Flat-Band-Enabled Triplet Excitonic Insulator in a Diatomic Kagome Lattice

The excitonic insulator (EI) state is a strongly correlated many-body ground state, arising from an instability in the band structure toward exciton formation. We show that the flat valence and conduction bands of a semiconducting diatomic Kagome lattice, as exemplified in a superatomic graphene lattice, can possibly conspire to enable an interesting triplet EI state, based on density-functional theory calculations combined with many-body $GW$ and Bethe-Salpeter equation. Our results indicate that massive carriers in flat bands with highly localized electron and hole wave functions significantly reduce the screening and enhance the exchange interaction, leading to an unusually large triplet exciton binding energy ($\ensuremath{\sim}1.1\text{ }\text{ }\mathrm{eV}$) exceeding the $GW$ band gap by $\ensuremath{\sim}0.2\text{ }\text{ }\mathrm{eV}$ and a large singlet-triplet splitting of $\ensuremath{\sim}0.4\text{ }\text{ }\mathrm{eV}$. Our findings enrich once again the intriguing physics of flat bands and extend the scope of EI materials.