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 ($\sim 1.1\mathrm{eV}$) exceeding the $GW$ band gap by $\sim 0.2\mathrm{eV}$ and a large singlet-triplet splitting of $\sim 0.4\mathrm{eV}$. Our findings enrich once again the intriguing physics of flat bands and extend the scope of EI materials.

Figure 1

(a) Unit cell of a $9\times 9$ superatomic graphene lattice. Gray and white circles represent C and H atoms, respectively. (b) First Brillouin zone showing the high-symmetry reciprocal paths used for band diagrams. (c) Comparison of band structures and band gaps obtained within DFT (left) and a single-shot $G_o{W}_o$ calculation (right).

Figure 2

(a) Optical absorbance for singlet excitons with a Gaussian peak broadening of 10 meV. $X_o$ indicates the first bright peak. (b) Density of states for singlet excitons, and (c) density of states for triplet excitons, noticing two peaks with negative formation energies (yellow filled). ${\mathrm{EI}}_o$ indicates the first triplet exciton, which is also the case of triplet EI. Insets in (b) and (c) represent spin-up electron (red arrow with filled circle) and spin-down hole (orange arrow with hollow circle) bound together forming an exciton.

Figure 3

Excitonic wave function analysis for the lowest triplet exciton (${\mathrm{EI}}_o$, upper) and for the lowest singlet exciton ($X_o$, lower): (a),(d) Reciprocal-space excitonic wave function distribution showing total contribution of all excitations at each reciprocal lattice point. (b),(e) Band excitation contributions indicated by spread of color on the bands. (c),(f) Real-space two-particle $e-h$ wave function distribution with hole fixed at the black dot plotted over a $6\times 6$ supercell. Only a small segment of the supercell is shown here since the electron is highly localized around the hole. The distribution amplitude is zero everywhere else. The orange arrow with a circle denotes the spin of hole left behind after excitation and the red arrow denotes the spin of electron.

Figure 4

Conduction and valence FBs wave function overlap for zero momentum singlet exciton ($Q=0$). Right: C and H atoms are indicated by large and small circles, respectively. The contributions are only from the C $p_z$ orbitals. The overlapped weights of these contributions to flat valence and conduction band wave functions are indicated by the size of red fills on the C atoms. Left: $k$ points in BZ for which overlaps are calculated.