  First-principles calculations and simulations are conducted to clarify the
nonmagnetic insulating ground state of the honeycomb lattice compound Na2RuO3
with 4d^4 electronic configuration and explore the evolutions of crystal
structure and electronic property under pressure. We reveal that individual
Coulomb correlation or spin-orbit coupling (SOC) effect cannot reproduce the
experimentally observed nonmagnetic insulating behavior of Na2RuO3, whereas the
Coulomb correlation enhanced SOC interactions give rise to an unusual
spin-orbital-entangled J = 0 nonmagnetic insulating state, which contrasts with
the SOC assisted Mott insulating state in d^5 ruthenates and iridates.
Furthermore, a pressure-induced structural dimerization transition has been
predicted around 15-17.5 GPa. The honeycomb lattice of the high-pressure
dimerized phase features with parallel pattern of the short Ru-Ru dimers
aligning along the crystallographic b direction. Accompanied with the
structural dimerization, the electronic structure shows striking reconstruction
by formation of molecular orbitals. Interestingly, the cooperation of Coulomb
correlation together with SOC can realize a nonmagnetic insulating state in the
high-pressure dimerized phase. The d^4 ruthenate Na2RuO3 with honeycomb lattice
will provide a new platform to explore unusual physics and rich phase diagram
due to the delicate interplay of lattice degree of freedom, electron
correlations, and SOC interactions.
