Fully Two-Dimensional Incommensurate Charge Modulation on the Pd-Terminated Polar Surface of PdCoO₂

Here, we use low-temperature scanning tunneling microscopy and spectroscopy to study the polar surfaces of PdCoO₂. On the CoO₂-terminated polar surface, we detect the quasiparticle interference pattern originating from the Rashba-like spin-split surface states. On the well-ordered Pd-terminated polar surface, we observe a regular lattice that has a larger lattice constant than the atomic lattice of PdCoO₂. In comparison with the shape of the hexagonal Fermi surface on the Pd-terminated surface, we identify this regular lattice as a fully two-dimensional incommensurate charge modulation that is driven by the Fermi surface nesting. More interestingly, we also find the moiré pattern induced by the interference between the two-dimensional incommensurate charge modulation in the Pd layer and its atomic lattice. Our results not only show a new charge modulation on the Pd surface of PdCoO₂ but also pave the way for fully understanding the novel electronic properties of this material.