Trion-phonon interaction in atomically thin semiconductors

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Trion-phonon interaction in atomically thin semiconductors

Raul Perea-Causin, Samuel Brem, and Ermin Malic

Phys. Rev. B 106, 115407 – Published 8 September 2022

Abstract

Optical and transport properties of doped monolayer semiconductors are dominated by trions, which are three-particle compounds formed by two electrons and one hole or vice versa. In this work, we investigate the trion-phonon interaction on a microscopic footing and apply our model to the exemplary case of a molybdenum diselenide ( ${MoSe}_{2}$ ) monolayer. We determine the trion series of states and their internal quantum structure by solving the trion Schrödinger equation. Transforming the system into a trion basis and solving equations of motion, including the trion-phonon interaction within the second-order Born-Markov approximation, provides a microscopic access to the trion dynamics. In particular, we investigate trion propagation and compute the diffusion coefficient and mobility. In the low density limit, we find that trions propagate less efficiently than excitons and electrons due to their stronger coupling with phonons and their larger mass. For increasing densities, we predict a drastic enhancement of diffusion caused by the build-up of a large pressure by the degenerate trion gas, which is a direct consequence of the fermionic character of trions. Our work provides microscopic insights into the trion-phonon interaction and its impact on trion transport in atomically thin semiconductors.

Received 11 May 2022
Revised 30 August 2022
Accepted 30 August 2022

DOI:https://doi.org/10.1103/PhysRevB.106.115407

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. Funded by Bibsam.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Excitons Trions

2-dimensional systems Transition metal dichalcogenides

Density matrix methods Second quantization

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Raul Perea-Causin ^1,*, Samuel Brem ², and Ermin Malic^2,1

¹Department of Physics, Chalmers University of Technology, 412 96 Gothenburg, Sweden
²Department of Physics, Philipps-Universität Marburg, 35032 Marburg, Germany

^*causin@chalmers.se

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Issue

Vol. 106, Iss. 11 — 15 September 2022

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Images

Figure 1
(a) Illustration of trion-phonon interaction in a TMD monolayer. Trion configuration in the (b) electron-hole and (c) exciton-electron picture for a ${MoSe}_{2}$ monolayer. The blue (red) shaded area illustrates the mostly 1s (2s/2p) exciton character of the ground (excited) trion state. Note that the energy axes $E_{x}$ and $E_{e}$ are different and the relative position of electron and exciton bands cannot be compared. (d) Trion eigenstates consisting of the ground (blue) and excited (red) bound states as well as the scattering continuum. A trion can scatter within its center-of-mass dispersion by absorbing or emitting a phonon (cf. orange arrow).
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Figure 2
Trion eigenstates in hBN-encapsulated ${MoSe}_{2}$ monolayer. (a) Trion eigenenergies vs. eigenstate number $λ$ , with the ground (higher) bound state marked by a purple (red) dot and the trion continuum states denoted in orange. The 1s, 2p, and 2s exciton binding energies are shown as a reference. (b) Trion probability distribution $P_{k}^{λ}$ as a function of the relative exciton-electron momentum $k$ for the ground and the higher bound trion state, as well as for an exemplary continuum state denoted with an orange dot in part a. (c) Probability distribution for the trion (exciton) ground state as a function of the exciton-electron (electron-hole) separation. (d) Excitonic weights $p_{ν}^{λ}$ (i.e., probability that the exciton within the trion state $λ$ is occupying the state $ν$ ) for the three considered trion states.
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Figure 3
Trion-phonon interaction. (a) Trion-phonon coupling strength as a function of momentum transfer $q$ explicitly showing the single electron and exciton contributions. The 1s exciton-phonon coupling strength is also shown for comparison (dashed blue line). The inset illustrates the wave function overlap between initial and final states. (b) Trion-phonon scattering rates as a function of kinetic energy at 5 and 20 K. The corresponding rates for 1s exciton-phonon scattering are plotted with dashed lines. (c) Temperature-dependent phonon-induced spectral broadening of the trion and 1s exciton states.
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Figure 4
Trion diffusion and mobility. (a) Temperature-dependent trion diffusion coefficient in the low-density limit (purple) and for trion densities of $1 \times 10^{11} {cm}^{- 2}$ (orange) and $4 \times 10^{11} {cm}^{- 2}$ (red). The low-density 1s exciton diffusion coefficient is shown in light-blue. (b) Trion, 1s exciton, and electron mobilities as a function of temperature.
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