Fig. 1: Crystal structure, topography, and spectroscopy of Co₃Sn₂S₂ .

a Single Chern insulator, with one chiral edge state. b Chern insulator bilayer system with step geometry and inter-layer coupling (represented by the purple lines).When the coupling is strong enough to turn the bilayer system trivial, chiral edge states appear at the edges of the exposed planes as well as at the interface of the bilayer and single layer. c Large stack of Chern insulators with intermediate inter-layer coupling to form a Weyl semimetal. For large regions of parameter space, the Weyl semimetal phase coincides with the conditions necessary for the counter-propagating chiral edge states seen in b (see Supplementary Note 1). d Unit cell of Co₃Sn₂S₂. Sn is represented by a large green sphere, Co by a medium yellow sphere, and S by a small blue sphere. e Several layers of the crystal as viewed from the (100) plane. Cleavage occurs between the Sn and S layers, as indicated by a dashed line. f Schematic of the kagome structure present in the Co₃Sn plane with Co forming 6 triangles surrounding a central Sn atom. g Spectra typical of S surface (I = 300 pA, V = 500 mV). Inset is 30 nm × 30 nm topography showing vacancies typical of S surface (I = 30 pA, V = 500 mV). The scale bar in the inset is 10 nm. h Spectra typical of Sn surface (I = 60 pA, V = 500 mV). Inset is 30 nm × 30 nm topography showing adatoms typical of Sn surface. (I = 110 pA, V = 80 mV). The scale bar in the inset is 10 nm.