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: Co3Sn and Sn2. On the Co3Sn 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 Co3Sn 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 Co3Sn 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.