Incommensurate Transverse Peierls Transition

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.

Supplementary materials are available upon request

References in corpus (22)

• Advanced capabilities for materials modelling with Quantum ESPRESSO
• EPW: Electron-phonon coupling, transport and superconducting properties using maximally localized Wannier functions
• Theory of Intertwined Orders in High Temperature Superconductors
• CsV${}_3$Sb${}_5$: a ${\mathbb{Z}}_2$ topological kagome metal with a superconducting ground state
• Unconventional Fermi surface instabilities in the Kagome Hubbard Model
• Time-reversal symmetry-breaking charge order in a kagome superconductor
• Competing electronic orders on Kagome lattices at van Hove filling
• Extended Phonon Collapse and the Origin of the Charge-Density-Wave in NbSe${}_2$
• Three-dimensional quantum Hall effect and metal-insulator transition in ZrTe5
• Chiral anomaly, Charge Density Waves, and Axion Strings from Weyl Semimetals
• Evidence for an axionic charge density wave in the Weyl semimetal (TaSe4)2I
• Evidence of an odd-parity hidden order in a spin-orbit coupled correlated iridate
• A global inversion-symmetry-broken phase inside the pseudogap region of YBa${}_2$Cu${}_3$O${}_y$
• Observation of a ferro-rotational order coupled with second-order nonlinear optical fields
• Theory for the Charge-Density-Wave Mechanism of 3D Quantum Hall Effect
• Thermodynamic insights into the intricate magnetic phase diagram of EuAl${}_4$
• Orthorhombic charge density wave on the tetragonal lattice of EuAl4
• Electric quadrupole second harmonic generation revealing dual magnetic orders in a magnetic Weyl semimetal
• Weyl nodal ring states and Landau quantization with very large magnetoresistance in square-net magnet EuGa${}_4$
• Ferro-rotational domain walls revealed by electric quadrupole second harmonic generation microscopy
• Origin of Charge Density Wave in Topological Semimetals SrAl4 and EuAl4
• Real-space Visualization of Charge Density Wave Induced Local Inversion-Symmetry Breaking in a Skyrmion Magnet

Cited by in corpus (1)

• Origin of multiple skyrmion phases in EuAl4