Fig. 1: Crystal structure and Fermi surface of KV₃Sb₅.

a Pristine crystal structure of KV₃Sb₅ with a V-kagome net from the top view. b The Tri-Hexagonal (TrH) lattice distortion caused by the 2 × 2 CDW transition^15,25. The K, V, Sb atoms are presented as gray, purple, and blue balls, respectively. c Schematic of the three-dimensional Brillouin zone and the two-dimensional Brillouin zone projected on the (001) surface in the pristine phase in a. High-symmetry points and high-symmetry momentum lines are marked. d The original (black lines) and 2 × 2 reconstructed (blue lines) Brillouin zones. The \(\bar{{{\Gamma }}}\), \(\bar{K}\), and \(\bar{M}\) (\(\bar{{{\Gamma }}}^{\prime}\), \(\overline{K^{\prime} }\), and \(\overline{M^{\prime} }\)) are the high-symmetry points of the pristine (2 × 2 reconstructed) Brillouin zones. The arrows indicate three wavevectors (marked as Q₁, Q₂, and Q₃) of electronic structure reconstruction. e Fermi surface mapping of KV₃Sb₅ measured at T = 20 K. Four Fermi surface sheets are observed marked as α (orange lines), β (red lines), γ (blue lines), and δ (green lines). For convenience, high-symmetry points are labeled with different indexes such as \({\bar{{{\Gamma }}}}_{1}\), \({\bar{{{\Gamma }}}}_{21}\), \({\bar{M}}_{11}\), \({\bar{M}}_{12}\), \({\bar{M}}_{21}\), \({\bar{K}}_{11}\), \({\bar{K}}_{12}\), and \({\bar{K}}_{21}\). f Symmetrized Fermi surface mapping of KV₃Sb₅. It is obtained from taking the second derivative with respect to momentum on the second Brillouin zone data in e. g The calculated Fermi surface at k_z = π/c corresponding to pristine crystal structure in a.