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

^{1}

^{2}

^{3}

^{*}

## 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.

## References

- Xu, X.; Yao, W.; Xiao, D.; Heinz, T.F. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys.
**2014**, 10, 343–350. [Google Scholar] [CrossRef] - Xia, F.; Wang, H.; Xiao, D.; Dubey, M.; Ramasubramaniam, A. Two-dimensional material nanophotonics. Nat. Photonics
**2014**, 8, 899–907. [Google Scholar] [CrossRef][Green Version] - Eda, G.; Maier, S.A. Two-Dimensional Crystals: Managing Light for Optoelectronics. ACS Nano
**2013**, 7, 5660–5665. [Google Scholar] [CrossRef] - Wang, Q.H.; Kalantar-Zadeh, K.; Kis, A.; Coleman, J.; Strano, M.S. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat. Nanotechnol.
**2012**, 7, 699–712. [Google Scholar] [CrossRef] - Molas, M.R.; Slobodeniuk, A.O.; Kazimierczuk, T.; Nogajewski, K.; Bartos, M.; Kapuściński, P.; Oreszczuk, K.; Watanabe, K.; Taniguchi, T.; Faugeras, C.; et al. Probing and Manipulating Valley Coherence of Dark Excitons in Monolayer WSe
_{2}. Phys. Rev. Lett.**2019**, 123, 096803. [Google Scholar] [CrossRef][Green Version] - Bussolotti, F.; Kawai, H.; Ooi, Z.E.; Chellappan, V.; Thian, D.; Pang, A.L.C.; Goh, K.E.J. Roadmap on finding chiral valleys: Screening 2D materials for valleytronics. Nano Futur.
**2018**, 2, 032001. [Google Scholar] [CrossRef] - Xiao, D.; Liu, G.B.; Feng, W.; Xu, X.; Yao, W. Coupled Spin and Valley Physics in Monolayers of MoS
_{2}and Other Group-VI Dichalcogenides. Phys. Rev. Lett.**2012**, 108, 196802. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kormányos, A.; Burkard, G.; Gmitra, M.; Fabian, J.; Zólyomi, V.; Drummond, N.D.; Fal’ko, V. k·p theory for two-dimensional transition metal dichalcogenide semiconductors. 2D Mater.
**2015**, 2, 022001. [Google Scholar] [CrossRef] - Koperski, M.; Molas, M.R.; Arora, A.; Nogajewski, K.; Slobodeniuk, A.O.; Faugeras, C.; Potemski, M. Optical properties of atomically thin transition metal dichalcogenides: Observations and puzzles. Nanophotonics
**2017**, 6, 1289–1308. [Google Scholar] [CrossRef] - Wang, G.; Chernikov, A.; Glazov, M.M.; Heinz, T.F.; Marie, X.; Amand, T.; Urbaszek, B. Colloquium: Excitons in atomically thin transition metal dichalcogenides. Rev. Mod. Phys.
**2018**, 90, 021001. [Google Scholar] [CrossRef][Green Version] - Yao, W.; Xiao, D.; Niu, Q. Valley-dependent optoelectronics from inversion symmetry breaking. Phys. Rev. B
**2008**, 77, 235406. [Google Scholar] [CrossRef][Green Version] - Chernikov, A.; Berkelbach, T.C.; Hill, H.M.; Rigosi, A.; Li, Y.; Aslan, B.; Reichman, D.R.; Hybertsen, M.S.; Heinz, T.F. Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer WS
_{2}. Phys. Rev. Lett.**2014**, 113, 076802. [Google Scholar] [CrossRef] [PubMed][Green Version] - Molas, M.R.; Slobodeniuk, A.O.; Nogajewski, K.; Bartos, M.; Bala, L.; Babiński, A.; Watanabe, K.; Taniguchi, T.; Faugeras, C.; Potemski, M. Energy Spectrum of Two-Dimensional Excitons in a Nonuniform Dielectric Medium. Phys. Rev. Lett.
**2019**, 123, 136801. [Google Scholar] [CrossRef][Green Version] - Berkelbach, T.C.; Hybertsen, M.S.; Reichman, D.R. Theory of neutral and charged excitons in monolayer transition metal dichalcogenides. Phys. Rev. B
**2013**, 88, 045318. [Google Scholar] [CrossRef][Green Version] - Jones, A.M.; Yu, H.J.; Ghimire, N.J.; Wu, S.; Aivazian, G.; Ross, J.S.; Zhao, B.; Yan, J.; Mandrus, D.G.; Xiao, D.; et al. Optical generation of excitonic valley coherence in monolayer WSe
_{2}. Nat. Nanotechnol.**2013**, 8, 634–638. [Google Scholar] [CrossRef] - Mak, K.F.; He, K.; Shan, J.; Heinz, T. Control of valley polarization in monolayer MoS
_{2}by optical helicity. Nat. Nanotechol.**2012**, 7, 494–498. [Google Scholar] [CrossRef] [PubMed] - Zeng, H.; Dai, J.; Yao, W.; Xiao, D.; Cui, X. Valley polarization in MoS
_{2}monolayers by optical pumping. Nat. Nanotechol.**2012**, 7, 490–493. [Google Scholar] [CrossRef] [PubMed] - Glazov, M.M.; Amand, T.; Marie, X.; Lagarde, D.; Bouet, L.; Urbaszek, B. Exciton fine structure and spin decoherence in monolayers of transition metal dichalcogenides. Phys. Rev. B
**2014**, 89, 201302. [Google Scholar] [CrossRef][Green Version] - Hao, K.; Moody, G.; Wu, F.; Dass, C.K.; Xu, L.; Chen, C.H.; Sun, L.; Li, M.Y.; Li, L.J.; MacDonald, A.H.; et al. Direct measurement of exciton valley coherence in monolayer WSe
_{2}. Nat. Phys.**2016**, 12, 677–682. [Google Scholar] [CrossRef][Green Version] - Robert, C.; Lagarde, D.; Cadiz, F.; Wang, G.; Lassagne, B.; Amand, T.; Balocchi, A.; Renucci, P.; Tongay, S.; Urbaszek, B.; et al. Exciton radiative lifetime in transition metal dichalcogenide monolayers. Phys. Rev. B
**2016**, 93, 205423. [Google Scholar] [CrossRef][Green Version] - Moody, G.; Dass, C.K.; Hao, K.; Chen, C.H.; Li, L.J.; Singh, A.; Tran, K.; Clark, G.; Xu, X.; Berghäuser, G.; et al. Intrinsic homogeneous linewidth and broadening mechanisms of excitons in monolayer transition metal dichalcogenides. Nat. Commun.
**2015**, 6, 8315. [Google Scholar] [CrossRef] [PubMed][Green Version] - Palummo, M.; Bernardi, M.; Grossman, J.C. Exciton Radiative Lifetimes in Two-Dimensional Transition Metal Dichalcogenides. Nano Lett.
**2015**, 15, 2794–2800. [Google Scholar] [CrossRef] [PubMed][Green Version] - Poellmann, C.; Steinleitner, P.; Leierseder, U.; Nagler, P.; Plechinger, G.; Porer, M.; Bratschitsch, R.; Schüller, C.; Korn, T.; Huber, R. Resonant internal quantum transitions and femtosecond radiative decay of excitons in monolayer WSe
_{2}. Nat. Mater.**2015**, 14, 889–893. [Google Scholar] [CrossRef] [PubMed] - Jakubczyk, T.; Delmonte, V.; Koperski, M.; Nogajewski, K.; Faugeras, C.; Langbein, W.; Potemski, M.; Kasprzak, J. Radiatively Limited Dephasing and Exciton Dynamics in MoSe
_{2}Monolayers Revealed with Four-Wave Mixing Microscopy. Nano Lett.**2016**, 16, 5333–5339. [Google Scholar] [CrossRef][Green Version] - Yan, T.; Ye, J.; Qiao, X.; Tan, P.; Zhang, X. Exciton valley dynamics in monolayer WSe
_{2}probed by the two-color ultrafast Kerr rotation. Phys. Chem. Chem. Phys.**2017**, 19, 3176–3181. [Google Scholar] [CrossRef] [PubMed][Green Version] - Miyauchi, Y.; Konabe, S.; Wang, F.; Zhang, W.; Hwang, A.; Hasegawa, Y.; Zhou, L.; Mouri, S.; Toh, M.; Eda, G.; et al. Evidence for line width and carrier screening effects on excitonic valley relaxation in 2D semiconductors. Nat. Commun.
**2018**, 9, 2598. [Google Scholar] [CrossRef] [PubMed][Green Version] - Castellanos-Gomez, A.; Buscema, M.; Molenaar, R.; Singh, V.; Janssen, L.; van der Zant, H.S.J.; Steele, G.A. Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping. 2D Mater.
**2014**, 1, 011002. [Google Scholar] [CrossRef] - Budania, P.; Baine, P.T.; Montgomery, J.H.; McNeill, D.W.; Neil Mitchell, S.; Modreanu, M.; Hurley, P.K. Comparison between Scotch tape and gel-assisted mechanical exfoliation techniques for preparation of 2D transition metal dichalcogenide flakes. Micro Nano Lett.
**2017**, 12, 970–973. [Google Scholar] [CrossRef] - Slobodeniuk, A.O.; Koutenský, P.; Bartoš, M.; Trojánek, F.; Malý, P.; Novotný, T.; Kozák, M. Semiconductor Bloch equation analysis of optical Stark and Bloch-Siegert shifts in monolayer WSe
_{2}and MoS_{2}. Phys. Rev. B**2022**, 106, 235304. [Google Scholar] [CrossRef] - Vaquero, D.; Salvador-Sánchez, J.; Clericò, V.; Diez, E.; Quereda, J. The Low-Temperature Photocurrent Spectrum of Monolayer MoSe
_{2}: Excitonic Features and Gate Voltage Dependence. Nanomaterials**2022**, 12, 322. [Google Scholar] [CrossRef] - Niu, Y.; Gonzalez-Abad, S.; Frisenda, R.; Marauhn, P.; Drüppel, M.; Gant, P.; Schmidt, R.; Taghavi, N.S.; Barcons, D.; Molina-Mendoza, A.J.; et al. Thickness-Dependent Differential Reflectance Spectra of Monolayer and Few-Layer MoS
_{2}, MoSe_{2}, WS_{2}and WSe_{2}. Nanomaterials**2018**, 8, 725. [Google Scholar] [CrossRef] [PubMed][Green Version] - Tonndorf, P.; Schmidt, R.; Böttger, P.; Zhang, X.; Börner, J.; Liebig, A.; Albrecht, M.; Kloc, C.; Gordan, O.; Zahn, D.R.T.; et al. Photoluminescence emission and Raman response of monolayer MoS
_{2}, MoSe_{2}, and WSe_{2}. Opt. Express**2013**, 21, 4908–4916. [Google Scholar] [CrossRef] - McIntyre, J.; Aspnes, D. Differential reflection spectroscopy of very thin surface films. Surf. Sci.
**1971**, 24, 417–434. [Google Scholar] [CrossRef] - Trovatello, C.; Katsch, F.; Borys, N.J.; Selig, M.; Yao, K.; Borrego-Varillas, R.; Scotognella, F.; Kriegel, I.; Yan, A.; Zettl, A.; et al. The ultrafast onset of exciton formation in 2D semiconductors. Nat. Commun.
**2020**, 11, 5277. [Google Scholar] [CrossRef] - Steinleitner, P.; Merkl, P.; Nagler, P.; Mornhinweg, J.; Schüller, C.; Korn, T.; Chernikov, A.; Huber, R. Direct Observation of Ultrafast Exciton Formation in a Monolayer of WSe
_{2}. Nano Lett.**2017**, 17, 1455–1460. [Google Scholar] [CrossRef] [PubMed][Green Version] - Yadav, D.; Trushin, M.; Pauly, F. Thermalization of photoexcited carriers in two-dimensional transition metal dichalcogenides and internal quantum efficiency of van der Waals heterostructures. Phys. Rev. Res.
**2020**, 2, 043051. [Google Scholar] [CrossRef] - Katsch, F.; Selig, M.; Knorr, A. Exciton-Scattering-Induced Dephasing in Two-Dimensional Semiconductors. Phys. Rev. Lett.
**2020**, 124, 257402. [Google Scholar] [CrossRef] - Katsch, F.; Selig, M.; Knorr, A. Theory of coherent pump–probe spectroscopy in monolayer transition metal dichalcogenides. 2D Mater.
**2019**, 7, 015021. [Google Scholar] [CrossRef] - Glazov, M.M.; Ivchenko, E.L.; Wang, G.; Amand, T.; Marie, X.; Urbaszek, B.; Liu, B.L. Spin and valley dynamics of excitons in transition metal dichalcogenide monolayers. Phys. Status Solidi (B)
**2015**, 252, 2349–2362. [Google Scholar] [CrossRef][Green Version] - Danovich, M.; Zólyomi, V.; Fal’ko, V.I.; Aleiner, I.L. Auger recombination of dark excitons in WS
_{2}and WSe_{2}monolayers. 2D Mater.**2016**, 3, 035011. [Google Scholar] [CrossRef] - Siday, T.; Sandner, F.; Brem, S.; Zizlsperger, M.; Perea-Causin, R.; Schiegl, F.; Nerreter, S.; Plankl, M.; Merkl, P.; Mooshammer, F.; et al. Ultrafast Nanoscopy of High-Density Exciton Phases in WSe
_{2}. Nano Lett.**2022**, 22, 2561–2568. [Google Scholar] [CrossRef] [PubMed] - Kim, J.; Hong, X.; Jin, C.; Shi, S.F.; Chang, C.Y.S.; Chiu, M.H.; Li, L.J.; Wang, F. Ultrafast generation of pseudo-magnetic field for valley excitons in WSe
_{2}monolayers. Science**2014**, 346, 1205–1208. [Google Scholar] [CrossRef] [PubMed][Green Version] - Sie, E.J.; McIver, J.W.; Lee, Y.H.; Fu, L.; Kong, J.; Gedik, N. Valley-selective optical Stark effect in monolayer WS
_{2}. Nat. Mater.**2015**, 14, 290–294. [Google Scholar] [CrossRef] [PubMed][Green Version] - Cunningham, P.D.; Hanbicki, A.T.; Reinecke, T.L.; McCreary, K.M.; Jonker, B.T. Resonant optical Stark effect in monolayer WS
_{2}. Nat. Commun.**2019**, 10, 5539. [Google Scholar] [CrossRef][Green Version] - Autler, S.H.; Townes, C.H. Stark Effect in Rapidly Varying Fields. Phys. Rev.
**1955**, 100, 703–722. [Google Scholar] [CrossRef] - Kuklinski, J.R.; Mukamel, S. Real versus virtual excitonic Stark effect in semiconductor quantum wells. Phys. Rev. B
**1990**, 42, 11938–11941. [Google Scholar] [CrossRef] [PubMed] - Maialle, M.Z.; de Andrada e Silva, E.A.; Sham, L.J. Exciton spin dynamics in quantum wells. Phys. Rev. B
**1993**, 47, 15776–15788. [Google Scholar] [CrossRef] [PubMed] - Vaquero, D.; Clericò, V.; Salvador-Sánchez, J.; Díaz, E.; Domínguez-Adame, F.; Chico, L.; Meziani, Y.M.; Diez, E.; Quereda, J. Fast response photogating in monolayer MoS
_{2}phototransistors. Nanoscale**2021**, 13, 16156–16163. [Google Scholar] [CrossRef] [PubMed] - Rybkovskiy, D.V.; Gerber, I.C.; Durnev, M.V. Atomically inspired k·p approach and valley Zeeman effect in transition metal dichalcogenide monolayers. Phys. Rev. B
**2017**, 95, 155406. [Google Scholar] [CrossRef][Green Version] - Slobodeniuk, A.O.; Basko, D.M. Spin–flip processes and radiative decay of dark intravalley excitons in transition metal dichalcogenide monolayers. 2D Mater.
**2016**, 3, 035009. [Google Scholar] [CrossRef][Green Version] - Slobodeniuk, A.O.; Basko, D.M. Exciton-phonon relaxation bottleneck and radiative decay of thermal exciton reservoir in two-dimensional materials. Phys. Rev. B
**2016**, 94, 205423. [Google Scholar] [CrossRef][Green Version] - Koirala, S.; Mouri, S.; Miyauchi, Y.; Matsuda, K. Homogeneous linewidth broadening and exciton dephasing mechanism in MoTe
_{2}. Phys. Rev. B**2016**, 93, 075411. [Google Scholar] [CrossRef][Green Version] - Dey, P.; Paul, J.; Wang, Z.; Stevens, C.E.; Liu, C.; Romero, A.H.; Shan, J.; Hilton, D.J.; Karaiskaj, D. Optical Coherence in Atomic-Monolayer Transition-Metal Dichalcogenides Limited by Electron-Phonon Interactions. Phys. Rev. Lett.
**2016**, 116, 127402. [Google Scholar] [CrossRef] [PubMed][Green Version] - Selig, M.; Berghäuser, G.; Raja, A.; Nagler, P.; Schüller, C.; Heinz, T.F.; Korn, T.; Chernikov, A.; Malic, E.; Knorr, A. Excitonic linewidth and coherence lifetime in monolayer transition metal dichalcogenides. Nat. Commun.
**2016**, 7, 13279. [Google Scholar] [CrossRef] [PubMed][Green Version] - Schmidt, R.; Berghäuser, G.; Schneider, R.; Selig, M.; Tonndorf, P.; Malić, E.; Knorr, A.; Michaelis de Vasconcellos, S.; Bratschitsch, R. Ultrafast Coulomb-Induced Intervalley Coupling in Atomically Thin WS
_{2}. Nano Lett.**2016**, 16, 2945–2950. [Google Scholar] [CrossRef]

**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.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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