Fig. 4: Topological classification of hybridization gaps in YbCr6Ge6.
From: Coexisting kagome and heavy fermion flat bands in YbCr6Ge6
Schematics of the role of Yb in YCG: a high-temperature state with Cr (dark blue) and Ge (light purple) kagome layers and Yb (cyan); b Low-temperature state where yellow regions denote Dirac-Kondo fermions, localized in-plane but dispersive out-of-plane; red arrows indicate the Kondo coupling JK. c DFT band structure of the high-temperature phase along the high-symmetry lines shown in Fig. 2b. The dashed line denotes the Fermi level EF. d DFT band structure of the low-temperature YCG phase computed with U = 2.6 eV for Cr 3d and U = 0 eV for Yb 4f, with the U values and EF calibrated to reproduce the low-energy dispersion obtained from the preceding DFT+DMFT calculations, consistent with ARPES. Compared with (c), hybridization opens multiple narrow gaps near EF. Colored shading highlights three representative hybridization-gap regions, and arrows indicate their correspondence to the parity-based topological classification in (e–g). Insets (blue boxes) enlarge the representative Dirac crossings. e–g Parity eigenvalues (±) at the time-reversal-invariant momenta for the three colored gaps in (d), used to determine the Fu–Kane Z2 indices. e Weak topological Kondo insulator (TKI) with (ν0; ν1ν2ν3) = (0; 001), implying ν2D(kz = 0) = ν2D(kz = π) = 1. f Strong TKI with ν2D(kz = π) = 1 and ν2D(kz = 0) = 0. g Dirac–Kondo semimetal (DKSM), where the kz = π plane hosts a nontrivial Z2 invariant while symmetry-protected DPs persist along the Γ–A and K–H lines, which prevents the opening of a full bulk gap. The blue Dirac cones indicate the locations of the DPs in the BZ.
