Abstract

The rich optical properties of transition metal dichalcogenide monolayers (TMD-MLs) render these materials promising candidates for the design of new optoelectronic devices. Despite the large number of excitonic complexes in TMD-MLs, the main focus has been placed on optically bright neutral excitons. Spin-forbidden dark excitonic complexes have been addressed for basic science purposes, but not for applications. We report on spin-forbidden dark excitonic complexes in ML WSe2 as an ideal system for the facile generation of radially polarized light beams. Furthermore, the spatially resolved polarization of photoluminescence beams can be exploited for basic research on excitons in two-dimensional materials.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (5)

M. Ersfeld, F. Volmer, P. de Melo, R. de Winter, M. Heithoff, Z. Zanolli, C. Stampfer, M. Verstraete, and B. Beschoten, “Spin States Protected from Intrinsic Electron–Phonon Coupling Reaching 100 ns Lifetime at Room Temperature in MoSe2,” Nano Lett. 19(6), 4083–4090 (2019).
[Crossref]

M. Paur, A. J. Molina-Mendoza, R. Bratschitsch, K. Watanabe, T. Taniguchi, and T. Mueller, “Electroluminescence from multi-particle exciton complexes in transition metal dichalcogenide semiconductors,” Nat. Commun. 10(1), 1709 (2019).
[Crossref]

E. Liu, J. van Baren, Z. Lu, M. M. Altaiary, T. Taniguchi, K. Watanabe, D. Smirnov, and C. H. Lui, “Gate Tunable Dark Trions in Monolayer WSe2,” Phys. Rev. Lett. 123(2), 027401 (2019).
[Crossref]

Z. Li, T. Wang, Z. Lu, M. Khatoniar, Z. Lian, Y. Meng, M. Blei, T. Taniguchi, K. Watanabe, S. A. McGill, S. Tongay, V. M. Menon, D. Smirnov, and S.-F. Shi, “Direct Observation of Gate-Tunable Dark Trions in Monolayer WSe2,” Nano Lett. 19(10), 6886–6893 (2019).
[Crossref]

L. Linhart, M. Paur, V. Smejkal, J. Burgdörfer, T. Mueller, and F. Libisch, “Localized Intervalley Defect Excitons as Single-Photon Emitters in WSe2,” Phys. Rev. Lett. 123(14), 146401 (2019).
[Crossref]

2018 (5)

J. Lindlau, M. Selig, A. Neumann, L. Colombier, J. Förste, V. Funk, M. Förg, J. Kim, G. Berghäuser, T. Taniguchi, K. Watanabe, F. Wang, E. Malic, and A. Högele, “The role of momentum-dark excitons in the elementary optical response of bilayer WSe2,” Nat. Commun. 9(1), 2586 (2018).
[Crossref]

Z. Ye, L. Waldecker, E. Ma, D. Rhodes, A. A. B. Kim, X. Zhang, M. Deng, Y. Jiang, Z. Lu, D. Smirnov, K. Watanabe, T. Taniguchi, J. Hone, and T. Heinz, “Efficient generation of neutral and charged biexcitons in encapsulated WSe2 monolayers,” Nat. Commun. 9(1), 3718 (2018).
[Crossref]

M. Barbone, A. Montblanch, D. Kara, C. Palacios-Berraquero, A. Cadore, D. D. Fazio, B. Pingault, E. Mostaani, H. Li, B. Chen, K. Watanabe, T. Taniguchi, S. Tongay, G. Wang, A. Ferrari, and M. Atatüre, “Charge-tuneable biexciton complexes in monolayer WSe2,” Nat. Commun. 9(1), 3721 (2018).
[Crossref]

Z. Li, T. Wang, Z. Lu, C. Jin, Y. Chen, Y. Meng, Z. Lian, T. Taniguchi, K. Watanabe, S. Zhang, D. Smirnov, and S.-F. Shi, “Revealing the biexciton and trion-exciton complexes in BN encapsulated WSe2,” Nat. Commun. 9(1), 3719 (2018).
[Crossref]

G. Wang, A. Chernikov, M. Glazov, T. Heinz, X. Marie, T. Amand, and B. Urbaszek, “Colloquium: Excitons in atomically thin transition metal dichalcogenides,” Rev. Mod. Phys. 90(2), 021001 (2018).
[Crossref]

2017 (14)

S. Manzeli, D. Ovchinnikov, D. Pasquier, O. Yazyev, and A. Kis, “2D transition metal dichalcogenides,” Nat. Rev. Mater. 2(8), 17033 (2017).
[Crossref]

G. Wang, C. Robert, M. Glazov, F. Cadiz, E. Courtade, T. Amand, D. Lagarde, T. Taniguchi, K. Watanabe, B. Urbaszek, and X. Marie, “In-Plane Propagation of Light in Transition Metal Dichalcogenide Monolayers: Optical Selection Rules,” Phys. Rev. Lett. 119(4), 047401 (2017).
[Crossref]

X. Zhang, T. Cao, Z. Lu, Y. Lin, F. Zhang, Y. Wang, Z. Li, J. Hone, J. Robinson, D. Smirnov, and S. L. T. and Heinz, “Magnetic brightening and control of dark excitons in monolayer WSe2,” Nat. Nanotechnol. 12(9), 883–888 (2017).
[Crossref]

F. Volmer, S. Pissinger, M. Ersfeld, S. Kuhlen, C. Stampfer, and B. Beschoten, “Intervalley dark trion states with spin lifetimes of 150 ns in WSe2,” Phys. Rev. B 95(23), 235408 (2017).
[Crossref]

M. R. Molas, C. Faugeras, A. O. Slobodeniuk, K. Nogajewski, M. Bartos, D. M. Basko, and M. Potemski, “Brightening of dark excitons in monolayers of semiconducting transition metal dichalcogenides,” 2D Mater. 4(2), 021003 (2017).
[Crossref]

Y. Zhou, G. Scuri, D. S. Wild, A. A. High, A. Dibos, L. A. Jauregui, C. Shu, K. De Greve, K. Pistunova, A. Y. Joe, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Probing dark excitons in atomically thin semiconductors via near-field coupling to surface plasmon polaritons,” Nat. Nanotechnol. 12(9), 856–860 (2017).
[Crossref]

H. Chen, V. Corboliou, A. S. Solntsev, D.-Y. Choi, M. A. Vincenti, D. de Ceglia, C. de Angelis, Y. Lu, and D. N. Neshev, “Enhanced second-harmonic generation from two-dimensional MoSe2 on a silicon waveguide,” Light: Sci. Appl. 6(10), e17060 (2017).
[Crossref]

A. Raja, A. Chaves, J. Yu, G. Arefe, H. M. Hill, A. F. Rigosi, T. C. Berkelbach, P. Nagler, C. Schüller, T. Korn, C. Nuckolls, J. Hone, L. E. Brus, T. F. Heinz, D. R. Reichman, and A. Chernikov, “Coulomb engineering of the bandgap and excitons in two-dimensional materials,” Nat. Commun. 8(1), 15251 (2017).
[Crossref]

E. Courtade, M. Semina, M. Manca, M. Glazov, C. Robert, F. Cadiz, G. Wang, T. Taniguchi, K. Watanabe, M. Pierre, W. Escoffier, E. Ivchenko, P. R. X. Marie, T. Amand, and B. Urbaszek, “Charged excitons in monolayer WSe2: Experiment and theory,” Phys. Rev. B 96(8), 085302 (2017).
[Crossref]

F. Cadiz, E. Courtade, C. Robert, G. Wang, Y. Shen, H. Cai, T. Taniguchi, K. Watanabe, H. Carrere, D. Lagarde, M. Manca, T. Amand, P. Renucci, S. Tongay, X. Marie, and B. Urbaszek, “Excitonic Linewidth Approaching the Homogeneous Limit in MoS2-Based van der Waals Heterostructures,” Phys. Rev. X 7(2), 021026 (2017).
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J. Wierzbowski, J. Klein, F. Sigger, C. Straubinger, M. Kremser, T. Taniguchi, K. Watanabe, U. Wurstbauer, A. Holleitner, M. Kaniber, K. Müller, and J. Finley, “Direct exciton emission from atomically thin transition metal dichalcogenide heterostructures near the lifetime limit,” Sci. Rep. 7(1), 12383 (2017).
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2016 (2)

D. Lloyd, X. Liu, J. W. Christopher, L. Cantley, A. Wadehra, B. L. Kim, B. B. Goldberg, A. K. Swan, and J. S. Bunch, “Band Gap Engineering with Ultralarge Biaxial Strains in Suspended Monolayer MoS2,” Nano Lett. 16(9), 5836–5841 (2016).
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Z. Zhu, J. Yuan, H. Zhou, J. Hu, J. Zhang, C. Wei, F. Yu, S. Chen, Y. Lan, Y. Yang, Y. Wang, C. Niu, Z. Ren, J. Lou, Z. Wang, and J. Bao, “Excitonic resonant emission-absorption of surface plasmons in transition metal dichalcogenides for chip-level electronic-photonic integrated circuits,” ACS Photonics 3(5), 869–874 (2016).
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2015 (8)

Y. Ye, Z. J. Wong, X. Lu, X. Ni, H. Zhu, X. Chen, Y. Wang, and X. Zhang, “Monolayer excitonic laser,” Nat. Photonics 9(11), 733–737 (2015).
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Y. You, X. Zhang, T. Berkelbach, M. Hybertsen, D. Reichman, and T. Heinz, “Observation of biexcitons in monolayer WSe2,” Nat. Phys. 11(6), 477–481 (2015).
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F. Withers, O. Del Pozo-Zamudio, A. Mishchenko, A. P. Rooney, A. Gholinia, K. Watanabe, T. Taniguchi, S. J. Haigh, A. K. Geim, A. I. Tartakovskii, and K. S. Novoselov, “Light-emitting diodes by band-structure engineering in van der waals heterostructures,” Nat. Mater. 14(3), 301–306 (2015).
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S. Manzeli, A. Allain, A. Ghadimi, and A. Kis, “Piezoresistivity and strain-induced band gap tuning in atomically thin MoS2,” Nano Lett. 15(8), 5330–5335 (2015).
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J. Miwa, S. Ulstrup, S. Sørensen, M. Dendzik, A. Cabo, M. Bianchi, J. Lauritsen, and P. Hofmann, “Electronic Structure of Epitaxial Single-Layer MoS2,” Phys. Rev. Lett. 114(4), 046802 (2015).
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S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, B. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2(10), 864–868 (2015).
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M. Dendzik, M. Michiardi, C. Sanders, M. Bianchi, J. A. Miwa, S. S. Grønborg, J. V. Lauritsen, A. Bruix, B. Hammer, and P. Hofmann, “Growth and electronic structure of epitaxial single-layer WS2 on Au(111),” Phys. Rev. B 92(24), 245442 (2015).
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D. Le, A. Barinov, E. Preciado, M. Isarraraz, I. Tanabe, T. Komesu, C. Troha, L. Bartels, T. S. Rahman, and P. A. Dowben, “Spin–orbit coupling in the band structure of monolayer WSe2,” J. Phys.: Condens. Matter 27(18), 182201 (2015).
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2014 (6)

M. Ugeda, A. Bradley, S. Shi, F. da Jornada, Y. Zhang, D. Qiu, W. Ruan, S. Mo, Z. Hussain, Z. Shen, F. Wang, S. Louie, and M. Crommie, “Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor,” Nat. Mater. 13(12), 1091–1095 (2014).
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A. Chernikov, T. Berkelbach, H. Hill, A. Rigosi, Y. Li, O. Aslan, D. Reichman, M. Hybertsen, and T. Heinz, “Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer WS2,” Phys. Rev. Lett. 113(7), 076802 (2014).
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K. He, N. Kumar, L. Zhao, Z. Wang, K. Mak, H. Zhao, and J. Shan, “Tightly Bound Excitons in Monolayer WSe2,” Phys. Rev. Lett. 113(2), 026803 (2014).
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Y. Zhang, T. Chang, B. Zhou, Y. Cui, H. Yan, Z. Liu, F. Schmitt, J. Lee, R. Moore, Y. Chen, H. Lin, H. Jeng, S. Mo, Z. Hussain, A. Bansil, and Z. Shen, “Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2,” Nat. Nanotechnol. 9(2), 111–115 (2014).
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P. J. Zomer, M. H. D. Guimarães, J. C. Brant, N. Tombros, and B. J. van Wees, “Fast pick up technique for high quality heterostructures of bilayer graphene and hexagonal boron nitride,” Appl. Phys. Lett. 105(1), 013101 (2014).
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J. S. Ross, P. Klement, A. M. Jones, N. J. Ghimire, J. Yan, D. G. Mandrus, T. Taniguchi, K. Watanabe, K. Kitamura, W. Yao, D. H. Cobden, and X. Xu, “Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 p-n junctions,” Nat. Nanotechnol. 9(4), 268–272 (2014).
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2013 (5)

A. Castellanos-Gomez, R. Roldán, E. Cappelluti, M. Buscema, F. Guinea, H. S. J. van der Zant, and G. A. Steele, “Local Strain Engineering in Atomically Thin MoS2,” Nano Lett. 13(11), 5361–5366 (2013).
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K. He, C. Poole, K. F. Mak, and J. Shan, “Experimental Demonstration of Continuous Electronic Structure Tuning via Strain in Atomically Thin MoS2,” Nano Lett. 13(6), 2931–2936 (2013).
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A. Jones, H. Yu, N. Ghimire, S. Wu, G. Aivazian, J. Ross, B. Zhao, J. Yan, D. Mandrus, D. Xiao, W. Yao, and X. Xu, “Optical generation of excitonic valley coherence in monolayer WSe2,” Nat. Nanotechnol. 8(9), 634–638 (2013).
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J. A. Schuller, S. Karaveli, T. Schiros, K. He, S. Yang, I. Kymissis, J. Shan, and R. Zia, “Orientation of luminescent excitons in layered nanomaterials,” Nat. Nanotechnol. 8(4), 271–276 (2013).
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X. Gan, Y. Gao, K. Fai Mak, X. Yao, R.-J. Shiue, A. van der Zande, M. E. Trusheim, F. Hatami, T. F. Heinz, J. Hone, and D. Englund, “Controlling the spontaneous emission rate of monolayer MoS2 in a photonic crystal nanocavity,” Appl. Phys. Lett. 103(18), 181119 (2013).
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2012 (5)

D. Xiao, G. Liu, W. Feng, X. Xu, and W. Yao, “Coupled Spin and Valley Physics in Monolayers of MoS2 and Other Group-VI Dichalcogenides,” Phys. Rev. Lett. 108(19), 196802 (2012).
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T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, B. Liu, and J. Feng, “Valley-selective circular dichroism of monolayer molybdenum disulphide,” Nat. Commun. 3(1), 887 (2012).
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G. Sallen, L. Bouet, X. Marie, G. Wang, C. R. Zhu, W. P. Han, Y. Lu, P. H. Tan, T. Amand, B. L. Liu, and B. Urbaszek, “Robust optical emission polarization in mos2 monolayers through selective valley excitation,” Phys. Rev. B 86(8), 081301 (2012).
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H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7(8), 490–493 (2012).
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K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7(8), 494–498 (2012).
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2011 (1)

Z. Zhu, Y. Cheng, and U. Schwingenschlögl, “Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors,” Phys. Rev. B 84(15), 153402 (2011).
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2010 (2)

K. Mak, C. Lee, J. Hone, J. Shan, and T. Heinz, “Atomically Thin MoS2: A New Direct-Gap Semiconductor,” Phys. Rev. Lett. 105(13), 136805 (2010).
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2009 (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
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2004 (1)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper Focus for a Radially Polarized Light Beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
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2002 (2)

Q. Zhan and J. Leger, “Microellipsometer with radial symmetry,” Appl. Opt. 41(22), 4630–4637 (2002).
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2000 (1)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
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Figures (7)

Fig. 1.
Fig. 1. (a) Optical micrograph of the gate-tunable WSe $_2$ ML device. Colored dashed lines indicate the edges of the flakes incorporated in the van der Waals heterostructure. The application of a gate voltage was facilitated by providing metal contacts to the few-layer graphene back gate and the few-layer WSe $_2$ flake, as sketched at the exterior of the micrograph. The scale bar is 20 µm. (b) Schematic drawing of the $\mu$ -photoluminescence experiment performed on the gate-tunable WSe $_2$ ML device. The sample is excited with a continuous wave laser (green), and the photoluminescence signal (red) is collected using an objective with a high numerical aperture. Please note that the exciting beam is focused through the same objective but displaced and tilted in this schematic drawing for illustrative reasons.
Fig. 2.
Fig. 2. Gate-dependent photoluminescence from a gate-tunable WSe $_2$ ML. (a) shows the photoluminescence spectra in the form of a color map. At the upper (lower) end of the graph, the ML is doped with electrons (holes). The vertical high-intensity lines in the graph represent the different excitonic complexes in the photoluminescence spectra. (b) shows two representative photoluminescence spectra for the hole-doped regime ( $0.30$ V, magenta line) and the neutral regime ( $0.63$ V, orange line). The spectra are normalized and offset for a better comparison.
Fig. 3.
Fig. 3. Pinhole-scanning experiment for the two-dimensional SOP analysis of the photoluminescence beam from a $p$ -doped WSe $_2$ ML. (a) shows a schematic drawing of the pinhole, which is scanned across the photoluminescence beam from the WSe $_2$ ML. (b) shows the total integrated photoluminescence intensity in the cross-section of the signal beam, as well as the combined linear polarization of the X $^0$ and the X $^+$ lines. The small deviations from a perfectly centrosymmetric cross-section may result from inhomogeneities in the sample or misalignments in the optical setup, but do not affect the results shown in (c) through (f). The scale bar is $1$ mm. The four-axis polarization basis is shown in the lower left corner of the graph; the same color coding of the polarization is used in (d) and (e). (c) shows the contribution of the dark positive trion to the total intensity, as well as its linear polarization. The length of the polarization lines is proportional to the degree of polarization at each position; a polarization line with a length equivalent to the step size in the spatially resolved intensity map (i.e., 200 µm) corresponds to a degree of polarization of $1$ . It can be seen that the relative contribution of the X $_{\mathrm {d}}^+$ emission increases towards the rim of the beam. It is also apparent that the X $_{\mathrm {d}}^+$ signal beam is radially polarized with a degree of polarization approaching unity at the rim of the beam. (d), (e), and (f) show polarization-resolved spectra at selected positions of the beam cross-section. The positions at which the spectra were taken are indicated in (c). Note that, for a better comparison, the spectra for different polarizations are normalized to the highest intensity of all spectra shown in a graph. While X $_{\mathrm {d}}^+$ is hardly polarized and has a relatively low intensity in (d), it becomes the dominant emission line in (e) and (f) with a high degree of polarization.
Fig. 4.
Fig. 4. Collection of light from an out-of-plane dipole using a high numerical aperture objective. The dipole radiation is strongest in the directions perpendicular to the dipole orientation. The polarization of the emitted light is $p$ -polarized. The high numerical aperture objective collects light emitted at high angles, leading to a high intensity at the rim of the transmitted beam, which is radially polarized.
Fig. 5.
Fig. 5. Knife-edge scanning experiment of the photoluminescence beam from a $p$ -doped WSe $_2$ ML. (a) shows a schematic drawing of the knife-edge, which is scanned across the photoluminescence beam from the WSe $_2$ ML. (b) shows the total photoluminescence intensity, as well as the X $_{\mathrm {d}}^+$ intensity, as a function of the knife-edge position. The intensity profiles have been normalized for a better comparison. (c) shows the linear Stokes parameters, $S_1$ and $S_2$ , for the X $_{\mathrm {d}}^+$ signal, as a function of the knife-edge position. (d), (e) and (f) show polarization-resolved photoluminescence spectra for different positions of the knife-edge. The knife-edge positions at which the spectra were taken are indicated in (c). The intensity comb observed, for instance, on the emission band at $1.65$ eV results from the operation of the charge coupled device used in the experiment.
Fig. 6.
Fig. 6. Scanning knife-edge experiments for a $p$ -doped WSe $_2$ ML at different temperatures of the WSe $_2$ ML. (a) shows the Stokes parameter, $S_1$ , of the total photoluminescence signal as a function of the knife-edge position for four different temperatures. (b) shows the evolution of the contribution from the dark excitonic states to the total photoluminescence signal, as a function of temperature.
Fig. 7.
Fig. 7. Pinhole-scanning experiment for the two-dimensional SOP analysis of the photoluminescence beam from an undoped WSe $_2$ ML. (a) shows the total integrated photoluminescence intensity in the cross-section of the signal beam. The scale bar is $1$ mm. The four-axis polarization basis is shown in the lower left corner of the graph. (b) shows the contribution of the dark positive exciton to the total intensity, as well as its linear polarization. The length of the polarization lines is proportional to the degree of polarization at each position; a polarization line with a length equivalent to the step size in the spatially resolved intensity map (i.e., 200 µm) corresponds to a degree of polarization of $1$ . It can be seen that the relative contribution of the X $_{\mathrm {d}}^0$ emission increases towards the rim of the beam. It is also apparent that the X $_{\mathrm {d}}^0$ signal beam is radially polarized with a degree of polarization approaching unity at the rim of the beam. (c) and (d) show selected polarization resolved spectra at different positions of the beam cross-section. The positions at which the spectra were taken are indicated in (b). Note that the spectra are normalized for a better comparison. While X $_{\mathrm {d}}^0$ is hardly polarized and has a relatively low intensity in (c), it becomes the dominant emission line in (d) with a high degree of polarization. The gate voltage applied for this measurement was $V_{\mathrm {g}}=-0.34$ V. However, it becomes clear from the photoluminescence spectrum that the charge state of the WSe $_2$ ML is equivalent to $V_{\mathrm {g}}=0.63$ V in Fig. 2. The discrepancy results from the transfer to another cryostat and hysteresis effects in the ML.

Tables (1)

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Table 1. Measurement parameters for spectra shown in this work. The table shows both the exposure times and the method for spatial selection for all spectra included in the figures of the main text.

Equations (1)

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S 1 = I H I V I H + I V S 2 = I D I A I D + I A

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