Motivated by the recent developments on cluster Mott insulating materials such as the cluster magnet ${\mathrm{LiZn}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$, we consider the strong plaquette charge ordered regime of the extended Hubbard model on a breathing kagome lattice and reveal the properties of the cluster Mottness. The plaquette charge order arises from the intersite charge interaction and the collective motion of three localized electrons on the hexagon plaquettes. This model leads naturally to a reduction of the local moments by 2/3, as observed in ${\mathrm{LiZn}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$. Furthermore, at low temperatures, each hexagon plaquette contains an extra orbital-like degree of freedom in addition to the remaining spin 1/2. We explore the consequence of this emergent orbital degree of freedom. We point out the interaction between the local moments is naturally described by a Kugel-Khomskii spin-orbital model. We develop a parton approach and suggest a spin-liquid ground state with spinon Fermi surfaces for this model. We further predict an emergent orbital order when the system is under a strong magnetic field. Various experimental consequences for ${\mathrm{LiZn}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$ are discussed, including an argument that the charge ordering must be short ranged if the charge per Mo is slightly off stoichiometric.

• Received 30 September 2017

DOI:https://doi.org/10.1103/PhysRevB.97.035124