Second harmonic generation control in twisted bilayers of transition metal dichalcogenides

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Second harmonic generation control in twisted bilayers of transition metal dichalcogenides

Ioannis Paradisanos, Andres Manuel Saiz Raven, Thierry Amand, Cedric Robert, Pierre Renucci, Kenji Watanabe, Takashi Taniguchi, Iann C. Gerber, Xavier Marie, and Bernhard Urbaszek

Phys. Rev. B 105, 115420 – Published 18 March 2022

Abstract

The twist angle in transition metal dichalcogenide heterobilayers is a compelling degree of freedom that determines electron correlations and the period of lateral confinement of moiré excitons. Here we perform polarization-resolved second harmonic generation (SHG) spectroscopy of $Mo S_{2} / W {Se}_{2}$ heterostructures. We demonstrate that by choosing suitable laser energies the twist angle between two monolayers can be measured directly on the assembled heterostructure. We show that the amplitude and polarization of the SHG signal from the heterostructure are determined by the twist angle between the layers and exciton resonances at the SH energy. For heterostructures with close to zero twist angle, we observe changes of exciton resonance energies and the appearance of new resonances in the linear and nonlinear susceptibilities.

Received 26 October 2021
Revised 18 February 2022
Accepted 23 February 2022

DOI:https://doi.org/10.1103/PhysRevB.105.115420

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)

Excitons Optoelectronics

Optical second-harmonic generation Spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ioannis Paradisanos ^1,*, Andres Manuel Saiz Raven¹, Thierry Amand¹, Cedric Robert¹, Pierre Renucci¹, Kenji Watanabe ², Takashi Taniguchi³, Iann C. Gerber¹, Xavier Marie¹, and Bernhard Urbaszek ^1,†

¹Université de Toulouse, INSA-CNRS-UPS, LPCNO, 135 Avenue Rangueil, 31077 Toulouse, France
²Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
³International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

^*[email protected]
^†[email protected]

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Issue

Vol. 105, Iss. 11 — 15 March 2022

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Images

Figure 1
SHG spectroscopy on monolayers and heterostructure region. (a) Differential reflectivity (red line) and wavelength-dependent SHG of $1 L − Mo S_{2}$ . For the SHG spectra, the energy in the $x$ axis corresponds to twice the fundamental laser energy ( $2 \times E_{L}$ ). (b) Polar plot of SHG in $1 L − Mo S_{2}$ at $2 \times E_{L} = 1.92$ eV. We measure over an angle range of $120^{\circ}$ and generate the rest of the plot by repeating the data. (c) Same as panel (a) but for $1 L − W {Se}_{2}$ . (d) Same as panel (b) but at $2 \times E_{L} = 1.72$ eV in $1 L − W {Se}_{2}$ . (e) Schematic drawing of the different areas of the heterostructure with access also to monolayer regions. The twist angle $θ_{t}$ is indicated. (f) Same as panels (a) and (c) but for the heterostructure region. (g) Polar plots for the heterostructure region but at two different values of $E_{L}$ : blue triangles for $2 \times E_{L} = 1.72$ eV and black circles for $2 \times E_{L} = 1.92$ eV. All the polar plots are fitted with a $\cos^{2} 3 (θ - θ_{0})$ function (red lines), where $θ$ is the angle of the pump laser polarization and $θ_{0}$ is a free parameter to extract the armchair orientation with respect to the laboratory axis (here the $x$ axis).
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Figure 2
SHG spectroscopy and polarization-resolved SHG for three different $Mo S_{2} / W {Se}_{2}$ heterostructures. From top to bottom: Differential reflectivity (red lines) and wavelength-dependent SHG of (a) HS1 studied in Fig. 1, (b) HS2, and (c) HS3. For the SHG spectra, the energy in the $x$ axis corresponds to twice the fundamental laser energy ( $2 \times E_{L}$ ). The A-exciton states of $Mo S_{2}$ and $W {Se}_{2}$ are indicated with black and blue shaded regions, respectively. The respective polar plots when twice the excitation energy is in resonance with the corresponding A excitons of $Mo S_{2}$ (black) and $W {Se}_{2}$ (blue) are shown in panels (d), (e), and (f). Schematic representation of the moiré pattern of $1 L − Mo S_{2} / 1 L − W {Se}_{2}$ heterostructures with twist angles $θ_{t}$ of (g) $HS 1 = 29 . 8^{\circ}$ , (h) $HS 2 = 4 . 3^{\circ}$ , and (i) $HS 3 = 0 . 8^{\circ}$ . The extracted moiré period is 0.62, 3.84, and 8.45 nm, respectively. Regions with main excitonic transitions are shaded blue and gray. A magenta stripe is shown at 2.1 eV to indicate $2 \times E_{L}$ used for the experiments presented in Fig. 3.
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Figure 3
Polarization-angle-dependent SHG and fitting. Using higher excitation energies ( $2 \times E_{L} = 2.1$ ) eV for (a) HS1, (b) HS2, and (c) HS3. Experimental points are presented with magenta spheres and the fitting of the total SHG signal is shown in green lines. The twist angle values $θ_{t}$ used in Eq. (1) for the total fit are the experimental values $29 . 8^{\circ}, 4 . 3^{\circ}$ , and $0 . 8^{\circ}$ for HS1, HS2, and HS3, respectively. The amplitude ratio $L_{1} (Mo S_{2}$ ): $L_{2} (W {Se}_{2}$ ) is 1.5, 1, and 0.6, while the phase, $φ$ , is kept at $79^{\circ}$ in all cases. The SHG modulation of the individual layers that construct the total SHG is shown in black and blue lines for $Mo S_{2}$ and $W {Se}_{2}$ , respectively. For HS1 (a) where there is a finite minimum to maximum ratio due to the phase shift and large twist angle, a fitting with zero phase shift is shown as a dashed red line for comparison.
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