Fig. 4. Temperature dependence and extraction of intervalley scattering length.

(A) Measured V_nl as a function of temperature at different V_g for monolayer MoS₂. (B) Temperature dependence of multilayer MoS₂ at different V_g (dots) and the calculated trends (lines) using the modified ohmic equation, ${\mathit{V}}_{\text{ohmic}}=\frac{{\mathit{V}}_{\text{ds}}}{({2\mathit{R}}_{\mathrm{C}}+{\mathrm{\rho }}_{\text{sh}}\frac{{\mathit{L}}_1}{{\mathit{W}}_1})}{\mathrm{\rho }}_{\text{sh}}\frac{\mathit{W}}{{\mathit{W}}_1}{\mathit{e}}^{\frac{-\mathrm{\pi }\mathit{L}}{\mathit{W}}}$, with the consideration of the contact resistance contribution (see section S1). Note that the trends of V_nl with respect to temperature in (A) and (B) are completely opposite. (C) Device geometry and corresponding valley-circuit model that define the geometric parameters in Eq. 1. Details are given in section S3. (D) Temperature dependence of ${\mathit{R}}_{\text{nl}}^{\text{norm}}$ (normalized to the maximum point) measured at V_g = 58 V [orange dots in (A)]. The empirical fittings use $\mathrm{\lambda }(\mathit{T})=5.5{\mathit{T}}^{-0.47}-0.16$ (dashed blue line) and $\mathrm{\lambda }=15{\mathit{T}}^{-0.73}$ at T > 100 K (green line). Inset: Calculated temperature dependence of valley Hall angle, θ. (E) λ (T) extracted from R_nl and the power-law dependence described in (D). Inset: Theoretically calculated intervalley scattering length (solid line) and $\mathrm{\lambda }\propto {\mathit{T}}^{-0.6}$ to guide the eye (dashed line).