Defect-induced large spin-orbit splitting in monolayer ${\mathrm{PtSe}}_2$

The effect of spin-orbit coupling on the electronic properties of monolayer (ML) ${\mathrm{PtSe}}_2$ is dictated by the presence of the crystal inversion symmetry to exhibit a spin-polarized band without the characteristic of spin splitting. Through fully relativistic density-functional theory calculations, we show that large spin-orbit splitting can be induced by introducing point defects. We calculate the stability of native point defects such as a Se vacancy (${\mathrm{V}}_{\text{Se}}$), a Se interstitial (${\mathrm{Se}}_i$), a Pt vacancy (${\mathrm{V}}_{\text{Pt}}$), and a Pt interstitial (${\mathrm{Pt}}_i$) and find that both the ${\mathrm{V}}_{\text{Se}}$ and ${\mathrm{Se}}_i$ have the lowest formation energy. We also find that, in contrast to the ${\mathrm{Se}}_i$ case exhibiting spin degeneracy in the defect states, the large spin-orbit splitting up to 152 meV is observed in the defect states of the ${\mathrm{V}}_{\text{Se}}$. Our analyses of orbital contributions to the defect states show that the large spin splitting is originated from the strong hybridization between Pt-$d_{x{}^2+y{}^2}+d_{xy}$ and Se-$p_x+p_y$ orbitals. Our study clarifies that the defects play an important role in the spin-splitting properties of the ${\mathrm{PtSe}}_2$ ML, which is important for designing future spintronic devices.

Figure 1

The relaxed structures of native point defects induced by vacancy and interstitial in the ${\mathrm{PtSe}}_2$ ML compared with the pristine system: (a) a pristine, (b) a Se vacancy (${\mathrm{V}}_{\text{Se}}$), (c) a Se interstitial (${\mathrm{Se}}_i$), (d) a Pt vacancy (${\mathrm{V}}_{\text{Pt}}$), and (e) a Pt interstitial (${\mathrm{Pt}}_i$). The Pt-Se, Pt-Pt, ${\mathrm{Se}}_i$-Se, and ${\mathrm{Pt}}_i$-Pt bond lengths are indicated by the red arrows.

Figure 2

The electronic band structure of (a) the pristine, (b) the ${\mathrm{V}}_{\text{Se}}$, and (c) the ${\mathrm{Se}}_i$, where the calculations are performed without inclusion the effect of the spin-orbit coupling (SOC). The electronic band structure of (d) the pristine, (e) the ${\mathrm{V}}_{\text{Se}}$, and (f) the ${\mathrm{Se}}_i$ with inclusion of the effect of the SOC. The Fermi level is indicated by the dashed black lines.

Figure 3

Density of states projected to the atomic orbitals for (a) the ${\mathrm{V}}_{\text{Se}}$ and (b) ${\mathrm{Se}}_i$. The NN and NNN Se denote the nearest- and next-nearest-neighboring Se atoms, respectively.

Figure 4

Relation between the point group symmetry of the ${\mathrm{V}}_{\text{Se}}$, the spin splitting, and the orbital contributions to the defect states in the first Brillouin zone. (a) Symmetry operation in the real space of the ${\mathrm{V}}_{\text{Se}}$ corresponding to (b) the first Brillouin zone. (c) The spin splitting in the defect states calculated along the first Brillouin zone. Here, the ${\mathrm{\Delta }}_1$ and ${\mathrm{\Delta }}_2$ represent the spin splitting for the lower and upper unoccupied antibonding states, respectively, while ${\mathrm{\Delta }}_3$ represents the spin splitting of the occupied bonding state. (d) Orbital-resolved electronic band structures calculated in the defect states. The radii of the circles reflect the magnitudes of spectral weight of the particular orbitals to the band.