Fig. 3: CDW-induced band splitting and gap opening in the measured band structures of KV₃Sb₅ at 20 K and their comparison with band-structure calculations.

a–c Band structures measured along the \(\bar{{{\Gamma }}}\)-\(\bar{M}\) (a), \(\bar{K}\)-\(\bar{M}\)-\(\bar{K}\) (b), and \(\bar{K}\)-\(\bar{{{\Gamma }}}\) (c) high-symmetry directions, respectively. The locations of the momentum cuts, 1, 2, and 3 for (a), (b), and (c), respectively, are shown in the inset of c. d–f Detailed band structures around \(\bar{M}\) and \(\bar{K}\) points measured along \(\bar{{{\Gamma }}}\)-\(\bar{M}\) (d), \(\bar{K}\)-\(\bar{M}\)-\(\bar{K}\) (e), and \(\bar{K}\)- \(\bar{{{\Gamma }}}\) (f) directions, respectively. These are symmetrized second derivative images obtained from the band structures of k = 0.4–0.64 1/Å in a, 0 ~ 0.45 1/Å in b, and −0.72 ~ −0.3 1/Å in c, and symmetrized with respect to the \(\bar{M}\) (a), \(\bar{M}\) (b), and \(\bar{K}\) (c) points, respectively. The measured band structures are indicated by guidelines and the associated CDW gaps and SOC gap are also marked. g Calculated band structure of KV₃Sb₅ with pristine crystal structure in Fig. 1a at k_z = π/c with SOC. h The calculated band structures of KV₃Sb₅ with reconstructed TrH crystal structure in Fig. 1b at k_z = π/c with SOC. In addition to the original high-symmetry points \(\bar{{{\Gamma }}}\), \(\bar{M}\) and \(\bar{K}\), new high-symmetry points from the reconstructed Brillouin zone (Fig. 1c), \(\overline{M^{\prime} }\) and \(\overline{K^{\prime} }\), are marked. Three CDW gaps open at \(\bar{M}\): \(\bar{M}\)G1, \(\bar{M}\)G2 and \(\bar{M}\)G3, and four CDW gaps open at \(\overline{M^{\prime} }\): \(\bar{M}\)PG1, \(\bar{M}\)PG2, \(\bar{M}\)PG3, and \(\bar{M}\)PG4. The SOC gap opening at the Dirac point at \(\bar{K}\) is marked by DG. i EDCs at \(\bar{M}\) from band structures in a and b. j EDC at \(\overline{M^{\prime} }\) from band structure in c. The CDW gap size is measured by the separation between related EDC peaks. k EDCs at \(\bar{K}\) from band structures in b and c.