Optical polarization and intervalley scattering in single layers of MoS2 and MoSe2

Single layers of MoS2 and MoSe2 were optically pumped with circularly polarized light and an appreciable polarization was initialized as the pump energy was varied. The circular polarization of the emitted photoluminescence was monitored as a function of the difference between the excitation energy and the A-exciton emission at the K-point of the Brillouin zone. Our results show a threshold of twice the LA phonon energy, specific to the material, above which phonon-assisted intervalley scattering causes depolarization. In both materials this leads to almost complete depolarization within ~100 meV above the threshold energy. We identify the extra kinetic energy of the exciton (independent of whether it is neutral or charged) as the key parameter for presenting a unifying picture of the depolarization process.

Scientific RepoRts | 6:25041 | DOI: 10.1038/srep25041 In this work, we measure the energy-dependent valley polarization in both MoS 2 and MoSe 2 under zero magnetic field, and model the polarization relaxation. We probe the valley population dynamics in MoSe 2 and MoS 2 by selectively populating the K and K' valleys with circularly polarized light while systematically varying the laser excitation energy. For both systems, the difference in the excitation energy and PL emission energy, Δ E = E pump − E PL , governs the depopulation of carriers in each valley. Adding more energy above a distinct threshold characteristic of the longitudinal acoustic (LA) phonon for each material enables inter-valley scattering and produces a sharp decrease in the observed circular polarization. LA phonons in these two systems have different energies (30 meV for MoS 2 and 19 meV for MoSe 2 ) 24,25 , and we show that the threshold for the excess energy required to initiate the depolarization process clearly reflects the material specific phonon energy. In addition, our results show that independent of how many carriers are excited, i.e. whether you create neutral or charged excitons, the scattering process is the same. We find that the key parameter for the depolarization process is the extra kinetic energy of the exciton -depolarization is due to intervalley scattering that begins to occur when the exciton energy exceeds a threshold corresponding to twice the LA phonon energy.

Results
Flakes of MoS 2 and MoSe 2 mechanically exfoliated from bulk crystals were used in this study. Monolayer MoX 2 regions were identified with an optical microscope ( Fig. 2(a,b)) and confirmed with Raman spectroscopy at room temperature ( Fig. 2(c,d)). Raman spectroscopy confirms single-layer regions through the shapes and relative positions of the out-of-plane A 1g and in-plane E 1 2g Raman active modes [26][27][28] (see Methods section). In Fig. 2(c) the 18 cm −1 splitting between E 1 2g (384 cm −1 ) and A 1g (402 cm −1 ) modes verifies the monolayer nature of the MoS 2 sample 26 . Raman spectra from MoSe 2 taken under the same conditions are shown in Fig. 2(d) for several layer thicknesses. The identification of the single layer 27 is based on the absence of the B 2g mode at 353 cm −1 , which can be clearly seen in Fig. 2(d). A micro-PL setup was used to collect the PL in a backscattering geometry (see methods section). The PL spectra were analyzed as σ + and σ − using a combination of quarter-wave plate (liquid crystal retarder) and linear polarizer placed before the spectrometer entrance slit. The degree of circular polarization is defined as P circ = (I + − I − )/(I + + I − ), where I + (I − ) is the intensity of the σ + (σ − ) component of the PL.
Temperature dependent PL emission from MoS 2 and MoSe 2 are shown in Fig. 3(a,b), respectively (full experimental details are described elsewhere) 11 . In these spectra, the samples were excited with a laser at 2.33 eV (532 nm). The dominant emission peak is the A-exciton, a feature that originates from the lowest energy transition at the K-point of the Brillouin zone (see Fig. 1(c)). At low temperature, we measure the A-exciton at 1.89 eV for MoS 2 , and at 1.625 eV for MoSe 2 reflective of the smaller bandgap of MoSe 2 . The width of the emission from MoS 2 is very broad (FWHM = 0.09 eV) so it is not possible to distinguish features within the spectra and we assign this feature to the neutral exciton, X 0 . However, the emission from MoSe 2 is much narrower (FWHM = 0.01 eV), and it is possible to distinguish two clear peaks separated by 0.03 eV that become apparent as the sample is heated ( Fig. 3(b)). These peaks have been identified as a neutral exciton (X 0 ) and a charged exciton (T) 18 . It is not possible to determine whether the lower energy peak is a positive or negative charged exciton based solely on the emission energy, because the effective mass of electrons and holes in this material is similar.
As the temperature is increased the relative luminescence of charged vs. neutral exciton changes, with the neutral exciton eventually becoming the dominant feature. Note that the charged exciton is still visible at temperatures much higher than is seen in other quasi-2D systems such as GaAs QWs 29 . The temperature dependence of the exciton emission channels for both systems shows a typical semiconductor behavior (Fig. 3(c,d), solid is the energy position of a given feature at zero temperature, S is a dimensionless coupling constant, and 〈 ħω 〉 is an average phonon energy. The fitting parameters obtained here are S = 1.16 (2.18) and 〈 ħω 〉 = 19 meV (14.5 meV) for MoS 2 (MoSe 2 ).
To examine the valley spin dynamics, we measure the helicity dependent PL from these monolayers. Because of the optical selection rules ( Fig. 1(c)), when pumped with light of positive (σ + ) or negative (σ − ) helicity, either the K or K' valley will be selectively populated 6 . Information on the depolarization process comes from analyzing the polarization of the subsequent PL. Figure 4(a,b) show representative PL spectra analyzed for σ + (solid red line) and σ − (dashed blue line) at T = 5 K for MoS 2 and MoSe 2 , respectively, at selected σ + excitation energies. By using a combination of sharp, long-pass filters, stray light was suppressed at the spectrometer entrance. In addition, as the excitation energy approached the PL emission energy, the excited Raman modes were cut-off from entering the detection system. This experimental setup limited our lowest excitation energies to 1.984 eV (625 nm) for MoS 2 and 1.722 eV (720 nm) for MoSe 2 . It is clear from Fig. 4 that, for both materials, the higher the excitation energy, the lower the polarization of the emission 31 .
The degree of circular polarization is shown in Fig. 5 as a function of the excess energy, ∆ E = E pump − E PL , the difference between the excitation energy E exc and PL emission energy, E PL (the inset of Fig. 5 is a graphical representation). Data are plotted for MoSe 2 (solid red circles) and MoS 2 (solid blue circles) and are derived from spectra where the temperature was held constant and the laser energy was varied, or the laser energy was fixed The absence of the B 2g mode is the fingerprint for the single layer. All spectra were taken at 300 K with an excitation wavelength of 488 nm. and the emission energy was varied via a change in temperature 8,11,19 . Since this plot incorporates the energy difference between excitation and PL emission rather than the specific energy of the neutral and charged excitons, the behavior observed for both materials can be shown. Data for MoS 2 from the literature are also plotted in  1.96 eV). The open squares with a slash are data from Ref 19 obtained at fixed excitation energy of 1.96 eV but at temperatures ranging from 5 to 300 K. To the best of our knowledge, these data represent the trends seen in the literature for MoS 2 . All data follow the same depolarization trend line when plotted as a function of excess energy. Using this methodology, all of the data collapse onto a single curve for each material, independent of whether the polarization of the trion or neutral exciton is considered. The data clearly demonstrate that as the excess energy increases the emitted circular polarization decreases.

Discussion
To explain this behavior, we begin by noting that due to the optical selection rules 6 intra-valley scattering cannot result in a reduction in the observed polarization even if the pump energy exceeds the spin-orbit splitting (160 meV for MoS 2 , 180 meV for MoSe 2 ) 8 . Therefore, inter-valley scattering is required to account for the reduced polarization observed, and the change in momentum necessary for such scattering implicates a phonon-mediated process 8,11 . Close to resonance the emitted circular polarization is expected to be essentially 100%, since there is not enough energy in the system to facilitate intervalley scattering. As the laser excitation energy increases or as the temperature changes for a fixed pumping energy, the available excess energy ∆ E increases and phonon-assisted scattering is enabled above some material-dependent energy threshold. For MoS 2 , the combined data set clearly interpolate to 100% polarization at ∆ E = 60 meV, corresponding to twice the LA phonon energy 11 .
Intervalley scattering requires participation from in-plane longitudinal phonons. From the phonon-dispersion curves for single layers of MoS 2 and MoSe 2 the lowest energy phonon available for scattering are longitudinal   acoustic phonons with energies of 30 meV for MoS 2 24 and 19 meV for MoSe 2 25 . Intervalley scattering becomes accessible when the excitation energy exceeds a threshold value that is the sum of the exciton Coulombic formation energy (PL emission energy) and twice the lowest acoustic-phonon energy available in the system (essentially a phonon for each the electron and hole). That is 60 meV for MoS 2 and 38 meV for MoSe 2 . There are two mechanisms that could be responsible for the electron or hole spin-flip during this phonon mediated intervalley scattering event. One is that the spin-flip is mediated by short range scattering from impurities. The presence of a background carrier population could enhance the probability of such a process 31 . The other mechanism is that intervalley scattering proceeds through the nearly spin-degenerate Γ valley of the Brillioun zone 32 .
The MoSe 2 data (solid red symbols) exhibit a similar behavior -the measured polarization rapidly increases as the excess energy ∆E decreases. The narrow linewidths in MoSe 2 allow us to distinguish the particular emission channels X 0 and T. Therefore, for MoSe 2 , we can plot the polarization of both the neutral and charged exciton. Note that due to the low intensity of the X 0 data, it is difficult to see the polarization on the same scale as the trion emission, therefore a typical set of X 0 emission spectra are shown in the inset of Fig. 4(b). As with MoS 2 , all the data coalesce onto the same depolarization curve as a function of excess energy. The solid red line is a model fit described below, and intercepts 100% polarization at ∆E = 38 meV, corresponding to twice the MoSe 2 LA phonon energy of 19 meV from the literature 25 . These data make it clear that depolarization and intervalley scattering are governed by the excess energy, ∆E, imparted to the photoexcited carriers through optical pumping.
To model this behavior, we begin with a familiar rate equation model in which the emitted circular polarization can be expressed as = + τ τ ( ) , where τ r is the exciton lifetime and τ s the intervalley scattering time 8,11 . Both τ r and τ s depend on temperature, or more specifically on the thermal energy given to the exciton during optical excitation. We associate this additional thermal energy with the excess energy, ∆E. It has been shown that τ r depends linearly on temperature 33 , therefore we expect it to have a linear dependence with ∆E. In addition, the increase in the excess energy leads to an increase of the phonon population. We assign the intervalley scattering rate τ s −1 to be proportional to the phonon population kT / q and substitute kT with (∆E − ћω q ). Taking into account these dependencies on ∆E we can fit the data using the relation Here ћω q is twice the LA phonon energy, the minimum energy necessary for the exciton (electron and hole) to scatter from one valley to the other and reduce the optical polarization, and C is a scaling constant. These two values, C and ћω q , are the only fitting parameters. Note that this fitting relation is valid only for ∆E > ћω q . The solid lines in Fig. 5 are fits to the data and yield values for 2LA of 54 meV for MoS 2 and 38 ± 4 meV for the MoSe 2 , in good agreement with the respective literature values of 60 and 38 meV 24,25 . The data for MoS 2 diverge systematically from the fitted line above 150 meV. The main reason for this discrepancy may be that our simple rate equation model does not take into account the spin-orbit interaction (150 meV for MoS 2 ) 11 .
Even though the optical response of 2-dimensional crystals is dominated by the formation of excitons, we used the phonon-assisted intervalley scattering model, which is based on a single particle picture. This is a straightforward way to describe the sharp depolarization of the emitted PL as a function of the excess energy that includes a threshold energy. However, the thermally activated relaxation of the carriers may not represent all aspects of physics that could describe the spin relaxation in this system. Recently, alternative interpretations based on the excitonic picture explain the PL depolarization as valley-decoherence due to long-range exciton exchange, i.e. direct intervalley electron-hole exchange 32,[34][35][36][37][38] . Both of these mechanisms may be at play with different relative contributions that varies across different material systems. Our observation of a threshold depolarization energy, however, is more easily explained with the phonon model we have presented.
In summary, at zero magnetic field, we initialized circular polarization in MoS 2 and MoSe 2 using energy-dependent circularly-polarized optical pumping and measured the valley polarization process as a function of the excess energy absorbed by the carriers. Independent of the emission channel or the material studied (MoS 2 or MoSe 2 ), all the data can be modeled by a single depolarization mechanism, intervalley scattering mediated by LA phonons. The threshold needed for depolarization is found to be twice the LA phonon energy of the corresponding material, and the exciton kinetic energy greater than this is the key parameter for the depolarization. Generating high chirality photoluminescence in Mo-based two-dimensional structures enables applications in valley-photonics.

Methods
Sample preparation and characterization. All samples used in this study were mechanically exfoliated from bulk crystals. The MoS 2 was deposited onto a 285-nm SiO 2 layer on a Si substrate, while the MoSe 2 flakes were deposited on a 90-nm SiO 2 layer on a Si substrate. The typical size of monolayer regions are 5-10 μ m across for MoS 2 and 1-2 μ m for MoSe 2 and were identified with an optical microscope and confirmed with Raman spectroscopy at room temperature and 488 nm excitation. Raman spectroscopy has been established as a reliable tool for determining the specific number of layers in transition metal dichalcogenides [26][27][28] . In MoS 2 , the 18 cm −1 energy difference between the two main vibrational modes, E 1 2g at 384 cm −1 and A 1g at 402 cm −1 , is the fingerprint for the accurate determination of the single layer. In MoSe 2 , the in-plane E 1 2g (287 cm −1 ) and the out-of-plane A 1g (242 cm −1 ) modes are much lower in energy than in MoS 2 because of the larger mass of the Se atom. Also, the in-plane and out-of-plane modes switch positions relative to the MoS 2 , i.e, the out-of-plane mode is softer than the in-plane one. This can be verified by measuring thicker layers of MoSe 2 and observing a Davydov splitting in the A 1g mode for multi-layer flakes. The single layer is identified by the absence of the B 2g mode at 353 cm −1 .
Optical measurements. The photoluminescence data were taken in a backscattering geometry using a micro-PL setup (spatial resolution of 1 μ m) with a 50× objective and incorporating a continuous-flow He-cryostat. The MoS 2 samples were excited with either a continuous-wave 2.33 eV (532 nm) solid-state laser or Scientific RepoRts | 6:25041 | DOI: 10.1038/srep25041 a tunable pulsed laser while the MoSe 2 flakes were excited by a continuous-wave Ti:Sapphire laser. The pulsed source was an optical parametric amplifier (pumped by a Ti:Sapphire laser) tunable from 1.77-2.48 eV (700-500 nm) at a 250-kHz repetition rate with a double-pass grating (500 g/mm) geometry to reduce the spectral bandwidth to < 5 meV (1 nm). The photoluminescence emission was collected, passed though a polarization analyzer, and dispersed by a single monochromator equipped with a multichannel charge coupled device (CCD) detector.