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We investigate the evolutions of structural parameters, optical properties,and electronic structures of a van der Waals kagome semiconductorPd$_{3}$P$_{2}$S$_{8}$ with Se doping. When the doping level of Se increases,the bandgaps of Pd$_{3}$P$_{2}$(S$_{1-x}$Se$_{x}$)$_{8}$ single crystalsdecrease gradually, accompanying with the expanded unit cells. Thefirst-principles calculations show that there is a flat band (FB) near theFermi level in bulk Pd$_{3}$P$_{2}$S$_{8}$. This FB mainly originates from the$d_{z^2}$-like orbitals of Pd atoms in the Pd kagome lattice, which have afinite interlayer electron hopping perpendicular to the PdS$_4$ square plane.The interlayer hopping can be reinforced with Se doping, inducing a strongerinterlayer coupling via the chalcogen atoms at apical sites, which reduces thebandgap and enhances the cleavage energy. In contrast, the varnishinginterlayer hopping in the two-dimensional limit results in the formation ofultra-FB in the monolayers of these compounds. The easy exfoliation and theexistence of unique ultra-FB near $E_{\rm F}$ makePd$_{3}$P$_{2}$(S$_{1-x}$Se$_{x}$)$_{8}$ a model system to explore the exoticphysics of FB in 2D kagome lattice.

Evolution of ultra-flat band in van der Waals kagome semiconductor Pd$_{3}$P$_{2}$(S$_{1-x}$Se$_{x}$)$_{8}$