  The excitonic insulator (EI) state is a strongly correlated many-body ground
state, arising from an instability in the band structure towards 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 (DFT) calculations combined with
many-body GW and Bethe-Salpeter Equation(BSE). Our results indicate that
massive carriers in flat bands with highly localized electron and hole
wavefunctions significantly reduce the screening and enhance the exchange
interaction, leading to an unusually large triplet exciton binding energy (~1.1
eV) exceeding the GW band gap by ~0.2 eV and a large singlet-triplet splitting
of ~0.4 eV. Our findings enrich once again the intriguing physics of flat bands
and extend the scope of EI materials.
