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Here we report a combined study of low-temperature scanning tunnelingmicroscopy (STM) and dynamical mean-field theory (DMFT) on PdCrO$_2$, adelafossite metal with an antiferromagnetic order below ~37.5 K. First, on theCrO$_2$-terminated polar surface we detect a gap-like feature both below andabove the N\'eel temperature. The DMFT calculations indicate that this gap isopened due to the strong correlations of Cr-3d electrons, suggesting the hiddenMott nature of the gap. Then, we observe two kinds of Pd-terminated polarsurfaces. One is a well-ordered Pd surface with theFermi-surface-nesting-induced incommensurate charge modulation, while the otherone is a reconstructed Pd surface with the individual nano-scale non-periodicdomain structures. On the well-ordered Pd surface, the interference between theincommensurate charge modulation and the atomic lattice forms the periodicmoir\'e pattern. Our results provide important microscopic information forfully understanding the correlated electronic properties of this class ofmaterials.

Probing hidden Mott gap and incommensurate charge modulation on the polar surfaces of PdCrO$_2$