Fig. 1: Longitudinal and transverse Peierls transitions.
From: Incommensurate Transverse Peierls Transition and Signature of Chiral Charge Density Wave in EuAl4
a Schematic of a classical Peierls transition in 1D. The interaction between a LA phonon and isotropic s-orbital conduction electrons yields a CDW instability. b The LA Kohn anomaly induced by the classical Peierls transition. c Transverse Peierls transition driven by the coupling between conduction electrons with anisotropic orbital characters, such as p-orbitals, and TA phonons. d The TA Kohn anomaly induced by the TPT. Distinct from the LA wave, the TA wave is a vector wave (similar to an electromagnetic wave) and hence can carry finite angular momentum. e, f depict linearly polarized and circularly polarized TA waves, respectively. The linearly polarized lattice distortion breaks (screw) rotational symmetry, Cn, giving rise to a C2 nematic CDW. The circular polarized lattice distortion preserves (screw) rotational symmetry, Cn, and can host a chiral CDW. g Temperature dependence of the incommensurate-CDW superlattice peak at (2, 2, 2-0.183) showing a CDW transition at TCDW = 142 K. Inset shows the crystal structure of EuAl4. Magenta and silver circles represent Eu and Al atoms, respectively.
