Temporal and spatial valley dynamics in two-dimensional semiconductors probed via Kerr rotation

Monolayer transition metal dichalcogenides (TMDCs) offer a tantalizing platform for control of both spin and valley degrees of freedom, which may enable future optoelectronic devices with enhanced and novel functionalities. Here, we investigate the valley dynamics of two prototypical members of TMDCs, namely $\mathrm{Mo}{\mathrm{S}}_2$ and $\mathrm{WS}{\mathrm{e}}_2$, using time-resolved Kerr rotation (TRKR) at temperatures from 10 K to 300 K. This pump-probe technique enables sub-picosecond temporal resolution, providing insight into ultrafast valley dynamics, which is inaccessible by polarized and time-resolved photoluminescence spectroscopy. Bi-exponential decay dynamics were observed for both materials at low temperatures, and the fast decay component indicated a rapid exciton valley depolarization time $(<10\mathrm{ps})$ due to strong Coulomb exchange interactions between the $K$ valleys. However, the slow decay components (several tens of picoseconds) were attributed to different origins in the two materials, which were further elucidated by temperature-dependent TRKR measurements. Moreover, the spatial dependence of the TRKR intensity across $\mathrm{Mo}{\mathrm{S}}_2$ monolayer flakes indicated a weaker valley polarization near the edges, which is likely associated with quenched excitons near the grain boundaries or a disordered edge region in chemical vapor deposition–grown monolayers. These temporal and spatial TRKR measurements reveal insight into the complex dynamics of valley excitonic states, which will be critical for valleytronic applications of monolayer TMDCs.

Figure 1

TRKR measurements of valley dynamics. (a) Schematic diagram of the experimental setup. (SHG OPO: second-harmonic generation of optical parametric oscillator; PBS: polarizing beam-splitter; $\lambda /4$: quarter-wave plate.) (b) Diagram of the valley-dependent optical selection rules for the interband transitions. (c) Valley dynamics measured by TRKR for a CVD-grown $\mathrm{Mo}{\mathrm{S}}_2$ monolayer at $T=10\mathrm{K}$ with a laser excitation energy of 1.93 eV. The solid line shows a bi-exponential fit to the experimental data.

Figure 2

Excitation energy dependence of valley dynamics of monolayer $\mathrm{Mo}{\mathrm{S}}_2$ at $T=10\mathrm{K}$. (a) Measured Kerr rotation as a function of pump-probe delay time for a range of excitation energies as indicated in the figure. Bi-exponential fits to the data are also shown. (b) The two decay components that were extracted from the bi-exponential fits to the TRKR data as a function of excitation energy. (c) Measured Kerr rotation at a pump-probe delay time of $\mathrm{\Delta }t=0.5\mathrm{ps}$ as a function of excitation energy. The solid circles represent experimental data, and the colors correspond to the excitation energies indicated in (a). The prediction from Eq. (1) is shown by the red solid line. (d) The real and imaginary parts of the difference in the complex optical response function (${\alpha }_{+}-{\alpha }_{-}$) for ${\sigma }^{+}$ and ${\sigma }^{-}$ polarized light. The imaginary part was calculated from the real part using the Kramers-Kronig relations.

Figure 3

PL spectra and valley dynamics of $\mathrm{Mo}{\mathrm{S}}_2$ and $\mathrm{WS}{\mathrm{e}}_2$ monolayers. (a) PL spectrum of a monolayer $\mathrm{Mo}{\mathrm{S}}_2$ measured at $T=10\mathrm{K}$. (b) TRKR measured for a monolayer $\mathrm{Mo}{\mathrm{S}}_2$ at a temperature of $T=10\mathrm{K}$. An excitation energy of 1.93 eV was used in this experiment as indicated by the arrow in (a). (c) PL spectrum of an exfoliated $\mathrm{WS}{\mathrm{e}}_2$ monolayer flake at $T=10\mathrm{K}$. (d) TRKR measured for a $\mathrm{WS}{\mathrm{e}}_2$ monolayer flake [exfoliated from the same crystal as the monolayer measured in (c)] at a temperature of $T=10\mathrm{K}$. An excitation energy of 1.75 eV was used in this experiment as indicated by the arrow in (c). The opposite TRKR signal was observed for ${\sigma }^{+}$ and ${\sigma }^{-}$ pump polarizations for both monolayer $\mathrm{Mo}{\mathrm{S}}_2$ and $\mathrm{WS}{\mathrm{e}}_2$. The solid lines in (b) and (d) are fits to a bi-exponential decay function.

Figure 4

Temperature dependence of valley dynamics measured by TRKR. (a) The valley dynamics of a monolayer $\mathrm{Mo}{\mathrm{S}}_2$ flake at different temperatures. The solid lines are fits to a bi-exponential decay function. (b) The extracted two decay components for $\mathrm{Mo}{\mathrm{S}}_2$ as a function of temperature. Different colors represent three different $\mathrm{Mo}{\mathrm{S}}_2$ flakes. The green symbols represent the extracted decay components obtained at room temperature for another monolayer flake before the sample was cooled down. (c) The valley dynamics of a monolayer $\mathrm{WS}{\mathrm{e}}_2$ flake at different temperatures. The solid lines are fits to either a bi-exponential or a single-exponential decay function. (d) The extracted two decay components of the same $\mathrm{WS}{\mathrm{e}}_2$ monolayer flake as a function of temperature.

Figure 5

Spatial distributions of valley dynamics. Two-dimensional maps of TRKR intensity at a fixed pump-probe delay time ($\mathrm{\Delta }t=0.5\mathrm{ps}$) for six monolayer $\mathrm{Mo}{\mathrm{S}}_2$ flakes and their corresponding optical microscopy images at (a–c) $T=10\mathrm{K}$ and (d–f) room temperature. The TRKR intensity was normalized for each 2D map. The red dashed line represents the edges of each flake. Laser spot diameter: $\sim 1.5\mu \mathrm{m}$. Scanning resolution: $0.5\mu \mathrm{m}$.