Microscopic Evidence for π-Trihexagonal Charge Density Wave in CsV₃Sb₅ from NQR and DFT

Kagome materials, with their unique geometry of corner-sharing triangles and hexagons, provide a fertile ground for exploring emergent quantum phenomena. The interplay between geometric frustration, electronic correlations, and non-trivial band topology has a significant impact on the emergence of these phenomena.

The recently discovered vanadium-based Kagome materials AV₃Sb₅ (A = Cs, K, Rb) are no exception, exhibiting unconventional superconductivity and a distinctive charge density wave (CDW) order.

Determining the CDW ground state structure remains challenging because of conflicting findings. Ultrafast time-resolved reflectivity measurements suggest a coexistence of a Star of David (SoD) and inverse Star of David (ISD) patterns[1], while ⁵¹V nuclear magnetic resonance results detect an SoD pattern [2]. Finally, synchrotron x-ray diffraction measurements detected the 2×2×2 ISD structure, which upon cooling becomes the 2×2×4 structure composed of a three-layer ISD and an SoD layer [3].

In this work, we focus on CsV₃Sb₅ and track the evolution of the local charge distribution and structural configuration using a combination of nuclear quadrupole resonance (NQR) and density functional theory (DFT).

By examining the temperature evolution of the ¹²¹Sb NQR spectrum, we identify the transition to the CDW state. Furthermore, we simulate the NQR spectrum for different CDW patterns and extract all the relative features. A comparison of the theoretical and experimental spectral features reveals that the ISD structure with a π-shift along the c-axis is the most stable distortion pattern.

[1] Q. Den et al. Coherent phonon pairs and rotational symmetry breaking of charge density wave order in the kagome metal CsV₃Sb₅ . arXiv:2503.07442, 2025.

[2] J. Luo et al. Possible star-of-david pattern charge density wave with additional modulation in the kagome superconductor CsV₃Sb₅. npj Quantum Materials, vol. 7, Mar. 2022.

[3] L. Kautzsch et al. Structural evolution of the kagome superconductors AV₃Sb₅ (A = Cs, K, Rb) through charge density wave order. Physical Review Materials, vol. 7, Feb. 2023.