Strong Anisotropic Spin-Orbit Interaction Induced in Graphene by Monolayer ${\mathrm{WS}}_2$

We demonstrate strong anisotropic spin-orbit interaction (SOI) in graphene induced by monolayer ${\mathrm{WS}}_2$. Direct comparison between graphene-monolayer ${\mathrm{WS}}_2$ and graphene-bulk ${\mathrm{WS}}_2$ systems in magnetotransport measurements reveals that monolayer transition metal dichalcogenide can induce much stronger SOI than bulk. Detailed theoretical analysis of the weak antilocalization curves gives an estimated spin-orbit energy ($E_{\mathrm{so}}$) higher than 10 meV. The symmetry of the induced SOI is also discussed, and the dominant $z\to -z$ symmetric SOI can only explain the experimental results. Spin relaxation by the Elliot-Yafet mechanism and anomalous resistance increase with temperature close to the Dirac point indicates Kane-Mele SOI induced in graphene.

Figure 1

Data taken from mono $A$. (a) Sketch of the $G$-mono samples. (b) Resistance as a function of the gate voltage. (c) $\mathrm{\Delta }\sigma (B)\equiv \sigma (B)-\sigma (0)$ at three different temperatures. Without any subtraction, the sharp WAL peak and flat tail are observed, signatures of the strong SOI induced in graphene. The $V_g$ range we average over for these experimental data is shown in (b) with the black marker.

Figure 2

Comparison of the magnetoconductivity curves for (a) $G$-mono and (b) $G$-bulk with the best theoretical fits (black solid curves). (a) $\mathrm{\Delta }\sigma (B)$ from mono $A$. The inset shows the optical image of the sample with the red dashed outline for graphene. (b) Magnetoconductivity curve for bulk $B$ averaged over a similar gate voltage range and similar doping level as that of (a) (see the left inset). The right inset shows the image of bulk $B$. The scale bar for the two sample images represents $10\mu \mathrm{m}$.

Figure 3

Comparison of the spin-orbit energy ($E_{\mathrm{so}}$) estimated from the theoretical fitting of both $G$-mono and $G$-bulk. For each type, the data taken from the two samples with different mobilities ($\mu$) are shown. The mobilities are $12000{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ (mono $A$), $7000{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ (mono $B$), $9000{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ (bulk $A$), and $7000{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ (bulk $B$). Inset: Fitting parameters obtained for mono $B$. ${\tau }_{\mathrm{asy}}$ is found to be comparable to ${\tau }_{\varphi }$ and much larger than ${\tau }_{\mathrm{so}}$.

Figure 4

(a) The experimental results and fitting curves with different $E_{\mathrm{so}}$ and $E_{\mathrm{asy}}$ for mono $A$. Larger $E_{\mathrm{so}}$ and smaller $E_{\mathrm{asy}}$ give a better fit. Inset: Three different terms in Eq. (1) as a function of $B$ for the best fit. (b) ${ϵ}_F^2{\tau }_p/{\tau }_{\mathrm{so}}$ as a function of ${ϵ}_F^2{\tau }_p^2$ for $G$-mono and $G$-bulk. The theoretical fit based on Eq. (2) is shown with a solid (dashed) line for mono and bulk $A$ ($B$). (c) Gate voltage dependence of resistance at different temperatures taken from mono $A$.