Interlayer Charge-density-wave Vector Phase Induced Structural Chirality

Chiral charge density waves (CDWs) have attracted intense interest due to their exotic quantum properties, yet the microscopic origin of structural chirality emerging from correlated charge order remains elusive. Here, we reveal that the interlayer phases of CDW wave vectors, an overlooked degree of freedom, play a crucial role in driving chiral structural displacements in layered CDW materials. By explicitly incorporating the interlayer phases in first-principles calculations, we successfully obtained the chiral structure of the CDW phases of AV$_3$Sb$_5$ (A= K, Rb, and Cs) and 1T-TiSe$_2$. The electronic and optical properties of the predicted chiral structures are consistent with experimental measurements of these materials in their CDW phases. We further predict that 1T-NbSe$_2$ is a promising material candidate for realizing chiral CDW order. Beyond materials prediction, our theory reveals that the chiral CDW can be manipulated by electron filling. Our study opens new avenues for discovering, designing, and engineering chiral CDW materials.

💡 Research Summary

The authors introduce a previously overlooked degree of freedom in layered charge‑density‑wave (CDW) systems: the interlayer phase φℓi of each CDW wave vector. While traditional CDW theory describes the lattice modulation as u(R)=u0 ε cos(Q·R+ϕ), it assumes the same phase for all layers, thereby preserving bulk inversion and rotational symmetries. By extending the description to uℓi(r∥)=u0 εi cos(qi·r∥+ϕi+φℓi), where φℓi can differ from layer to layer, the authors show that each layer can retain its in‑plane symmetry while the stacking sequence breaks overall crystal symmetry, generating structural chirality.

A “phase‑tagged” wave‑vector formalism is introduced: q‑vectors with φℓi=0 are denoted q_i, while those with φℓi=π are denoted q_i′. Specific sets of interlayer phases (e.g., φ1=