Orbital-selective Dirac fermions and extremely flat bands in frustrated kagome-lattice metal CoSn

Abstract

Layered kagome-lattice 3 d transition metals are emerging as an exciting platform to explore the frustrated lattice geometry and quantum topology. However, the typical kagome electronic bands, characterized by sets of the Dirac-like band capped by a phase-destructive flat band, have not been clearly observed, and their orbital physics are even less well investigated. Here, we present close-to-textbook kagome bands with orbital differentiation physics in CoSn, which can be well described by a minimal tight-binding model with single-orbital hopping in Co kagome lattice. The capping flat bands with bandwidth less than 0.2 eV run through the whole Brillouin zone, especially the bandwidth of the flat band of out-of-plane orbitals is less than 0.02 eV along Γ− M . The energy gap induced by spin-orbit interaction at the Dirac cone of out-of-plane orbitals is much smaller than that of in-plane orbitals, suggesting orbital-selective character of the Dirac fermions.

Spin-polarized Dirac cone, flat band and saddle point in kagome magnet YMn6Sn6

“…For the FB1, it is degenerate with the QB bottom at the center of the BZ (Γ) without SOC. With the consideration of SOC, the two bands further hybridize and open a gap ∼ 40 ± 10 meV, which is similar to the results in PM CoSn [28]. The FB2 declines weakly close to M and K points.…”

“…At the K point, a linearly dispersing Dirac point (DP2) is also found at around 45 meV below E F , which is also characteristic of the band structure as a result of kagome lattice as previously observed in FeSn and CoSn [25,28,29]. According to our DFT+DMFT calculated orbital-resolved electronic structures in FM configuration, the DP2 arises from the spin-polarized band with minority-spin state, as shown in the Fig.…”

“…The band structure studies of 3d transition-metal kagome compounds, which are usually strong correlated and exhibit magnetism, remain challenging albeit theoretical predictions [19][20][21][22][23][24][25][26][27][28][29][30][31][32]. A typical electronic structure of the kagome lattice is the existence of Dirac point (DP) at the Brillouin zone (BZ) corner, a saddle point (SP) at BZ boundary, and a FB over the whole BZ (Fig.…”

“…Topological non-trivial electronic properties were observed in kagome lattices constituted of 3d-transition metallic element, i.e., large intrinsic anomalous Hall effect originating from the Berry curvature of Dirac cone-type dispersion of K point both in ferromagnetic (FM) and antiferromagnetic (AFM) materials [18,[20][21][22][23][24]. Another important feature is the dispersionless electronic structure in magnetic kagome materials [25,[30][31][32] and in paramagnetic (PM) kagome materials [27][28][29]. In PM kagome materials, extremely flat bands close to E F have been reported in CoSn [28,29] and YCr 6 Ge 6 [27].…”

“…Another important feature is the dispersionless electronic structure in magnetic kagome materials [25,[30][31][32] and in paramagnetic (PM) kagome materials [27][28][29]. In PM kagome materials, extremely flat bands close to E F have been reported in CoSn [28,29] and YCr 6 Ge 6 [27]. However, in magnetic systems, the direct evidence of the FBs is either unobserved (Fe 3 Sn 2 , Co 3 Sn 2 S 2 [22,30]), or far away from E F (FeSn [25]), due to the strong correlation of 3d electrons, the complexity with magnetic structure, and the interplay between electron correlation and topological properties.…”