Thermally Driven Pure Spin and Valley Currents via the Anomalous Nernst Effect in Monolayer Group-VI Dichalcogenides

The spin and valley-dependent anomalous Nernst effects are analyzed for monolayer ${\mathrm{MoS}}_2$ and other group-VI dichalcogenides. We find that pure spin and valley currents can be generated perpendicular to the applied thermal gradient in the plane of these two-dimensional materials. This effect provides a versatile platform for applications of spin caloritronics. A spin current purity factor is introduced to quantify this effect. When time reversal symmetry is violated, e.g., two-dimensional materials on an insulating magnetic substrate, a dip-peak feature appears for the total Nernst coefficient. For the dip state it is found that carriers with only one spin and from one valley are driven by the temperature gradient.

Figure 1

(a) Illustration of the anomalous Nernst coefficient as a function of the Fermi energy for different spin states in each Dirac cone. The vertical dotted lines indicate the positions of the maxima of the valence bands with corresponding spin states and Dirac cones. (b) Spin current purity corresponding to the curves shown in (a). (c) A pure spin current and valley current can be generated when lowering the Fermi level into the bands of $K\uparrow$ ($-K\downarrow$). (d) Schematic illustration for the corresponding mixed spin (valley) current when further lowering the Fermi level into $K\downarrow$ ($-K\uparrow$). The 2D material is chosen as ${\mathrm{MoS}}_2$ and the temperature is $T=300\mathrm{K}$.

Figure 2

(a) The spin current purity factor $\eta$ for the materials of Table 1 at $T=300\mathrm{K}$. (b) The temperature dependence of $\eta$ for ${\mathrm{MoS}}_2$.

Figure 3

The ANCs [(a), (b)] and SNC [(c), (d)] for the $K$ cone are calculated as a function of the Fermi energy for different materials and temperatures, respectively. The temperature in (a) and (c) is taken at 300 K. ${\mathrm{MoS}}_2$ is fixed in (b) and (d).

Figure 4

A proposed $\mathsf{H}$-shaped detector for detecting the spin Nernst effect in TMDCs. The spin current, generated in the right leg by a temperature gradient, is injected into the left leg through a horizontal bridge, which can be converted into a detectable charge voltage drop $\mathrm{\Delta }{V}_{\mathrm{ISHE}}$ by the inverse spin Hall effect.

Figure 5

The total ANC as a function of the Fermi energy for different materials at 300 K with the magnetization of magnet $M_z=6\mathrm{T}$.