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Here we use low-temperature scanning tunneling microscopy and spectroscopy tostudy the polar surfaces of PdCoO2. On the CoO2-terminated polar surface, wedetect the quasiparticle interference pattern originating from the Rashbaspin-split surface states. On the well-ordered Pd-terminated polar surface, weobserve a regular lattice which has larger lattice constant than the atomiclattice of PdCoO2. In comparison with the shape of the hexagonal bulk Fermisurface, we identify this regular lattice as a fully two-dimensionalincommensurate charge modulation that is driven by the Fermi surface nesting.More interestingly, we also find the moir\'e pattern induced by theinterference between the two-dimensional incommensurate charge modulation inthe Pd layer and the underlying CoO2 lattice. Our results not only show a newcharge modulation on the Pd surface of PdCoO2, but also pave the way for fullyunderstanding the novel electronic properties of this material.

Fully two-dimensional incommensurate charge modulation on the Pd-terminated polar surface of PdCoO2