Multipath Optical Recombination of Intervalley Dark Excitons and Trions in Monolayer ${\mathrm{WSe}}_{2}$

Multipath Optical Recombination of Intervalley Dark Excitons and Trions in Monolayer ${WSe}_{2}$

Erfu Liu, Jeremiah van Baren, Ching-Tarng Liang, Takashi Taniguchi, Kenji Watanabe, Nathaniel M. Gabor, Yia-Chung Chang, and Chun Hung Lui

Phys. Rev. Lett. 124, 196802 – Published 14 May 2020

Abstract

Excitons and trions (or exciton polarons) in transition metal dichalcogenides (TMDs) are known to decay predominantly through intravalley transitions. Electron-hole recombination across different valleys can also play a significant role in the excitonic dynamics, but intervalley transitions are rarely observed in monolayer TMDs, because they violate the conservation of momentum. Here we reveal the intervalley recombination of dark excitons and trions through more than one path in monolayer ${WSe}_{2}$ . We observe the intervalley dark excitons, which can recombine by the assistance of defect scattering or chiral-phonon emission. We also reveal that a trion can decay in two distinct paths—through intravalley or intervalley electron-hole recombination—into two different final valley states. Although these two paths are energy degenerate, we can distinguish them by lifting the valley degeneracy under a magnetic field. In addition, the intra- and inter-valley trion transitions are coupled to zone-center and zone-corner chiral phonons, respectively, to produce distinct phonon replicas. The observed multipath optical decays of dark excitons and trions provide insight into the internal quantum structure of trions and the complex excitonic interactions with defects and chiral phonons in monolayer valley semiconductors.

Received 24 September 2019
Accepted 24 March 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.196802

Physics Subject Headings (PhySH)

Excitons Phonons Trions Valleytronics

Transition metal dichalcogenides Two-dimensional electron gas

First-principles calculations Photoluminescence

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Erfu Liu ¹, Jeremiah van Baren¹, Ching-Tarng Liang², Takashi Taniguchi³, Kenji Watanabe⁴, Nathaniel M. Gabor^1,5, Yia-Chung Chang², and Chun Hung Lui ^1,*

¹Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
²Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan
³International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science (NIMS), 1-1 Namiki Tsukuba, Ibaraki 305-0044, Japan
⁴National Institute for Materials Science (NIMS), 1-1 Namiki Tsukuba, Ibaraki 305-0044, Japan
⁵Canadian Institute for Advanced Research, MaRS Centre West Tower, 661 University Avenue, Toronto, Ontario ON M5G 1M1, Canada

^*Corresponding author. joshua.lui@ucr.edu

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Vol. 124, Iss. 19 — 15 May 2020

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Figure 1
Intervalley electron-hole recombination processes in monolayer ${WSe}_{2}$ . (a) Band configurations for the intravalley bright exciton ( $A^{0}$ ), intravalley dark exciton ( $D^{0}$ ), and intervalley momentum-forbidden dark exciton ( $I^{0}$ ). The arrows and color denote the electron spin. (b) Recombination of $I^{0}$ mediated by defects or zone-corner chiral phonons. We denote the irreducible representations of the electronic states at the $K$ and $K^{'}$ points in the $C_{3 h}$ point group. (c),(d) Trion decay through emission of zone-center or zone-corner chiral phonons. $Γ_{5}$ ( $K_{3}$ ) is the representation of chiral phonons at the $Γ$ ( $K^{'}$ ) point in the $D_{3 h}$ ( $C_{3 h}$ ) point group. $Ω^{\pm}$ and $σ^{\pm}$ denote the chirality of the emitted phonons and photons, respectively.
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Figure 2
Gate-dependent PL of monolayer ${WSe}_{2}$ . (a) PL map at $T \sim 4 K$ and zero magnetic field under 532-nm continuous laser excitation with incident laser power $P \sim 10 μ W$ . We denote the bright exciton and trions ( $A^{0}$ , $A^{+}$ , $A_{1}^{-}$ , and $A_{2}^{-}$ ), dark exciton and trions ( $D^{0}$ , $D^{+}$ , and $D^{-}$ ), intervalley dark exciton ( $I^{0}$ ), zone-center chiral-phonon replicas of dark states with $\sim 21 .4 meV$ redshift ( $D_{p}^{0}$ , $D_{p}^{+}$ , and $D_{p}^{-}$ ), and zone-corner chiral-phonon replicas of dark states with $\sim 26.5 meV$ redshift ( $I_{p}^{0}$ , $I_{p}^{+}$ , and $I_{p}^{-}$ ). (b) Cross-cut PL spectra on the electron side, charge-neutrality point, and the hole side with respective gate voltages $V_{g} = + 2$ , $- 0.2$ , and $- 2 V$ . (c)–(e) The PL energy, full width at half maximum (FWHM), and integrated PL intensity of different excitonic peaks as a function of the gate voltage. The numbers in (c) denote the energy separation in the units of meV.
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Figure 3
Magnetic-field-dependent and helicity-resolved PL in monolayer ${WSe}_{2}$ . (a),(b) PL maps at magnetic fields $B = 0 - 17 T$ on the electron side. (c),(d) Similar PL maps near the charge-neutrality point. (e),(f) Similar PL maps on the hole side. The top and bottom rows show PL with right- and left-handed helicity, respectively. The emission lines and their $g$ factors are denoted on the top.
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Figure 4
Splitting of intra- and inter-valley trion emission under a magnetic field. (a),(b) Schematic configurations and energy levels of different trion transitions. The application of a magnetic field splits the fourfold degenerate trion emission into four distinct emission lines, labeled as $I_{K}^{+}$ , $D_{K^{'}}^{+}$ , $D_{K}^{+}$ , and $I_{K^{'}}^{+}$ from high to low energy. Here $D$ and $I$ denote intra- and inter-valley transitions, respectively; the $K$ and $K^{'}$ subscripts denote the valley of the electron in the trion. (c) The left-handed PL map on the hole side of monolayer ${WSe}_{2}$ at $B = 15 T$ . The different transitions and energy separations are denoted. The gate-dependent oscillations of PL intensity come from Landau quantization [39, 71]. (d) Log-scale magnetic-field-dependent PL map of positive trions at $B = 0 - 17 T$ , $V_{g} = - 5 V$ . (e) Energy separation between the two split trion peaks in (d) as a function of the magnetic field. The line is a linear fit that gives an effective $g$ factor of $2.35 \pm 0.03$ .
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Physical Review Letters

Multipath Optical Recombination of Intervalley Dark Excitons and Trions in Monolayer WSe2

Erfu Liu, Jeremiah van Baren, Ching-Tarng Liang, Takashi Taniguchi, Kenji Watanabe, Nathaniel M. Gabor, Yia-Chung Chang, and Chun Hung Lui

Phys. Rev. Lett. 124, 196802 – Published 14 May 2020

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Multipath Optical Recombination of Intervalley Dark Excitons and Trions in Monolayer ${WSe}_{2}$