Electronic and magnetic properties of single chalcogen vacancies in ${\mathrm{MoS}}_2/\mathrm{Au}\left(111\right)$

Two-dimensional (2D) transition-metal dichalcogenides (TMDCs) are considered highly promising platforms for next-generation optoelectronic devices. Owing to its atomically thin structure, device performance is strongly impacted by a minute amount of defects. Although defects are usually considered to be disturbing, defect engineering has become an important strategy to control and design new properties of 2D materials. Here, we produce single S vacancies in a monolayer of ${\mathrm{MoS}}_2$ on Au(111). Using a combination of scanning tunneling and atomic force microscopy, we show that these defects are negatively charged and give rise to a Kondo resonance, revealing the presence of an unpaired electron spin exchange coupled to the metal substrate. The strength of the exchange coupling depends on the density of states at the Fermi level, which is modulated by the moiré structure of the ${\mathrm{MoS}}_2$ lattice and the Au(111) substrate. In the absence of direct hybridization of ${\mathrm{MoS}}_2$ with the metal substrate, the S vacancy remains charge neutral. Our results suggest that defect engineering may be used to induce and tune magnetic properties of otherwise nonmagnetic materials.

Figure 1

Characterization of single top-layer sulfur vacancies in ${\text{MoS}}_{\text{2}}$. (a) STM topography of a ${\text{MoS}}_{\text{2}}$ island after sputtering. Several defects appear with a dark center and a bright threefold rim (closeup view in inset). The constant-current STM image was recorded at a setpoint of 100 mV and 200 pA, the inset at 300 mV and 200 pA. The scale bar in the inset is 5 Å. (b) Constant-height $\mathrm{\Delta }f$ image, resolving the atomic structure of the terminating layer. Some S atoms are missing. These are at the location of the bright-rim defects in (a). The $\mathrm{\Delta }f$ image was recorded at a setpoint of 1 mV and 200 pA.

Figure 2

Electronic structure of top-layer vacancies. (a) $dI/dV$ spectra recorded on the locations indicated in the insets, revealing the semiconducting band gap of ${\text{MoS}}_{\text{2}}$ and a zero-bias resonance on the defect's rim (feedback opened at −2 V and 200 pA, $V_{\text{mod}}=\text{5}\text{mV}$). (b) $dI/dV$ spectrum around the Fermi level recorded on the rim of the defect (feedback opened at 300 mV and 200 pA, with an additional tip approach by 100 pm, $V_{\text{mod}}=\text{2}\text{mV}$). The STM topographies in the insets were recorded at 300 mV and 200 pA. The scale bars in the insets are 5 Å.

Figure 3

Identification of the zero-bias peak as a Kondo resonance. (a) Extracted half-widths of two vacancies probed at different sample temperatures. To obtain the half-widths, we fitted the resonances with a Frota function and converted the Frota parameter to the half-width $\mathrm{\Gamma }$ [35, 36]. The Fermi-Dirac temperature broadening of the tip was subtracted from the linewidths [37]. The temperature-dependent curve was fitted with the Fermi-liquid description of the Kondo problem [38, 39]. The topographies of the defects are shown as insets, with the locations of the spectra marked by a cross and a triangle, according to the symbols in the plot. (b) $dI/dV$ spectra recorded on the rim of the vacancy shown in the right inset in (a) and marked by a triangle at zero magnetic field (black) and in an applied magnetic field of 3 T. The blue dashed lines represent fits with one (0 T) or two separated (3 T) Frota functions, which are split by $600\pm 100\mu \mathrm{V}$. Inset: linear fit of the Zeeman splitting of the Kondo resonance at different magnetic fields. The extracted $g$ factor is given in the main text. The STM topographies in the insets in (a) were recorded at a setpoint of 50 mV and 3 nA (left) and 1 mV and 100 pA (right). The scale bars in the insets are 0.5 nm (left) and 1 nm (right). The $dI/dV$ spectra were recorded after opening the feedback loop at 5 mV and 3 nA and with a modulation amplitude of $V_{\text{mod}}=\text{50}\text{µV}$.

Figure 4

Influence of the moiré structure on the defect appearance. (a) STM images recorded at 300 mV, 200 pA. (b) Same area and defect as in (a) recorded at 5 mV, 200 pA. Whereas the high bias voltage reveals a threefold shape, the images recorded close to the Kondo resonance show a broken symmetry imposed by the moiré modulated density of states.

Figure 5

Charge distribution around a sulfur vacancy. (a) Closeup STM topography of a sulfur vacancy (recorded at 300 mV and 200 pA). (b) LCPD extracted from a densely spaced grid of $\mathrm{\Delta }f-V$ spectra over the same area as in (a). The $\mathrm{\Delta }f-V$ spectra were recorded at a setpoint of 300 mV and 200 pA, with the tip being additionally approached towards the surface by 100 pm.

Figure 6

Sulfur vacancies on quasi-freestanding ${\text{MoS}}_{\text{2}}$. (a) STM topography of point defects on a quasi-freestanding ${\text{MoS}}_{\text{2}}$. (b) $dI/dV$ spectra recorded on a patch of quasi-freestanding ${\text{MoS}}_{\text{2}}$ (black) and on a point defect, the latter marked by a red cross in the topography in (a). The topography was taken at a setpoint of 800 mV and 100 pA, the spectra were recorded at a setpoint of 2 V and 3 nA (red) and 800 mV and 100 pA (black).