Coexisting Kagome and Heavy Fermion Flat Bands in YbCr$_6$Ge$_6$

Abstract

Flat bands, emergent in strongly correlated electron systems, stand at the frontier of condensed matter physics, providing fertile ground for unconventional quantum phases. Recent observations of dispersionless bands at the Fermi level in kagome lattice open the possibility of unifying the disjoint paradigms of topology and correlation-driven heavy fermion liquids. Here, we report the unprecedented coexistence of these mechanisms in the layered kagome metal YbCr6Ge6. At high temperatures, an intrinsic kagome flat band-arising from the frustrated hopping on the kagome lattice-dominates the Fermi level. Upon cooling, localized Yb 4f-states hybridize with the topological kagome flat bands, transforming this state into the Kondo resonance states that are nearly dispersionless across the entire Brillouin zone. Crystalline symmetry forbids hybridization along specific high-symmetry lines, which stabilizes Dirac crossings of heavy-fermion character. Topological analysis of the resulting gaps reveals both trivial and nontrivial Z2 invariants, establishing the emergence of a Dirac-Kondo semimetal phase. Taken together, these results identify YbCr6Ge6 as a prototype of a topological heavy-fermion system and a platform where geometric frustration, strong correlations, and topology converge, with broad implications for correlated quantum matter.

Figures (4)

• Figure 1: Atomic and electronic structure of Kondo kagome system YbCr$_6$Ge$_6$ (YCG). (a) Atomic structure of the kagome lattice system YCG, delineating the layered arrangement of Yb, Cr, and Ge. (b) Kagome layer composed of Cr atoms. (c) Honeycomb Ge layer with Yb atoms situated at the hexagonal centers. (d) Honeycomb Ge layer with perpendicular Ge dimers at the hexagonal centers. (e-g) Schematic illustrations of the Cr kagome bands and localized Yb $f$-orbitals (e) without hybridization, (f) in DFT, and (g) DFT+DMFT, respectively. The Dirac point (DP), van Hove singularities saddle point (SP), and KFB are highlighted. LS and KRS represent localized states and Kondo resonance states of Yb $f$-orbitals, respectively. (h) Brillouin zone (BZ) showing the high-symmetry points used in calculations. (i-k) DFT Band structures projected onto the $f$ orbitals (red), Cr $3d_{z^2}$ orbitals (blue), and Cr $d_{x^2-y^2}/d_{xy}$ (green), respectively, obtained with $U=0$ for both Cr $d$ and Yb $f$ orbitals. The zero-energy level is set at the charge-neutral electron filling.
• Figure 2: Momentum-resolved electronic structure of YCG measured by ARPES at 18 K. (a) $k_{x}$-$k_{y}$ constant-energy maps at the Fermi level (E$_F$) and E = E$_F$ - 0.3 eV, showing the $\alpha$ and $\beta$ bands crossing $E_{\rm F}$. (b) Schematic of the 3D BZ with a projection onto the 2D plane. (c) Energy-momentum (E-$k$) cut along $\overline{\Gamma}$-$\overline{\rm K}$-$\overline{\rm M}$ (cut I in (a)). DP, KRS, and KFB refer to Dirac point, Kondo resonance state, and kagome flat band, respectively. The $\alpha$ and $\beta$ bands are highlighted with red lines. The corresponding DFT+DMFT-calculated E-$k$ cut is also shown. (d) E-$k$ cut along $\overline{\rm M}$-$\overline{\Gamma}$-$\overline{\rm M}$ (cut II in (a)) with the corresponding 2D curvature intensity plot zhang2011precise. Due to the matrix element effect, parts of the $\alpha$ band are not visible and are represented with red dotted lines. (e) Energy distribution curves (EDCs) at $\overline{\Gamma}$, $\overline{\rm K}$, and $\overline{\rm M}$ points extracted from black rectangular regions in panel (a). (f) $k_{y}$-$k_{z}$ constant-energy map at $E$ = $E_{\rm F}$ - 0.3 eV with the corresponding 2D curvature intensity plot. (g) E-$k_{z}$ cut along $\Gamma$-${\rm A}$ (cut III in (e)). (h) $k_{z}$-dependent EDCs showing consistently strong peaks at $E_{\rm F}$.
• Figure 3: Temperature-dependent evolution of flat electronic structures. (a-c) ARPES-measured E-$k$ cuts along the $\overline{\rm M}$-$\overline{\Gamma}$-$\overline{\rm M}$ high-symmetry line at temperatures of 220 K, 80 K, and 18 K, respectively. (d,e) Temperature-dependent evolution of EDCs at $\overline{\Gamma}$ and $k_x$ = 1.0 $\AA^{-1}$. (f,g) DFT+DMFT calculated spectral functions along the ${\rm L}$-${\rm A}$-${\rm L}$ high-symmetry line at temperatures of 58 K and 290 K, respectively. $d$ indicates Cr kagome bands. (h) Temperature-dependent evolution of the spectral weight, calculated using DFT+DMFT and integrated in momentum space with a Fermi-Dirac distribution.
• Figure 4: (a,b) 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 $J_K$. (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 $E_F$. (d) DFT band structure of the low-temperature YCG phase computed with $U=2.6\,\mathrm{eV}$ for Cr $3d$ and $U=0\,\mathrm{eV}$ for Yb $4f$, with the $U$ values and $E_F$ 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 $E_F$. 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 $(\pm)$ at the time-reversal-invariant momenta for the three colored gaps in (d), used to determine the Fu--Kane $Z_2$ indices. (e) weak topological Kondo insulator (TKI) with $(\nu_0;\nu_1\nu_2\nu_3)=(0;001)$, implying $\nu_{2\mathrm{D}}(k_z=0)=\nu_{2\mathrm{D}}(k_z=\pi)=1$. (f) strong TKI with $\nu_{2\mathrm{D}}(k_z=\pi)=1$ and $\nu_{2\mathrm{D}}(k_z=0)=0$. (g) Dirac--Kondo semimetal (DKSM), where the $k_z=\pi$ plane hosts a nontrivial $Z_2$ invariant while symmetry-protected DPs persist along the $\Gamma$--$A$ 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.