Topological flat bands in frustrated kagome lattice CoSn

Abstract

Electronic flat bands in momentum space, arising from strong localization of electrons in real space, are an ideal stage to realize strongly-correlated phenomena. Theoretically, the flat bands can naturally arise in certain geometrically frustrated lattices, often with nontrivial topology if combined with spin-orbit coupling. Here, we report the observation of topological flat bands in frustrated kagome metal CoSn, using angle-resolved photoemission spectroscopy and band structure calculations. Throughout the entire Brillouin zone, the bandwidth of the flat band is suppressed by an order of magnitude compared to the Dirac bands originating from the same orbitals. The frustration-driven nature of the flat band is directly confirmed by the chiral d-orbital texture of the corresponding real-space Wannier functions. Spin-orbit coupling opens a large gap of 80 meV at the quadratic touching point between the Dirac and flat bands, endowing a nonzero Z 2 invariant to the flat band. These findings demonstrate that kagome-derived flat bands are a promising platform for novel emergent phases of matter at the confluence of strong correlation and topology.

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

“…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.…”

Kagome van-der-Waals Pd3P2S8 with flat band

“…Most of the experimental realizations have so far been limited to artificial kagome or bulk kagome systems, which contain 2D kagome embedded in a three-dimensional crystal [29][30][31][32][33][34][35][36] . Indeed, studies on the bulk kagome materials, including metallic kagome [31][32][33][34][35] , Herbertsmithite 18 , and other metal-organic frameworks 36 have been the playground for the exploration into several intriguing electric and magnetic properties of the frustrated systems and topological states. However, the interlayer interaction of these bulk materials, although weak, is likely to mask the very nature of kagome physics and hamper its emergent phenomena 31 .…”