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As a prototypical self-organization in the system with orbital degeneracy, wetheoretically investigate trimer formation on a triangular lattice, as observedin LiVO2. From the analysis of an effective spin-orbital coupled model in thestrong correlation limit, we show that the previously-proposed orbital-orderedtrimer state is not the lowest-energy state for a finite Hund's-rule coupling.Instead, exploring the ground state in a wide range of parameters for amultiorbital Hubbard model, we find an instability toward a differentorbital-ordered trimer state in the intermediately correlated regime in thepresence of trigonal crystal field. The trimer phase appears in the competingregion among a paramagnetic metal, band insulator, and Mott insulator. Theunderlying mechanism is nesting instability of the Fermi surface by asynergetic effect of Coulomb interactions and trigonal-field splitting. Theresults are compared with experiments in triangularlattice compounds, LiVX2(X=O, S, Se) and NaVO2.

Trimer Formation and Metal-Insulator Transition in Orbital Degenerate Systems on a Triangular Lattice