Ultrafast dynamics in monolayer transition metal dichalcogenides: Interplay of dark excitons, phonons, and intervalley exchange

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Ultrafast dynamics in monolayer transition metal dichalcogenides: Interplay of dark excitons, phonons, and intervalley exchange

Malte Selig, Florian Katsch, Robert Schmidt, Steffen Michaelis de Vasconcellos, Rudolf Bratschitsch, Ermin Malic, and Andreas Knorr

Phys. Rev. Research 1, 022007(R) – Published 26 September 2019

Abstract

Understanding the ultrafast coupling and relaxation mechanisms between valleys in transition metal dichalcogenide semiconductors is of crucial interest for future valleytronic devices. Recent ultrafast pump-probe experiments showed an unintuitive significant bleaching at the excitonic $B$ transition after optical excitation of the energetically lower excitonic $A$ transition. Here, we present a possible microscopic explanation for this surprising effect. It is based on the joint action of exchange coupling and phonon-mediated thermalization into dark exciton states and does not involve a population of the $B$ exciton. Our work demonstrates how intra- and intervalley coupling on a femtosecond timescale governs the optical valley response of 2D semiconductors.

Received 20 March 2019
Revised 27 August 2019

DOI:https://doi.org/10.1103/PhysRevResearch.1.022007

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Composite bosons Excitons Optoelectronics Phonons Spin dynamics Valleytronics

2-dimensional systems Honeycomb lattice Monolayer films Semiconductors Transition metal dichalcogenides

Bloch wave theory Classical electromagnetism Density matrix methods Electron-correlation calculations Second quantization

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Malte Selig ¹, Florian Katsch¹, Robert Schmidt², Steffen Michaelis de Vasconcellos², Rudolf Bratschitsch², Ermin Malic³, and Andreas Knorr¹

¹Nichtlineare Optik und Quantenelektronik, Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
²Institute of Physics and Center for Nanotechnology, University of Münster, 48149 Münster, Germany
³Chalmers University of Technology, Department of Physics, SE-412 96 Gothenburg, Sweden

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Vol. 1, Iss. 2 — September 2019

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Images

Figure 1
Schematic illustration of the optical selection rules in ${MoSe}_{2}$ . A pronounced spin-orbit coupling lifts the degeneracy of the electronic bands where the energetic ordering of the different spin bands (blue, red) is reversed between the $K$ and $K^{'}$ points [9, 24]. The spin splitting of the conduction band is on the order of few tens of meV and the splitting of the valence band is on the order of few hundreds of meV. This results in two distinct optical transitions at the $K$ ( $K^{'}$ ) point where the energetically lower (higher) is called the $A$ ( $B$ ) transition [9].
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Figure 2
Schematic illustration of the intervalley exchange in ${MoSe}_{2}$ [(a)–(d)] and the pump-probe experiment [(e)–(f)]. (a) Excitation resonantly to the $A$ transition with left handed polarized light $σ^{+}$ . (b) Exciton phonon scattering mediates the thermalization of excitons: exciton densities in $(K ↑, K ↑)$ states with nonvanishing center of mass momenta are created. (c) Excitons in $(K ↑, K ↑)$ and $(K^{'} ↓, K^{'} ↓)$ states are coupled through intervalley exchange coupling. (d) Exciton phonon scattering between excitonic $↓$ states occurs, which also leads to the population of $(K^{'} ↓, K ↓)$ states. (e) Exemplary for the bleaching of the $B$ transition with $σ^{+}$ probe pulse, we find contributions from electron of the $(K^{'} ↓, K ↓)$ exciton. (f) For the bleaching of the $A$ transition with $σ^{+}$ probe pulse, we find contributions from electron and hole of the $(K ↑, K ↑)$ exciton and from the hole of the $(K ↑, K^{'} ↑)$ exciton.
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Figure 3
Bleaching of the pump-probe signal at 77 K in ${MoSe}_{2}$ . Contributions from exciton states with spin $↑$ are denoted in blue, spin $↓$ contributions are denoted in red, as in Fig. 2. In the upper panel, we illustrate the excitons leading to the bleaching of the excitonic transition, which is depicted in the lower panel. Contributions from intravalley excitons are illustrated with solid lines, contributions from intervalley excitons are denoted with dashed lines. [(a) and (b)] Pump-probe signal at the $B$ transition, compare Eq. (2), in the pumped (a) and unpumped (b) valley after excitation of the $A$ transition. [(c) and (d)] Pump-probe signal at the $A$ transition, compare equation (1), in the pumped (c) and unpumped (d) valleys after excitation of the $A$ transition. Additionally, we depict the additional bleaching contribution of the optically injected coherence ${| P |}^{2}$ . The pump pulse with a HWHM of 20 fs centered at $t = 0$ ps is depicted in figure (c) in pink.
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Figure 4
Extracted density rise times in ${MoSe}_{2}$ . (a) shows the rise time of the direct exciton densities as a function of temperature and (b) shows the indirect exciton densities.
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