate transverse Peierls transition in EuAl$_4$, revealing a new type of lattice instability driven by transverse acoustic phonons in a topological semimetal.

Contribution

It provides the first experimental evidence of an incommensurate transverse Peierls transition in a Dirac semimetal, linking phonon softening to charge density wave formation and symmetry breaking.

Findings

Observation of complete softening of a transverse acoustic phonon at the CDW wavevector.

CDW induces lattice distortions breaking mirror symmetries but preserving four-fold rotation.

Evidence suggests the formation of a chiral charge density wave in EuAl$_4$.

Abstract

In one-dimensional quantum materials, conducting electrons and the underlying lattices can undergo a spontaneous translational symmetry breaking, known as Peierls transition. For nearly a century, the Peierls transition has been understood within the paradigm of electron-electron interactions mediated by longitudinal acoustic phonons. This classical picture has recently been revised in topological semimetals, where transverse acoustic phonons can couple with conducting p-orbital electrons and give rise to an unconventional Fermi surface instability, dubbed the transverse Peierls transition (TPT). Most interestingly, the TPT induced lattice distortions can further break rotation or mirror/inversion symmetries, leading to nematic or chiral charge density waves (CDWs). Quantum materials that host the TPT, however, have not been experimentally established. Here, we report the experimental discovery of an incommensurate TPT in the tetragonal Dirac semimetal EuAl$_4$. Using inelastic x-ray scattering with meV resolution, we observe the complete softening of a transverse acoustic phonon at the CDW wavevector upon cooling, whereas the longitudinal acoustic phonon is nearly unchanged. Combining with first principles calculations, we show that the incommensurate CDW wavevector matches the calculated charge susceptibility peak and connects the nested Dirac bands with Al 3$p_{x}$ and 3$p_{y}$ orbitals. Supplemented by second harmonic generation measurements, we show that the CDW induced lattice distortions break all vertical and diagonal mirrors whereas the four-fold rotational symmetry is retained below the CDW transition. Our observations strongly suggest a chiral CDW in EuAl$_4$ and highlight the TPT as a new avenue for chiral quantum states.