A higher-dimensional electronic modulation in a misfit chalcogenide (Pb_1-<i>x</i>Sn<i>_x</i>)₁₊_δ(TiSe₂)₂

We show spectroscopic imaging scanning tunneling microscopy of a misfit chalcogenide (Pb_1-xSn_x)_1+δ(TiSe₂)₂. The crystal structure of this material consists of a rocksalt-type Pb_1-xSn_xSe double-layer and two hexagonal TiSe₂ tri-layers, namely, layered stacking of rectangular and triangular sublattices. Despite this unique crystal structure, the low-energy electronic states of this material have been suggested to resemble those of 1T-TiSe₂. As a result of termination-resolved imaging spectroscopy, we find that the coupling between the two sublattices completely suppresses the charge density wave of 1T-TiSe₂ and induces a new electronic modulation characterized by a higher-dimensional description. Our finding not only provides an insight into the origin of the charge density wave of 1T-TiSe₂ but also suggests that the interplay between hexagonal and tetragonal sublattices is an interesting avenue for realizing novel electronic matters.