Competing charge and magnetic order in fermionic multicomponent systems

We consider the fermionic $\mathrm{SU}(3)$ Hubbard model on the triangular lattice at $1/3$ filling in the presence of a three-sublattice staggered potential which provides the possibility to investigate the competition of charge and magnetic order in three-component systems. We show that, depending on the strength of the staggered potential $\mathrm{\ensuremath{\Delta}}$, the Hubbard interaction $U$ destabilizes the band insulator at small $U$ into the Mott insulator at large $U$ in three different ways with different intermediate phases. This leads to a rich phase diagram in the $U\text{\ensuremath{-}}\mathrm{\ensuremath{\Delta}}$ plane. Our results indicate that multicomponent systems show not only exotic states in the Mott regime as has been considered previously, but also interesting competition between charge and magnetic orders which can lead to the emergence of charge-ordered magnetic insulators and charge-ordered magnetic metals.