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 spin-split surface states. On the well-ordered Pd-terminated polar surface, we observe a regular lattice which has larger lattice constant than the atomic lattice of PdCoO2. In comparison with the shape of the hexagonal bulk Fermi 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 moir\'e pattern induced by the interference between the two-dimensional incommensurate charge modulation in the Pd layer and the underlying CoO2 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.