Strong electron-hole symmetric Rashba spin-orbit coupling in graphene/monolayer transition metal dichalcogenide heterostructures

Despite its extremely weak intrinsic spin-orbit coupling (SOC), graphene has been shown to acquire considerable SOC by proximity coupling with exfoliated transition metal dichalcogenides (TMDs). Here we demonstrate strong induced Rashba SOC in graphene that is proximity coupled to a monolayer TMD film, $\mathrm{Mo}{\mathrm{S}}_2$ or $\mathrm{WS}{\mathrm{e}}_2$, grown by chemical-vapor deposition with drastically different Fermi level positions. Graphene/TMD heterostructures are fabricated with a pickup-transfer technique utilizing hexagonal boron nitride, which serves as a flat template to promote intimate contact and therefore a strong interfacial interaction between TMD and graphene as evidenced by quenching of the TMD photoluminescence. We observe strong induced graphene SOC that manifests itself in a pronounced weak-antilocalization (WAL) effect in the graphene magnetoconductance. The spin-relaxation rate extracted from the WAL analysis varies linearly with the momentum scattering time and is independent of the carrier type. This indicates a dominantly Dyakonov-Perel spin-relaxation mechanism caused by the induced Rashba SOC. Our analysis yields a Rashba SOC energy of ∼1.5 meV in graphene/$\mathrm{WS}{\mathrm{e}}_2$ and ∼0.9 meV in graphene/$\mathrm{Mo}{\mathrm{S}}_2$. The nearly electron-hole symmetric nature of the induced Rashba SOC provides a clue to possible underlying SOC mechanisms.

Figure 1

(a) Optical image of a graphene/$\mathrm{WS}{\mathrm{e}}_2/h\text{−}\mathrm{BN}$ (from bottom to top) heterostructure. The $\mathrm{Si}/\mathrm{Si}{\mathrm{O}}_2$ background surrounding the heterostructure is removed for clarity. The white dotted line delineates the boundary between areas with (left) and without graphene (right). The scale bar is 10 μm. (b) Raman spectra of the right area in (a). Inset: characteristic Raman peaks of $h\text{−}\mathrm{BN}$ and graphene. (c) PL mapping of the sample shown in (a). The white dashed rectangle indicates the area covered by the gold pad in (a). (d) PL spectra taken in blue and red regions in (c). Note the PL intensity from the left with graphene underneath is magnified by 10 times for comparison. Inset: graphene Dirac bands present in the gap of $\mathrm{WS}{\mathrm{e}}_2$.

Figure 2

Conductance $G$ and carrier density $n$ (inset) of (a) graphene/$\mathrm{WS}{\mathrm{e}}_2$ sample 1 and (b) graphene/$\mathrm{Mo}{\mathrm{S}}_2$ as a function of top gate voltage. Bottom left inset in (a): optical image of the device. Scale bar is $10\mu \mathrm{m}$. Insets in the carrier-density plot draw the relative Fermi level positions in graphene/$\mathrm{WS}{\mathrm{e}}_2$ in (a) and graphene/$\mathrm{Mo}{\mathrm{S}}_2$ in (b).

Figure 3

MC curves, $G$ vs. $B$, taken at different back gate voltages for (a) graphene/$\mathrm{WS}{\mathrm{e}}_2$ sample 2 and (b) graphene/$\mathrm{Mo}{\mathrm{S}}_2$. MC curves in (b) are shifted vertically for clarity. Dashed lines are the fits using Eq. (1). (c) and (d) Plots over a wide range of back gate voltages and magnetic fields from −10 to 10 mT corresponding to samples used in (a) and (b), respectively. Charge neutrality points are indicated by the black dot-dashed lines.

Figure 4

(a) Spin-relaxation rate ${\tau }_{\mathrm{SOC}}^{-1}$ (squares) and dephasing rate ${\tau }_{\phi }^{-1}\left(\mathrm{triangles}\right)$ as a function of carrier density $n$. These rates are extracted from graphene/$\mathrm{WS}{\mathrm{e}}_2$ sample 2. Half- filled (open) symbols stand for the hole (electron) side. (b) ${\tau }_{\mathrm{SOC}}^{-1}$ as a function of ${\tau }_p$ in three different samples: circles for graphene/$\mathrm{WS}{\mathrm{e}}_2$ sample 1, squares for graphene/$\mathrm{WS}{\mathrm{e}}_2$ sample 2, and triangles for graphene/$\mathrm{Mo}{\mathrm{S}}_2$. Open and half-filled symbols denote the electron and hole sides, respectively. Solid lines are guidelines to the eye.