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Motivated by the recent developments on cluster Mott insulating materialssuch as the cluster magnet LiZn$_2$Mo$_3$O$_8$, we consider the strongplaquette charge ordered regime of the extended Hubbard model on a breathingKagome lattice and reveal the properties of the cluster Mottness. The plaquettecharge order arises from the inter-site charge interaction and the collectivemotion of three localized electrons on the hexagon plaquettes. This model leadsnaturally to a reduction of the local moments by 2/3 as observed inLiZn$_2$Mo$_3$O$_8$. Furthermore, at low temperatures each hexagon plaquettecontains an extra orbital-like degree of freedom in addition to the remainingspin 1/2. We explore the consequence of this emergent orbital degree offreedom. We point out the interaction between the local moments is naturallydescribed by a Kugel-Khomskii spin-orbital model. We develop a parton approachand suggest a spin liquid ground state with spinon Fermi surfaces for thismodel. We further predict an emergent orbital order when the system is under astrong magnetic field. Various experimental consequences forLiZn$_2$Mo$_3$O$_8$ are discussed, including an argument that the chargeordering much be short ranged if the charge per Mo is slightly offstoichiometry.

Emergent orbitals in the cluster Mott insulator on a breathing Kagome lattice