Lateral Finite-Size Effect of Flat-band Spectral Weight in Kagome Metal CoSn

Driven by their unique lattice structure, kagome systems exhibit fascinating properties, prominent among which is the emergence of flat bands. Here we report a scanning tunneling microscopy and spectroscopy study on the lateral finite-size effect of flat-band spectral weight in the kagome metal CoSn. We identify two distinct cleaved surfaces: Co 3 Sn and Sn 2 . On the Co 3 Sn surface, we detect two electronic peaks located at 70 and 250 mV below the Fermi level, which correspond to the flat bands originating from Co d orbitals. Notably, the flat-band intensity exhibits a strong dependence on the lateral size of the kagome islands. The flat bands start to emerge in Co 3 Sn islands consisting of only a half-unit-wide kagome chain. As the island width increases, the flat-band intensity rises exponentially and reaches saturation when the island width reaches four-unit cells or larger. By analyzing the size-dependent intensity data, we extract the characteristic length scale for this saturation behavior. Furthermore, on the large Co 3 Sn surface, we observe a broad and non-dispersive wavevector with a periodicity close to √3×√3 in the Fourier-transformed differential conductance maps. These results not only reveal the novel lateral finite-size effect of flat-band spectral weight at the atomic scale, but also pave the way for a deeper understanding of the complex electronic structures in kagome materials.