Metal-insulator transition in ${\text{NiS}}_{2-x}{\text{Se}}_x$

The origin of the gap in ${\text{NiS}}_2$ as well as the pressure- and doping-induced metal-insulator transition in the ${\text{NiS}}_{2-x}{\text{Se}}_x$ solid solutions are investigated both theoretically using the first-principles band structures combined with the dynamical mean-field approximation for the electronic correlations and experimentally by means of infrared and x-ray absorption spectroscopies. The bonding-antibonding splitting in the S-S (Se-Se) dimer is identified as the main parameter controlling the size of the charge gap. The implications for the metal-insulator transition driven by pressure and Se doping are discussed.

Figure 1

(Color online) The crystal structure of ${\text{NiS}}_2$: Ni atoms red (bright), S atoms blue (dark). The S-S dimer is highlighted in the center of the figure.

Figure 2

(Color online) The calculated pressure dependence of the equilibrium $\text{Ni-}X$ and $X\text{−}X$ distances. The isolated points mark the experimental values of Refs. 11 (star) and 27 (cross).

Figure 3

(Color online) The calculated $\left(U=5\text{eV},T=580\text{K}\right)$ orbitally resolved spectra of ${\text{NiS}}_2$ [$\text{Ni-}d:e_g^{\sigma }$ (black) and $t_{2g}=e_g^{\pi }\left(\text{red}\right)+a_{1g}$ (red dashed); $\text{S-}p$: total (blue, thick) and $p_{\sigma }$ (blue shaded)] compared to the experimental $\text{XPS}+\text{BIS}$ (gray, shaded) (Ref. 11). $a$, $b$, and $c$ are defined in the text. Inset shows the conduction-band $e_g^{\sigma }$ spectra for $U=5$, 6, 7, and 8 eV.

Figure 4

(Color online) The calculated $\text{S-}p$ spectral density obtained from $\text{LDA}+\text{DMFT}$ (full line), augmented with the $\text{S-}p$ contribution from the high energy LDA bands (dashed line), compared to experimental XES spectra of Ref. 28 (circles) and XAS (diamonds) spectra of this work.

Figure 5

(Color online) The calculated $\left(U=4.5\text{eV},T=580\text{K}\right)$ orbital resolved spectra of ${\text{NiSe}}_2$ compared to the experimental $\text{XPS}+\text{BIS}$ (Ref. 11) spectra (the same notation as in Fig. 3). The position of the calculated high-energy band is marked with the dotted line. Left inset shows the $e_g^{\sigma }$ densities for various interaction strengths $U$ (eV). In the right inset, the effect of reducing the Se-Se distance $\left(\text{Å}\right)$ on the spectra $\left(U=4.5\text{eV}\right)$ is shown.

Figure 6

(Color online) The bare $\text{S}\left(\text{Se}\right)\text{−}p$ spectral densities and band structures. [(a) and (b)] The spectral densities in the left panel are obtained from a Wannier function Hamiltonian, while [(c) and (d)] the band structures in the middle panel are based on a linearized augmented plane-wave (LAPW) calculation with removed Ni-like basis functions. Dashed bands for ${\text{NiSe}}_2$ correspond to a reduced Se-Se distance.

Figure 7

(Color online) The comparison of ${\text{NiS}}_2$ spectra in the insulating state at ambient pressure (upper panel) and in the metallic state under compression (lower panel). Black line marks the $e_g^{\sigma }$ and shaded area (blue) is the total $\text{S}p$ contribution. The $t_{2g}$ spectra which exhibit very little change with pressure are not shown.

Figure 8

(Color online) (a) Room-temperature optical conductivity spectra of ${\text{NiS}}_{2-x}{\text{Se}}_x$ ($x=0;0.3;0.5;0.7$, as indicated in figure) at ambient pressure. In the inset, the corresponding reflectivity $R\left(\omega \right)$ is reported. (b) Optical conductivity of ${\text{NiS}}_2$ (solid) and ${\text{NiS}}_{1.7}{\text{Se}}_{0.3}$ (dashed) for increasing pressure.

Figure 9

(Color online) (a) The gap vs pressure for ${\text{NiS}}_2$ and ${\text{NiS}}_{1.7}{\text{Se}}_{0.3}$ (note the mutual horizontal offset). (b) SW transfer $\Delta \text{SW}$ for ${\text{NiS}}_2$ at 5 GPa and for ${\text{NiS}}_{1.3}{\text{Se}}_{0.7}$ at ambient pressure.