Large Spin-Orbit Splitting of Deep In-Gap Defect States of Engineered Sulfur Vacancies in Monolayer ${\mathrm{WS}}_2$

Structural defects in 2D materials offer an effective way to engineer new material functionalities beyond conventional doping. We report on the direct experimental correlation of the atomic and electronic structure of a sulfur vacancy in monolayer ${\mathrm{WS}}_2$ by a combination of CO-tip noncontact atomic force microscopy and scanning tunneling microscopy. Sulfur vacancies, which are absent in as-grown samples, were deliberately created by annealing in vacuum. Two energetically narrow unoccupied defect states followed by vibronic sidebands provide a unique fingerprint of this defect. Direct imaging of the defect orbitals, together with ab initio GW calculations, reveal that the large splitting of $252\pm 4\mathrm{meV}$ between these defect states is induced by spin-orbit coupling.

Figure 1

Sulfur vacancy and O substituent. (a),(b) STM topography ($I=20\mathrm{pA}$, $V=1.1\mathrm{V}$) of CVD-grown monolayer ${\mathrm{WS}}_2$. (a) After low-temperature sample annealing ($\approx 250°\mathrm{C}$), no chalcogen vacancy defects were observed. Oxygen substituents at sulfur sites are most abundant. (b) By in-vacuum annealing at about $600°\mathrm{C}$, sulfur vacancies can be generated (white arrows). (c)–(f) STM topography ($I=20\mathrm{pA}$, $V=1.1\mathrm{V}$) of an oxygen substituting sulfur (${\mathrm{O}}_{\mathrm{S}}$) in the (c) top and (d) bottom sulfur plane as well as a sulfur vacancy in the (e) top and (f) bottom sulfur plane. (g)–(j) Corresponding CO-tip NCAFM images of the same defects as in (c)–(f). The unit cell has been indicated as a guide for the eye. Yellow, S atom; blue, W atom. (k)–(n) DFT calculated defect geometry.

Figure 2

Sulfur vacancy defect states. (a) STS spectra recorded on a sulfur bottom vacancy and the pristine ${\mathrm{WS}}_2$ monolayer on bilayer graphene. The valence band maximum (VBM), conduction band minimum (CBM), the Fermi level ($E_F$), the filled-state defect resonance, and the unoccupied in-gap defect states are indicated. The VBM at K is resolved at a closer tunneling distance [45]. The spectrum position is marked by the red circle in (c). (b) STS spectra of the deep unoccupied $V_{\mathrm{S}}$ defect states. The two zero-phonon lines (ZPLs) and the subsequent vibronic satellite peaks are labeled. The splitting between the ZPL peaks is due to spin-orbit coupling. (c) Constant-height $dI/dV$ maps of the two $V_{\mathrm{S}}$ defect states corresponding to the ZPL resonances of both the top and bottom $V_{\mathrm{S}}$. The ${\mathrm{WS}}_2$ unit cell has been indicated (to scale). Yellow, S; blue, W.

Figure 3

Tip-induced sulfur vacancy charging on $\mathrm{Gr}(1\mathrm{ML})/\mathrm{SiC}$ substrates. (a) STS spectra recorded on a $V_{\mathrm{S}}$ on ${\mathrm{WS}}_2(1\mathrm{ML})$ on $\mathrm{Gr}(1\mathrm{ML})/\mathrm{SiC}$ (blue) and on $\mathrm{Gr}(2\mathrm{ML})/\mathrm{SiC}$ (red). The $V_{\mathrm{S}}$ defect states on $\mathrm{Gr}(1\mathrm{ML})/\mathrm{SiC}$ are at lower energies than on $\mathrm{Gr}(2\mathrm{ML})/\mathrm{SiC}$, and a pronounced charging peak is observed at about $-1.2\mathrm{V}$ along with an upward shift of the valence band. ${\mathrm{WS}}_2$ on $\mathrm{Gr}(1\mathrm{ML})/\mathrm{SiC}$ (light gray) has as a lower VBM than ${\mathrm{WS}}_2$ on $\mathrm{Gr}(2\mathrm{ML})/\mathrm{SiC}$ (dark gray). (b) Schematic of the tip-induced band bending at a bias and tip position where the $V_{\mathrm{S}}$ (red line) becomes resonant with the Fermi level of the substrate (at the “charging ring”). The $V_{\mathrm{S}}$ state at zero field energy is indicated by the red dashed line. (c) $dI/dV$ map of $V_{\mathrm{S}}$ on $\mathrm{Gr}(1\mathrm{ML})/\mathrm{SiC}$ at $-1.45\mathrm{V}$. The charging peak is visible as a circular feature around the defect. Inside the ring, the defect is charged, outside, it is neutral. (d) STS spectra at negative sample bias recorded across the $V_{\mathrm{S}}$. (e) $dI/dV$ intensity at $-1.3\mathrm{V}$ recorded as a function of tip height across the defect.

Figure 4

Calculated DFT and $GW$ defect levels including SOC. All calculations were done on a $5\times 5$ supercell containing a single sulfur vacancy. (a) DFT-LDA level constant height slice of the orbital density of the in-gap defect state 8 Å above (corresponding to $V_{\mathrm{S}}$ top) and 8 Å below (corresponding to $V_{\mathrm{S}}$ bottom) the ${\mathrm{WS}}_2$ monolayer. The ${\mathrm{WS}}_2$ unit cell has been indicated (to scale). Yellow, S; blue, W. (b) Comparison of the band structure excluding and including SOC. The formerly degenerate defect state (purple) splits into two states (red and blue) with dominant contributions of $J=3/2$ and $J=5/2$ of the total angular momentum. The black dashed line indicates the occupied defect resonance overlapping the valence band. (c) Comparison of the defect state energies calculated at the DFT and $GW$ level and the corresponding experimental values (on a monolayer graphene substrate). Screening effects by the substrate have not been considered in the calculations. The gray boxes represent the delocalized states of the ${\mathrm{WS}}_2$ layer with the CBM and VBM. The VBM of the DFT, $GW$ calculations, and the experiment has been aligned for comparability. The spin split in-gap defect states are marked in red and blue; the black dashed line shows the energy level of the occupied defect state. $E_F$ denotes the experimental Fermi level.