Evolution of ultraflat band in the van der Waals kagome semiconductor Pd3P2(S1−xSex)8

We investigate the evolution of structural parameters, optical properties, and electronic structures of the van der Waals kagome semiconductor ${\mathrm{Pd}}₃{\mathrm{P}}₂{\mathrm{S}}₈$ with Se doping. When the doping level of Se increases, the band gaps of ${\mathrm{Pd}}₃{\mathrm{P}}₂{({\mathrm{S}}_{1\ensuremath{-}x}{\mathrm{Se}}_x)}₈$ single crystals decrease gradually, accompanied by the expanded unit cells. First-principles calculations show that there is a flat band (FB) near the Fermi level in bulk ${\mathrm{Pd}}₃{\mathrm{P}}₂{\mathrm{S}}₈$. This FB mainly originates from the ${d}_{{z}²}$-like orbitals of Pd atoms in the Pd kagome lattice, which has finite interlayer electron hopping perpendicular to the ${\mathrm{PdS}}₄$ square plane. The interlayer hopping can be reinforced with Se doping, inducing a stronger interlayer coupling via the chalcogen atoms at apical sites, which reduces the band gap and enhances the cleavage energy. In contrast, the vanishing interlayer hopping in the two-dimensional limit results in the formation of an ultra-FB in the monolayers of these compounds. The easy exfoliation and the existence of a unique ultra-FB near ${E}_{\mathrm{F}}$ make ${\mathrm{Pd}}₃{\mathrm{P}}₂{({\mathrm{S}}_{1\ensuremath{-}x}{\mathrm{Se}}_x)}₈$ a model system to explore the exotic physics of a FB in a two-dimensional kagome lattice.