Trimer Formation and Metal-Insulator Transition in Triangular-Lattice Systems LiV{\it{X}}$_2$ ({\it{X}}=O,Se,S)

Geometrically-frustrated systems sometimes lift their degeneracy by spontaneous formation of multisite clusters via coupling to other degrees of freedom. A fascinating example is found in a triangular-lattice system LiVO$_2$, which exhibits a three-site trimer formation. The origin was argued to be an orbital ordering under strong electronic correlation [1], however, recent experiments on a series of LiV{\it{X}}$_2$ ({\it{X}}=O,Se,S) suggest that the system is intermediately correlated and rather close to a metal-insulator transition [2]. In this contribution,we revisit this problem within a multiorbital Hubbard model in a wide range of Coulomb interaction by strong-coupling perturbation and Hartree-Fock approximation. We find a new trimer state under substantial trigonal crystal-field splitting; it is located in the vicinity of a metal-insulator transition and not adiabatically connected to the trimer state previously proposed. We discuss the origin of this new trimerization and the relation to experimental results.\\[4pt] [1] H. F. Pen {\it et al}., Phys. Rev. Lett. {\bf 78}, 1323 (1997).\\[0pt] [2] N. Katayama {\it et al}., Phys. Rev. Lett. {\bf 103}, 146405 (2009).