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Ultrafast Dynamics of Valley-Polarized Excitons in WSe_{2} Monolayer Studied by Few-Cycle Laser Pulses

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

2D | Two-dimensional |

TMDs | Transition metal dichalcogenide monolayers |

FWHM | Full width at half maximum |

## Appendix A. Photoluminescence Characterization of the WSe_{2} Monolayer Used in the Experiments

## Appendix B. Verification of the Valley Selective Transient Reflectivity for Opposite Combinations of Circular Polarizations

**Figure A2.**(

**a**) Change of transient reflectivity of the sample integrated form the regions of spectra of interest for co-rotating circular polarizations of the pulses ${\sigma}_{\mathrm{pump}}^{+}/{\sigma}_{\mathrm{probe}}^{+}$ and ${\sigma}_{\mathrm{pump}}^{-}/{\sigma}_{\mathrm{probe}}^{-}$. The blue dotted curve shows the measurement response function obtained as cross-correlation of pump and probe pulses in a thin BBO crystal. (

**b**) Change of transient reflectivity of the sample integrated from the regions of spectra of interest for counter-rotating circular polarizations of the pulses ${\sigma}_{\mathrm{pump}}^{+}/{\sigma}_{\mathrm{probe}}^{-}$ and ${\sigma}_{\mathrm{pump}}^{-}/{\sigma}_{\mathrm{probe}}^{+}$. All curves are measured with the pump fluence of 42.88 $\mathsf{\mu}$J/cm${}^{2}$.

## Appendix C. Band Structure of the Monolayer WSe_{2}

**Figure A3.**Band structure of WSe${}_{2}$ monolayer. Green and orange solid curves represent spin-up and spin-down bands in the K${}^{\pm}$ valleys, respectively. Double-headed wavy arrows represent such spin-allowed optical transitions in each valley. The blue/red arrows indicate the lower-energy (A-exciton) transitions realized in the experiment. The grey arrows represent the B-exciton transitions, which, however, are not activated by the pump pulse used in the experiment. The blue/red color of the corresponding arrows indicates the left/right circular polarization of light, which couples electromagnetically with the corresponding bands.

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**Figure 1.**Detailed layout of the experimental setup. Laser—Ti:sapphire laser oscillator Rainbow (Femtolasers/Spectra Physics), $\lambda $/4—achromatic quarter-wave plate, PER—periscope, CM—chirped mirrors, GW—glass wedges, ND—neutral densit filter, DCP—dispersion compensating plate, DL—delay line, PM—parabolic mirror.

**Figure 2.**(

**a**) Evolution of transient reflectivity for ${\sigma}_{\mathrm{pump}}^{+}/{\sigma}_{\mathrm{probe}}^{+}$ combination of circular polarizations of pulses (upper panel) compared to an opposite combination of polarizations ${\sigma}_{\mathrm{pump}}^{+}/{\sigma}_{\mathrm{probe}}^{-}$ (lower panel). Both measurements are performed with the pump fluence of 65 $\mathsf{\mu}$J/cm${}^{2}$. (

**b**) Time evolution of the transient reflectivity spectrally integrated over the exciton resonance (region marked by dashed lines in (

**a**)).

**Figure 3.**Valley polarization dynamics of 1sA excitons in WSe${}_{2}$ monolayer. The data are obtained by subtracting the transient reflectivity dynamics of the exciton line for counter-rotating polarizations of pump and probe pulses (red curve shown in Figure 2b) from the dynamics measured with co-rotating polarizations (black curve in Figure 2b). The data are spectrally integrated in the photon energy region 1.61–1.67 eV. The dashed curves correspond to double-exponential fitting functions.

**Figure 4.**(

**a**) Decay times ${\tau}_{1}$ and ${\tau}_{2}$ from the double exponential fits of the valley polarization dynamics shown as dashed curves in Figure 3. (

**b**) The maxima of the transient reflectivity signal as a function of the pump fluence for both combinations of circular polarizations of pump and probe pulses. Curves correspond to fits according to the phenomenological description of absorption saturation (see text for details).

**Figure 5.**(

**a**) Ultrafast dynamics of transient reflectivity of WSe${}_{2}$ monolayer measured with linearly polarized pump and probe pulses with crossed polarizations. (

**b**) Transient reflectivity spectra in different time delays between the pump and probe pulses.

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**MDPI and ACS Style**

Koutenský, P.; Slobodeniuk, A.; Bartoš, M.; Trojánek, F.; Malý, P.; Kozák, M.
Ultrafast Dynamics of Valley-Polarized Excitons in WSe_{2} Monolayer Studied by Few-Cycle Laser Pulses. *Nanomaterials* **2023**, *13*, 1207.
https://doi.org/10.3390/nano13071207

**AMA Style**

Koutenský P, Slobodeniuk A, Bartoš M, Trojánek F, Malý P, Kozák M.
Ultrafast Dynamics of Valley-Polarized Excitons in WSe_{2} Monolayer Studied by Few-Cycle Laser Pulses. *Nanomaterials*. 2023; 13(7):1207.
https://doi.org/10.3390/nano13071207

**Chicago/Turabian Style**

Koutenský, Petr, Artur Slobodeniuk, Miroslav Bartoš, František Trojánek, Petr Malý, and Martin Kozák.
2023. "Ultrafast Dynamics of Valley-Polarized Excitons in WSe_{2} Monolayer Studied by Few-Cycle Laser Pulses" *Nanomaterials* 13, no. 7: 1207.
https://doi.org/10.3390/nano13071207