Optimal Charge-to-Spin Conversion in Graphene on Transition-Metal Dichalcogenides

When graphene is placed on a monolayer of semiconducting transition metal dichalcogenide (TMD) its band structure develops rich spin textures due to proximity spin-orbital effects with interfacial breaking of inversion symmetry. In this work, we show that the characteristic spin winding of low-energy states in graphene on a TMD monolayer enables current-driven spin polarization, a phenomenon known as the inverse spin galvanic effect (ISGE). By introducing a proper figure of merit, we quantify the efficiency of charge-to-spin conversion and show it is close to unity when the Fermi level approaches the spin minority band. Remarkably, at high electronic density, even though subbands with opposite spin helicities are occupied, the efficiency decays only algebraically. The giant ISGE predicted for graphene on TMD monolayers is robust against disorder and remains large at room temperature.

Figure 1

(a) Graphene on a ${MX}_2$ monolayer. (b) Typical band structure with spin-split bands with opposite spin helicity. (c) Tangential winding of spin texture in regimes I and II. (d) Ratio between the static spin-charge susceptibility and charge conductivity (in units of $2v$) [thick line (Born limit); dashed line (strong scattering limit, $u_0\to \infty$)].

Figure 2

Diagrammatic expansion of the response function. (a) Bethe-Salpeter equation for the charge current vertex in the $R\text{−}A$ sector. (b) Skeleton expansion of the $T$-matrix ladder. The full (open) square denotes a $T$ ($T^{†}$) matrix insertion, while the circles represent electron-impurity interaction vertices. The red $\times$ stands for impurity density insertion ($n$).

Figure 3

Main figure: Fermi energy dependence of the ISGE efficiency at selected values of $\mathrm{\Delta }$ for $\lambda =15\mathrm{meV}$ and ${\lambda }_{\mathrm{sv}}=0$. The $x$ axis is rescaled as $x_{\epsilon }=|\epsilon -{\epsilon }_0|/|2\tilde{\lambda }-{\epsilon }_0|$ for clarity. Insets: (a) $\gamma$ as function of chemical potential $\mu$ at selected temperatures for a prototypical heterostructure with $\lambda =10\mathrm{meV}$, ${\lambda }_{\mathrm{sv}}=\mathrm{\Delta }=0$ (Ref. [13]); $k_B{T}^{*}=25\mathrm{meV}$ (room temperature). (b) Variation of $\gamma$ with ${\lambda }_{\mathrm{sv}}$ for a Fermi energy slightly below (above) the RPG’s edge [${\epsilon }_{\pm }=2\tilde{\lambda }\times (1.00\pm 0.05)$] for $\mathrm{\Delta }=\lambda /2$ and $\lambda =15\mathrm{meV}$. All calculations are performed in the weak scattering limit.