Tuning the Fröhlich exciton-phonon scattering in monolayer MoS2

Charge carriers in semiconducting transition metal dichalcogenides possess a valley degree of freedom that allows for optoelectronic applications based on the momentum of excitons. At elevated temperatures, scattering by phonons limits valley polarization, making a detailed knowledge about strength and nature of the interaction of excitons with phonons essential. In this work, we directly access exciton-phonon coupling in charge tunable single layer MoS2 devices by polarization resolved Raman spectroscopy. We observe a strong defect mediated coupling between the long-range oscillating electric field induced by the longitudinal optical phonon in the dipolar medium and the exciton. This so-called Fröhlich exciton phonon interaction is suppressed by doping. The suppression correlates with a distinct increase of the degree of valley polarization up to 20% even at elevated temperatures of 220 K. Our result demonstrates a promising strategy to increase the degree of valley polarization towards room temperature valleytronic applications.

(a) shows a scheme of a field effect device we use for Raman and PL spectroscopy in dependence of the free electron density. We use a PDMS stamping technique [1] to transfer monolayer MoS 2 flakes onto silicon substrates with a 300 nm thick SiO 2 layer as dielectric. for an applied gate voltage of V TG = 1 V in a PE field effect device [3]. Further, the authors demonstrated that the energy of the A 1 phonon mode is sensitive to the electron density and they correlated the energy shift of the A 1 mode to a change of the electron density. As a determination of the absolute charge carrier density in the MoS 2 flake is beyond the scope of our devices, we use ref. 3 to estimate the change of the charge carrier density from the energy shift of the A 1 mode measured by Raman spectroscopy. Supplementary Figure 1(c) shows non-resonant Raman spectra in the circular co-polarized configuration for two gate voltages V TG = −0.5 V (corresponding to n 0 of sample A with PE gate) and V TG = 0 V (corresponding to n ++ of sample A with PE gate). Lorentzian fits to the data reveal energies of 405.5 cm −1 and 403.3 cm −1 for the A 1 mode, respectively. The shift of 2.2 cm −1 corresponds to a change of the electron density of ∼ 10 13 cm −2 according to ref. [3]. For n 0 , we assume an electron density in the order of ∼ 10 11 cm −2 , what is supported by the comparison of our PL spectra to the spectra shown in ref. [4]. Overall, the estimation results in a ratio of n ++ /n 0 ∼ 100.
In order to avoid asymmetric electric fields in the MoS 2 flake, we simultaneously use the electrolyte top gate and the silicon back gate with a ratio of V BG /V TG = 80. We would like to note, however, that an asymmetric field does not affect the conclusions drawn in the manuscript [cf.
One peculiarity of the PE is its helical crystallization. Therefore, it can cause changes in the degree of circular polarization by turning circular polarized light into linear polarized light and by causing depolarization. For this reason, the measurements on the PE gate were conducted in the configuration shown in Fig S1(b), which makes it possible to monitor the degree of circular polarization during the measurements individually for each device since the change in the degree of circular polarization caused by the PE gate changes from sample to sample.

Supplementary Note 2: Matrix element of the Fröhlich exciton-phonon interaction
The Fröhlich exciton-phonon interaction for an exciton is derived by combining the electronphonon Fröhlich interaction of an electron and a hole [7,8]: (1) For the electron and hole masses we use m e = 0.46 and m h = 0.54 [9]. For the exciton radius a 0 we assume a 0 = 1 nm [10]. C F contains the frequency of the LO phonon ω LO , the volume V , the number of unit cells per unit volume N and the high and low frequency dielectric constants ε ∞ and ε 0 . For the plot shown in Fig. 3(a) of the manuscript we assume C F to be a constant and set it arbitrarily to 10 −4 .
Supplementary Figure 3 -Temperature dependence of Raman spectra of CVD grown MoS 2 . Circular co-polarized (σ + , σ + ) and cross-polarized (σ + , σ − ) Raman spectra of a CVD grown monolayer MoS 2 flake on a SiO 2 /Si substrate. Black lines represent measured spectra; filled curves are Lorentzian fits to the data. (a) Low temperature and non-resonant excitation, (b) low temperature and resonant excitation, (c) room temperature and non-resonant excitation and (d) room temperature and resonant excitation. The polarization dependence is qualitatively the same for both temperatures and it matches the data from exfoliated flakes for the case of low electron densities shown in the main part of the manuscript. We note that exfoliated MoS 2 monolayers can intrinsically be in the low or high electron density regime. This large variation in the intrinsic charge carrier density from sample to sample might explain conflicting reports in literature for pristine MoS 2 monolayers demonstrating the E phonon being cross-polarized [11] or co-polarized [12] under resonant excitation.   Fig. 1 of the manuscript]. The plots show the original data (black scatter) together with a multi-peak fit consisting of four Gaussian peaks that represent the PL of the neutral and charged A exciton (A 0 and A -), the B exciton and a defect peak. For increasing gate voltage from −2 V to 1 V we observe a bleaching of both the neutral and the charged exciton emission. The A 0 peak broadens from ≈ 45 meV to ≈ 70 meV and its energy slightly blue shifts by ≈ 4 meV ± 10 meV. The Apeak redshifts by 35 meV, corresponding to half of its full width at half maximum of ≈ 70 meV. The trends are consistent to existing literature for MoS 2 [4] and other TMDs [13]. The dashed line indicates the energy of light scattered by the E phonon and shows that the resonance condition for the light scattering is satisfied for all gate voltages. (b) Circular co-polarized Raman spectra corresponding to the spectra PL spectra shown in (a). Measured data is shown as black scatters. Solid lines are Lorentzian peaks fitted to the data. Grey lines are peaks of resonant Raman modes that are discussed in literature. In ciruclar co-polarized configuration the A 1 mode is a contribution due to the deformation potential, whereas we ascribe the E mode contribution [yellow line] to the Fröhlich interaction. For increasing gate voltages we observe decreasing intensities for both contributions, however the intensity of the E mode decreases faster than that of the A 1 mode [intensity ratio plotted in Supplementary Figure 9(c)]. . The data shows that the intensity of E CO decreases much faster than the intensity of A 1CO with increasing electron density. From the temperature dependence shown in (g) we can exclude that the gate dependence of the resonance condition is responsible for the faster suppression of the E mode. Therefore, we conclude that this effect is caused by screening of the Fröhlich scattering with increasing electron density.