  Vanadium oxides have been highly attractive for over half a century since the
discovery of the metal insulator transition near room temperatures. Here NaxVO2
is studied through a systematic comparison with other layered sodium metal
oxides with early 3d transition metals, first disclosing a unified evolution
pattern of Na density waves through in situ XRD analysis. Combining ab-initio
simulations and theoretical modelings, a sodium-modulated Peierls-like
transition mechanism is then proposed for the bonding formation of metal ion
dimers. More importantly, the unique trimer structure in NaxVO2 is shown to be
very sensitive to the onsite Coulomb repulsion value, suggesting a delicate
balance between strong electronic correlations and orbital effects that can be
precisely modulated by both Na compositions and atomic stackings. This unveils
a unique opportunity to design strongly correlated materials with tailored
electronic transitions through electrochemical modulations and crystallographic
designs, to elegantly balance various competition effects. We think the
understanding will also help further elucidate complicated electronic behaviors
in other vanadium oxide systems.
