Resonance Profiles of Valley Polarization in Single-Layer ${\mathrm{MoS}}_2$ and ${\mathrm{MoSe}}_2$

In this Letter, we present photoluminescence measurements with different excitation energies on single-layer ${\mathrm{MoS}}_2$ and ${\mathrm{MoSe}}_2$ in order to examine the resonance behavior of the conservation of circular polarization in these transition metal dichalcogenides. We find that the circular polarization of the emitted light is conserved to 100% in ${\mathrm{MoS}}_2$ and 84%/79% ($A/A^{-}$ peaks) in ${\mathrm{MoSe}}_2$ close to resonance. The values for ${\mathrm{MoSe}}_2$ surpass any previously reported value. However, in contrast to previous predictions, the degree of circular polarization decreases clearly at energies less than the two-phonon longitudinal acoustic phonon energy above the resonance. Our findings indicate that at least two competing processes underly the depolarization of the emission in single-layer transition metal dichalcogenides.

Figure 1

(a) Schematic illustration of the reciprocal space of hexagonal systems; the two arrows are of the same length and orientation, indicating that $K$ to $K^{\prime }$ scattering requires the momentum of a $K$-point phonon. (b) Illustration of the two bands contributing to the $A$ and $B$ excitonic transitions at the $K$ and $K^{\prime }$ points; black arrows indicate the electron and hole spin of corresponding bands.

Figure 2

Typical circular-polarization resolved PL spectra in resonance with the $A$ (a) and $B$ exciton (b) of ${\mathrm{MoS}}_2$ and spectra in resonance (c) and out of resonance (d) with the trion of ${\mathrm{MoSe}}_2$. Arrows indicate the excitation energies. Narrow peaks in the vicinity of asterisks (*) are due to Raman scattering and were excluded for fitting.

Figure 3

Degree of circular polarization $\rho$ of the $A$ exciton of ${\mathrm{MoS}}_2$ (a) and $A^{-}$ trion of ${\mathrm{MoSe}}_2$ (b) plotted as a function of the photon excess energy $\mathrm{\Delta }E$ (red and blue symbols). Data and model from Ref. [9], and data from Refs. [13, 21] are displayed for comparison. Further comparison to the data referenced within Ref. [9] is given in the Supplemental Material [15]. Photoluminescence spectra are plotted as a guidance for the energy scale, superimposed Raman lines are marked with an asterisk (*). For ${\mathrm{MoSe}}_2$, a fit following $a/\sqrt{\mathrm{\Delta }E}$ is included (dashed line). The inset depicts the definition of the excess energy $\mathrm{\Delta }E$.