Fig. 1. Electronic confinement and flat band in ideal kagome lattice and kagome metal CoSn.

a Confinement of electron in kagome lattice with nearest-neighbor hopping. Plus and minus signs indicate the phase of flat band eigenstate at neighboring sublattices. Any hoppings outside the hexagon (arrows) are canceled by destructive quantum interferences, resulting in the perfect localization of electron in the blue-colored hexagon. b Tight-binding band structure of kagome lattice featuring flat band (blue solid line) and two Dirac bands with linear crossing at K (black solid lines). Inclusion of spin–orbit coupling gaps both Dirac crossing and quadratic touching between the flat band and the Dirac band (dotted lines). c In-plane structure of kagome layer in CoSn consists of kagome network of Co atoms and space-filling Sn atoms. d Three-dimensional structure of CoSn with alternating stacking of the kagome layer A and Sn layer S. e Relativistic density functional theory (DFT) band structure of CoSn. Orange, cyan, and brown-colored regions highlight the manifestation of the kagome flat band flat bands with different d-orbital characters. Inset shows the bulk Brillouin zone of CoSn. The DFT Fermi level is shifted down by 140 meV to fit the experimental Fermi level.