Valley-Dependent Spin Transport in Monolayer Transition-Metal Dichalcogenides

We study valley-dependent spin transport theoretically in monolayer transition-metal dichalcogenides in which a variety of spin and valley physics are expected because of spin-valley coupling. The results show that the spins are valley-selectively excited with appropriate carrier doping and valley polarized spin current (VPSC) is generated. The VPSC leads to the spin-current Hall effect, transverse spin accumulation originating from the Berry curvature in momentum space. The results indicate that spin excitations with spin-valley coupling lead to both valley and spin transport, which is promising for future low-consumption nanodevice applications.

Figure 1

A ferromagnetic insulator is fixed to the TMDC monolayer and a diffusive spin current ${\mathit{j}}_s$ is generated by an external microwave irradiation.

Figure 2

The left diagrams represent (a) intravalley and (b) intervalley spin-transfer processes with magnon absorption. The solid and wavy arrows represent electrons and magnons, respectively. The right figures show schematic band structure and transition of an electron with spin flip.

Figure 3

(a) The first and second panels from the left show the valence bands in the $K_{+}$ and $K_{-}$ valleys, respectively. The third panel from the left shows the spin current at the interface. The solid and dotted curves represent the valley-resolved spin current in the $K_{+}$ and $K_{-}$ valleys, respectively. The fourth panel from the left shows the valley-polarized spin current at several temperatures. The units of the spin current are given by $I_0=[g(\mathrm{\Omega })/\pi ][(|J_0{|}^2{\mathrm{\Delta }}^2)/(\hslash v{)}^4]\hslash \mathrm{\Omega }$. (b) (i) The up-spin (blue arrows) and down-spin (red arrows) electrons flowing in opposite directions lead to the transverse spin accumulation. (ii) When the spin current is finite in the $K_{+}$ and $K_{-}$ valleys, the transverse spin accumulation cancels.

Figure 4

Numerical solution of spin diffusion equation with system size $L_x/{\lambda }_s=L_y/{\lambda }_s=5$ and Hall angle $\theta =0.3$. (a) Spin accumulation ${\mu }_s$ plotted as a function of $x$ and $y$ and (b) as a function of $y$ for several values of $x$. The units of the spin accumulation are given by ${\mu }_0=e{j}_0{\lambda }_s/{\sigma }_{xx}$.

Figure 5

(a) Valley accumulation ${\mu }_v={\mu }^{K_{+}}-{\mu }^{K_{-}}$ is induced by spin excitation with the intervalley spin-transfer processes. The dotted line represents the chemical potential $\mu$ in equilibrium. (b) Valley accumulation with spin-valley locking leads to the inverse spin Hall effect.