Magnetic and electrical anisotropy with correlation and orbital effects in dimerized honeycomb ruthenate Li$_2$RuO$_3$

Li2RuO3 undergoes a structural transition at a relatively high temperature of 550 K with a distinct dimerization of Ru-Ru bonds on the otherwise isotropic honeycomb lattice. It exhibits a unique herringbone dimerization pattern with a largest ever reported value of the bond shrinkage of about ~ 0.5 r{A}. Despite extensive studies, both theoretical and experimental, however, its origin and its effect on physical properties still remain to be understood. In this work, using high quality single crystals we investigated the anisotropy of resistivity ($rho$) and magnetic susceptibility ($chi$) to find a very clear anisotropy: $rho$$_c*$ > $rho$$_b$ > $rho$$_a$ and $chi$$_b$ > $chi$$_a$ > $chi$$_c*$. For possible theoretical interpretations, we carried out density functional calculations to conclude that these anisotropic behavior is due to the correlation effects combined with the unique orbital structure and the dimerization of Ru 4d bands.