Excitonic properties of semiconducting monolayer and bilayer $\mathrm{MoT}{\mathrm{e}}_{2}$

Excitonic properties of semiconducting monolayer and bilayer $MoT e_{2}$

C. Robert, R. Picard, D. Lagarde, G. Wang, J. P. Echeverry, F. Cadiz, P. Renucci, A. Högele, T. Amand, X. Marie, I. C. Gerber, and B. Urbaszek

Phys. Rev. B 94, 155425 – Published 17 October 2016

Abstract

$MoT e_{2}$ belongs to the semiconducting transition-metal dichalcogenide family with certain properties differing from the other well-studied members $(Mo, W) {(S, Se)}_{2}$ . The optical band gap is in the near-infrared region, and both monolayers and bilayers may have a direct optical band gap. We first simulate the single-particle band structure of both monolayer and bilayer $MoT e_{2}$ with density-functional-theory- $G W$ calculations. We find a direct (indirect) electronic band gap for the monolayer (bilayer). By solving in addition the Bethe-Salpeter equation, we find similar energies for the direct exciton transitions in monolayers and bilayers. We then study the optical properties by means of photoluminescence (PL) excitation, reflectivity, time-resolved PL, and power-dependent PL spectroscopy. With differential reflectivity, we find a similar oscillator strength for the optical transition observed in PL in both monolayers and bilayers suggesting a direct transition in both cases. We identify the same energy for the $B$ -exciton state in the monolayer and the bilayer. Following circularly polarized excitation, we do not find any exciton polarization for a large range of excitation energies. At low temperatures $(T = 10 K)$ , we measure similar PL decay times on the order of 4 ps for both monolayer and bilayer excitons with a slightly longer one for the bilayer. Finally, we observe a reduction of the exciton-exciton annihilation contribution to the nonradiative recombination in bilayers.

Received 10 June 2016
Revised 22 September 2016

DOI:https://doi.org/10.1103/PhysRevB.94.155425

Physics Subject Headings (PhySH)

Excitons

Transition metal dichalcogenides

Density functional theory Luminescence Photoluminescence

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

C. Robert^1,*, R. Picard¹, D. Lagarde¹, G. Wang¹, J. P. Echeverry¹, F. Cadiz¹, P. Renucci¹, A. Högele², T. Amand¹, X. Marie¹, I. C. Gerber^1,†, and B. Urbaszek¹

¹Université de Toulouse, INSA-CNRS-UPS, LPCNO, 135 Avenue de Rangueil, 31077 Toulouse, France
²Fakultät für Physik, Center for NanoScience (CeNS), Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, 80539 München, Germany, EU

^*cedric.robert@insa-toulouse.fr
^†igerber@insa-toulouse.fr

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Vol. 94, Iss. 15 — 15 October 2016

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Figure 1
Quasiparticle band structure for a freestanding $MoT e_{2}$ (a) ML and (b) BL, at the $G_{0} W_{0}$ level of theory, extracted from a Wannier localization procedure. The energy at the valence-band maximum (in K) is set to zero for the sake of comparison. The imaginary part of the transverse dielectric constant $ɛ_{2}^{xx} (ω)$ as a func-tion of photon energy (in eV) for the $MoT e_{2}$ (c) ML and (d) BL. The red bars represent the relative oscillator strengths for the optical transitions, whereas the dashed line indicates the $G_{0} W_{0}$ band gap.
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Figure 2
(a) PL spectra of the $MoT e_{2}$ ML (black) and BL (red) at 10 K. The inset: optical microscope image used for the identification of ML and BL regions. (b) PL spectra of the $MoT e_{2}$ ML from 10 to 100 K. The sample is excited with a cw HeNe laser (633 nm) at a power of 50 µW.
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Figure 3
(a) PLE spectra (PL intensity of the $X_{A}^{1 s}$ peak as a function of excitation energy) of the $MoT e_{2}$ ML (black square points) and BL (red circle points) at 10 K. The sample is excited with a cw Ti:sapphire laser for wavelengths between 750 nm (1.65 eV) and 950 nm (1.31 eV) and with a tunable laser diode for wavelengths between 950 nm (1.31 eV) and 1000 nm (1.24 eV). The laser power is 50 µW. (b) PL spectra of the $MoT e_{2}$ ML (black) and BL (red) at 10 K on a quartz substrate (top panel) and differential reflectivity $Δ R / R = (R_{flake} - R_{quartz}) / R_{quartz}$ (bottom panel). For the PL experiment, the sample is excited with a cw HeNe laser (633 nm) at a power of 50 μW. (c) PL spectra of the $MoT e_{2}$ ML (black) and BL (red) at 10 K for two different excitation laser energies. The sample is excited at a power of 50 µW.
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Figure 4
Time-resolved photoluminescence of the neutral exciton $X_{A}^{1 s}$ in the $MoT e_{2}$ ML (black) and BL (red) following a resonant excitation on the $B$ exciton $[E (laser) = 1.458 eV (850 nm)]$ at 10 K. The instrument response is obtained by detecting the backscattered laser pulse on the sample surface, see the hatched area labeled “LASER.”
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Figure 5
Dependence of the $X_{A}^{1 s}$ PL intensity with the laser power in the $MoT e_{2}$ ML (black square points) and BL (red circles points) at 10 K (filled symbols) and 200 K (opened symbols). The sample is excited with a cw HeNe laser (633 nm). The green dashed lines indicate linear slopes. The black circle highlights the nonlinear dependence of the $X_{A}^{1 s}$ PL intensity in the $MoT e_{2}$ ML at 200 K. With our estimated spot size and assuming an absorption of 10%, a power of 100 µW is equivalent to a density of absorbed photons of $4 . 10^{21} c m^{- 2} s^{- 1}$ .
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Physical Review B

covering condensed matter and materials physics

Excitonic properties of semiconducting monolayer and bilayer $MoT e_{2}$

C. Robert, R. Picard, D. Lagarde, G. Wang, J. P. Echeverry, F. Cadiz, P. Renucci, A. Högele, T. Amand, X. Marie, I. C. Gerber, and B. Urbaszek

Phys. Rev. B 94, 155425 – Published 17 October 2016

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Physical Review B

covering condensed matter and materials physics

Excitonic properties of semiconducting monolayer and bilayer MoTe2

C. Robert, R. Picard, D. Lagarde, G. Wang, J. P. Echeverry, F. Cadiz, P. Renucci, A. Högele, T. Amand, X. Marie, I. C. Gerber, and B. Urbaszek

Phys. Rev. B 94, 155425 – Published 17 October 2016

Abstract

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Excitonic properties of semiconducting monolayer and bilayer $MoT e_{2}$