Competing Charge and Magnetic Order in Fermionic Multi-Component Systems

We consider the fermionic SU($3$) Hubbard model on the triangular lattice 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 $\Delta$, the Hubbard interaction $U$ destabilizes the band insulator (BI) at small $U$ into the Mott insulator (MI) at large $U$ in three different ways with different intermediate phases. This leads to a rich phase diagram in the $U$-$\Delta$ plane. Our results indicate that multi-component systems show not only exotic states in the Mott regime as has been considered previously, but also interesting competition between charge and magnetic orders.