Phonon-Assisted Intervalley Scattering Determines Ultrafast Exciton Dynamics in ${\mathrm{MoSe}}_{2}$ Bilayers

Phonon-Assisted Intervalley Scattering Determines Ultrafast Exciton Dynamics in ${MoSe}_{2}$ Bilayers

Sophia Helmrich, Kevin Sampson, Di Huang, Malte Selig, Kai Hao, Kha Tran, Alexander Achstein, Carter Young, Andreas Knorr, Ermin Malic, Ulrike Woggon, Nina Owschimikow, and Xiaoqin Li

Phys. Rev. Lett. 127, 157403 – Published 8 October 2021

Abstract

While valleys (energy extrema) are present in all band structures of solids, their preeminent role in determining exciton resonances and dynamics in atomically thin transition metal dichalcogenides (TMDC) is unique. Using two-dimensional coherent electronic spectroscopy, we find that exciton decoherence occurs on a much faster timescale in ${MoSe}_{2}$ bilayers than that in the monolayers. We further identify two population relaxation channels in the bilayer, a coherent and an incoherent one. Our microscopic model reveals that phonon-emission processes facilitate scattering events from the $K$ valley to other lower-energy $Γ$ and $Λ$ valleys in the bilayer. Our combined experimental and theoretical studies unequivocally establish different microscopic mechanisms that determine exciton quantum dynamics in TMDC monolayers and bilayers. Understanding exciton quantum dynamics provides critical guidance to the manipulation of spin-valley degrees of freedom in TMDC bilayers.

Received 19 September 2020
Revised 23 April 2021
Accepted 23 August 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.157403

Physics Subject Headings (PhySH)

Excitons Phonons Quantum coherence & coherence measures

Quantum wells Semiconductor compounds Transition metal dichalcogenides

Femtosecond laser spectroscopy Four-wave mixing Photoluminescence

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Sophia Helmrich¹, Kevin Sampson^2,3, Di Huang ², Malte Selig ⁴, Kai Hao², Kha Tran², Alexander Achstein¹, Carter Young ², Andreas Knorr⁴, Ermin Malic⁵, Ulrike Woggon ¹, Nina Owschimikow^1,*, and Xiaoqin Li ^2,3,†

¹Department of Optics and Atomic Physics, Technical University Berlin, Berlin 10623, Germany
²Department of Physics and Center for Complex Quantum Systems, The University of Texas at Austin, Austin, Texas 78712, USA
³Center for Dynamics and Control of Materials and Texas Materials Institute, 2501 Speedway, Austin, Texas 78712, USA
⁴Nichtlineare Optik und Quantenelektronik, Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
⁵Department of Physics, Philipps University Marburg, 35037 Marburg, Germany

^*nina.owschimikow@physik.tu-berlin.de
^†elaineli@physics.utexas.edu

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Vol. 127, Iss. 15 — 8 October 2021

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Figure 1
(a) Single-particle band structures of ${MoSe}_{2}$ ML (red dashed lines) and BL (blue solid lines) with spin-orbit coupling, showing the two highest valence and the lowest conduction bands adapted from Roldan et al. [21]. Details of the band evolution from ML to BL at the $K$ , $Λ$ , and $Γ$ points are shown in the blue, orange, and purple rectangles at right. (b) Reflectance spectra for ${MoSe}_{2}$ ML (red) and BL (blue) at 30 K. (c) Schematic of the 2DCES experiment in a box geometry.
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Figure 2
One-quantum rephasing spectra from ${MoSe}_{2}$ ML and BL. (a) Schematic showing the one-quantum rephasing pulse sequence. (b),(d) Amplitude spectra of a ${MoSe}_{2}$ ML (BL) at $1 \times 10^{12} {cm}^{- 2}$ excitation density and 30 K. The exciton and trion resonances are indicated by $X^{0}$ and $X^{T}$ in the ML. The cross-diagonal linewidth (homogenous linewidth) is extracted at the $X^{0}$ peak indicated by the dotted line. (c),(e) The extracted homogeneous linewidths are fitted with Lorentzian functions for ML and BL ${MoSe}_{2}$ , respectively. Here, $ω_{t^{'}} = ω_{t_{1}} + ω_{t_{3}}$ .
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Figure 3
Exciton dephasing as a function of temperature. (a),(c) Illustration of valley scattering processes influencing exciton dephasing in ${MoSe}_{2}$ (a) MLs and (c) BLs. The horizontal axis $Q$ stands for center-of-mass momentum, and vertical axis represents exciton energy. (b),(d) Calculated dephasing channels for ML (b) and BL (d), respectively. Linewidth broadening due to contributions from radiative decoherence, exciton intravalley scattering ( $K - K$ ), and intervalley scattering to $K - K^{'}$ , $K - Λ$ , $K - Λ^{'}$ , and $Γ - K$ are accumulated in each curve stacked vertically. Experimental homogeneous linewidths (extrapolated to zero-excitation density) are shown as tangerine (ML) and blue (BL) points.
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Figure 4
Zero-quantum spectra from a ${MoSe}_{2}$ BL used to extract population relaxation times. (a) Schematic showing the zero-quantum pulse sequence. (b) Zero-quantum spectrum of a ${MoSe}_{2}$ BL at $1 \times 10^{12} {cm}^{- 2}$ excitation density and 30 K. The vertical line cut at the peak of the $X^{0}$ resonance captures population relaxation dynamics. (c) Fitting the zero-quantum line cut with two Lorentzian functions reveals fast $54 \pm 2 fs$ and slow $810 \pm 10 fs$ decay components. (d) Calculated relaxation dynamics with two dominant components in the frequency domain in excellent agreement with experiment. (e) Theoretical calculation of time-domain population dynamics in the $K$ valley after excitation of $K - K$ excitons. In (c)–(e), the totals are offset from the components for clarity.
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Physical Review Letters

Phonon-Assisted Intervalley Scattering Determines Ultrafast Exciton Dynamics in MoSe2 Bilayers

Sophia Helmrich, Kevin Sampson, Di Huang, Malte Selig, Kai Hao, Kha Tran, Alexander Achstein, Carter Young, Andreas Knorr, Ermin Malic, Ulrike Woggon, Nina Owschimikow, and Xiaoqin Li

Phys. Rev. Lett. 127, 157403 – Published 8 October 2021

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Phonon-Assisted Intervalley Scattering Determines Ultrafast Exciton Dynamics in ${MoSe}_{2}$ Bilayers