Assignment of excitonic insulators in ab initio theories: The case of ${\mathrm{NiBr}}_2$

In this work we perform a detailed first-principles analysis of the electronic and optical properties of ${\mathrm{NiBr}}_2$ within the state-of-the-art $GW+\text{BSE}$ scheme to determine whether this system displays negative excitonic energies, which would identify it as an (half) excitonic insulator. Particular attention is paid to the convergence of the $GW$ band structure and to the consistency between approximations employed in the ground-state calculations and approximations employed in the linear response calculations. We show that these two issues play a crucial role in identifying the excitonic nature of ${\mathrm{NiBr}}_2$.

Figure 1

Spin-resolved band structure (majority- and minority-spin channels are reported in blue and red, respectively) for $GW$@PBE (left) and $GW$@PBE0 (right) are reported with a continuous line. The DFT band structures used as starting point for the $GW$ correction are reported with a dashed line. Energy zero is at the top of valence band.

Figure 2

Imaginary part of the macroscopic polarizability calculated within $GW\text{@PBE}+\text{BSE}$ (top panel), $GW\text{@PBE0}+\text{BSE}$ (middle panel), and $\text{PBE0}+\text{TDPBE0}$ (bottom panel). The results obtained within the corresponding independent particle approximation, i.e., ignoring electron-hole interaction, are also reported (dashed lines). Curves are vertically shifted for clarity. Bright and dark excitons energies are reported as vertical ticks.

Figure 3

Band contribution to the main excitonic peak $E_0$: (left panel) $GW\text{@PBE}+\text{BSE}$, (middle panel) $GW\text{@PBE0}+\text{BSE}$, (right panel) $\text{PBE0}+\text{TDPBE0}$. Note that the plotted band structures are the DFT ones. We also report the excitonic wave function in reciprocal space.