Quantum Transport and Observation of Dyakonov-Perel Spin-Orbit Scattering in Monolayer ${\mathrm{MoS}}_2$

Monolayers of group 6 transition metal dichalcogenides are promising candidates for future spin-, valley-, and charge-based applications. Quantum transport in these materials reflects a complex interplay between real spin and pseudospin (valley) relaxation processes, which leads to either positive or negative quantum correction to the classical conductivity. Here we report experimental observation of a crossover from weak localization to weak antilocalization in highly $n$-doped monolayer ${\mathrm{MoS}}_2$. We show that the crossover can be explained by a single parameter associated with electron spin lifetime of the system. At low temperatures and high carrier densities, the spin lifetime is inversely proportional to momentum relaxation time; this indicates that spin relaxation occurs via a Dyakonov-Perel mechanism.

Figure 1

(a) Transfer curves measured at different temperatures: 20, 40, 60, 80, and 100 K, from black to cyan. The red squares represent ${\tau }_p$ at $T=2\mathrm{K}$. Inset: optical microscope image of a rectangular device with current source ($S$) and drain ($D$) contacts (scale bar: $5\mu \mathrm{m}$). (b) Experimentally observed magnetoresistivity (MR) as a function of magnetic field and temperature measured at ${\mathrm{V}}_{\mathrm{bg}}=40\mathrm{V}$ and ${\mathrm{V}}_{\mathrm{tg}}=1\mathrm{V}$. (c) $\mathrm{\Delta }\sigma$ at $T=2$, 6, 10, and 45 K and fixed back-gate voltages of $V_{\mathrm{bg}}=40\mathrm{V}$ (left panel) and at fixed temperature of $T=2\mathrm{K}$ and different gate voltages of $V_{\mathrm{bg}}=20$, 60, and 70 V (right panel). The solid lines indicate experimental data, and the shaded lines the fits according to Eq. (2). To calculate $\mathrm{\Delta }\sigma$, the initial measured MR curve was symmetrized to avoid contributions from the sample geometry, so that $\rho (B)=[\rho (+B)+\rho (-B)]/2$.

Figure 2

(a) Intra- and intervalley scattering in the spin-split $K$ and $K$’ valleys of the conduction band. (b) A sketch of predicted MC behavior assuming large separations in the time scales of the relevant scattering mechanisms. Two parameters, $B_{\mathrm{SO}}$ and $B_{\mathrm{IV}}$ (and, accordingly, ${\tau }_{\mathrm{SO}}$ and ${\tau }_{\mathrm{IV}}$), define the crossover between WL and WAL.

Figure 3

(a) The crossover parameter ${\tau }_{\mathrm{SO}}$ as a function of ${\tau }_p^{-1}$. The blue dashed line is a linear fit and the grey dashed line is a theoretical prediction based on ${\lambda }_{\mathrm{int}}=3\mathrm{meV}$ [37, 38, 39]. (b) $L_{\mathrm{SO}}$ as a function of temperature.

Figure 4

Temperature dependence of $L_{\varphi }$ at $V_{\mathrm{bg}}=20\mathrm{V}$ and 40 V with guide to the eyes (solid lines). The dashed lines show agreement with $\propto T^{-0.5}$ dependence for $T>10\mathrm{K}$. Inset: density dependence of $L_{\varphi }$ at $T=2\mathrm{K}$.