Abstract

Questions hovering over the modulation of bandgap size and excitonic effect on nonlinear absorption in two-dimensional transition metal dichalcogenides (TMDCs) have restricted their application in micro/nano optical modulator, optical switching, and beam shaping devices. Here, degenerate two-photon absorption (TPA) in the near-infrared region was studied experimentally in mechanically exfoliated MoS2 from single layer to multilayer. The layer-dependent TPA coefficients were significantly modulated by the detuning of the excitonic dark state (2p). The shift of the quasiparticle bandgap and the decreasing of exciton binding energy with layers were deduced, combined with the non-hydrogen model of excitons in TMDCs and the scaling rule of semiconductors. Our work clearly demonstrates the layer modulation of nonlinear absorption in TMDCs and provides support for layer-dependent nonlinear optical devices, such as optical limiters and optical switches.

© 2019 Chinese Laser Press

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References

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2019 (1)

T. Deilmann and K. S. Thygesen, “Important role of screening the electron-hole exchange interaction for the optical properties of molecules near metal surfaces,” Phys. Rev. B 99, 045133 (2019).
[Crossref]

2018 (3)

F. Zhou, J. H. Kua, S. Lu, and W. Ji, “Two-photon absorption arises from two-dimensional excitons,” Opt. Express 26, 16093–16101 (2018).
[Crossref]

N. Dong, Y. Li, S. Zhang, N. McEvoy, R. Gatensby, G. S. Duesberg, and J. Wang, “Saturation of two-photon absorption in layered transition metal dichalcogenides: experiment and theory,” ACS Photon. 5, 1558–1565 (2018).
[Crossref]

T. Deilmann and K. S. Thygesen, “Interlayer excitons with large optical amplitudes in layered van der Waals materials,” Nano Lett. 18, 2984–2989 (2018).
[Crossref]

2017 (6)

M. M. Glazov, L. E. Golub, G. Wang, X. Marie, T. Amand, and B. Urbaszek, “Intrinsic exciton-state mixing and nonlinear optical properties in transition metal dichalcogenide monolayers,” Phys. Rev. B 95, 035311 (2017).
[Crossref]

G. Wang, C. Robert, M. 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, 047401 (2017).
[Crossref]

F. Zhou and W. Ji, “Two-photon absorption and subband photodetection in monolayer MoS2,” Opt. Lett. 42, 3113–3116 (2017).
[Crossref]

M. Drüppel, T. Deilmann, P. Krüger, and M. Rohlfing, “Diversity of trion states and substrate effects in the optical properties of an MoS2 monolayer,” Nat. Commun. 8, 2117 (2017).
[Crossref]

X. L. Li, W. P. Han, J. B. Wu, X. F. Qiao, J. Zhang, and P. H. Tan, “Layer-number dependent optical properties of 2D materials and their application for thickness determination,” Adv. Funct. Mater. 27, 1604468 (2017).
[Crossref]

F. Zhou and W. Ji, “Giant three-photon absorption in monolayer MoS2 and its application in near-infrared photodetection,” Laser Photon. Rev. 11, 1700021 (2017).
[Crossref]

2016 (4)

M. Reichert, A. L. Smirl, G. Salamo, D. J. Hagan, and E. W. Van Stryland, “Observation of nondegenerate two-photon gain in GaAs,” Phys. Rev. Lett. 117, 073602 (2016).
[Crossref]

T. Olsen, S. Latini, F. Rasmussen, and K. S. Thygesen, “Simple screened hydrogen model of excitons in two-dimensional materials,” Phys. Rev. Lett. 116, 056401 (2016).
[Crossref]

D. Y. Qiu, F. H. da Jornada, and S. G. Louie, “Screening and many-body effects in two-dimensional crystals: monolayer MoS2,” Phys. Rev. B 93, 235435 (2016).
[Crossref]

N. Dong, Y. Li, S. Zhang, N. McEvoy, X. Zhang, Y. Cui, L. Zhang, G. S. Duesberg, and J. Wang, “Dispersion of nonlinear refractive index in layered WS2 and WSe2 semiconductor films induced by two-photon absorption,” Opt. Lett. 41, 3936–3939 (2016).
[Crossref]

2015 (8)

B. Zhu, X. Chen, and X. Cui, “Exciton binding energy of monolayer WS2,” Sci. Rep. 5, 9218 (2015).
[Crossref]

T. C. Berkelbach, M. S. Hybertsen, and D. R. Reichman, “Bright and dark singlet excitons via linear and two-photon spectroscopy in monolayer transition-metal dichalcogenides,” Phys. Rev. B 92, 085413 (2015).
[Crossref]

J. H. Choi, P. Cui, H. P. Lan, and Z. Y. Zhang, “Linear scaling of the exciton binding energy versus the band gap of two-dimensional materials,” Phys. Rev. Lett. 115, 066403 (2015).
[Crossref]

Y. Li, N. Dong, S. Zhang, X. Zhang, Y. Feng, K. Wang, L. Zhang, and J. Wang, “Giant two-photon absorption in monolayer MoS2,” Laser Photon. Rev. 9, 427–434 (2015).
[Crossref]

H. C. Kim, H. Kim, J. U. Lee, H. B. Lee, D. H. Choi, J. H. Lee, W. H. Lee, S. H. Jhang, B. H. Park, H. Cheong, S. W. Lee, and H. J. Chung, “Engineering optical and electronic properties of WS2 by varying the number of layers,” ACS Nano 9, 6854–6860 (2015).
[Crossref]

J. Xiao, Z. Ye, Y. Wang, H. Zhu, Y. Wang, and X. Zhang, “Nonlinear optical selection rule based on valley-exciton locking in monolayer WS2,” Light: Sci. Appl. 4, e366 (2015).
[Crossref]

H. M. Hill, A. F. Rigosi, C. Roquelet, A. Chernikov, T. C. Berkelbach, D. R. Reichman, M. S. Hybertsen, L. E. Brus, and T. F. Heinz, “Observation of excitonic Rydberg states in monolayer MoS2 and WS2 by photoluminescence excitation spectroscopy,” Nano Lett. 15, 2992–2997 (2015).
[Crossref]

S. F. Zhang, N. N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. X. Li, X. Y. Zhang, Z. H. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9, 7142–7150 (2015).
[Crossref]

2014 (5)

C. Yim, M. O’Brien, N. McEvoy, S. Winters, I. Mirza, J. G. Lunney, and G. S. Duesberg, “Investigation of the optical properties of MoS2 thin films using spectroscopic ellipsometry,” Appl. Phys. Lett. 104, 103114 (2014).
[Crossref]

X. B. Yin, Z. L. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344, 488–490 (2014).
[Crossref]

Z. Ye, T. Cao, K. O’Brien, H. Zhu, X. Yin, Y. Wang, S. G. Louie, and X. Zhang, “Probing excitonic dark states in single-layer tungsten disulphide,” Nature 513, 214–218 (2014).
[Crossref]

K. He, N. Kumar, L. Zhao, Z. Wang, K. F. Mak, H. Zhao, and J. Shan, “Tightly bound excitons in monolayer WSe2,” Phys. Rev. Lett. 113, 026803 (2014).
[Crossref]

A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, O. B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, “Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2,” Phys. Rev. Lett. 113, 076802 (2014).
[Crossref]

2013 (2)

K. P. Wang, J. Wang, and J. T. Fan, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7, 9260–9267 (2013).
[Crossref]

D. Y. Qiu, F. H. da Jornada, and S. G. Louie, “Optical spectrum of MoS2: many-body effects and diversity of exciton states,” Phys. Rev. Lett. 111, 216805 (2013).
[Crossref]

2012 (7)

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

H.-P. Komsa and A. V. Krasheninnikov, “Effects of confinement and environment on the electronic structure and exciton binding energy of MoS2 from first principles,” Phys. Rev. B 86, 241201 (2012).
[Crossref]

T. Cheiwchanchamnangij and W. R. L. Lambrecht, “Quasiparticle band structure calculation of monolayer, bilayer, and bulk MoS2,” Phys. Rev. B 85, 205302 (2012).
[Crossref]

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, 887 (2012).
[Crossref]

H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7, 490–493 (2012).
[Crossref]

K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7, 494–498 (2012).
[Crossref]

G. Kioseoglou, A. T. Hanbicki, M. Currie, A. L. Friedman, D. Gunlycke, and B. T. Jonker, “Valley polarization and intervalley scattering in monolayer MoS2,” Appl. Phys. Lett. 101, 221907 (2012).
[Crossref]

2011 (1)

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

2010 (5)

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

M. Rumi and J. W. Perry, “Two-photon absorption: an overview of measurements and principles,” Adv. Opt. Photon. 2, 451 (2010).
[Crossref]

C. G. Lee, H. G. Yan, L. E. Brus, and T. F. Heinz, “Anomalous lattice vibrations of single and few-layer MoS2,” ACS Nano 4, 2695–2700 (2010).
[Crossref]

A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C. Y. Chim, G. Galli, and F. Wang, “Emerging photoluminescence in monolayer MoS2,” Nano Lett. 10, 1271–1275 (2010).
[Crossref]

P. Cudazzo, C. Attaccalite, I. V. Tokatly, and A. Rubio, “Strong charge-transfer excitonic effects and the Bose-Einstein exciton condensate in graphane,” Phys. Rev. Lett. 104, 226804 (2010).
[Crossref]

2007 (1)

G. S. He, Q. Zheng, A. Baev, and P. N. Prasad, “Saturation of multiphoton absorption upon strong and ultrafast infrared laser excitation,” J. Appl. Phys. 101, 083108 (2007).
[Crossref]

2005 (1)

J. He, J. Mi, H. P. Li, and W. Ji, “Observation of interband two-photon absorption saturation in CdS nanocrystals,” J. Phys. Chem. B 109, 19184–19187 (2005).
[Crossref]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref]

2000 (1)

G. B. Serapiglia, E. Paspalakis, C. Sirtori, K. L. Vodopyanov, and C. C. Phillips, “Laser-induced quantum coherence in a semiconductor quantum well,” Phys. Rev. Lett. 84, 1019–1022 (2000).
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1996 (1)

B. Taheri, H. Liu, B. Jassemnejad, D. Appling, R. C. Powell, and J. J. Song, “Intensity scan and two photon absorption and nonlinear refraction of C60 in toluene,” Appl. Phys. Lett. 68, 1317–1319 (1996).
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1991 (1)

A. M. Fox and D. A. B. Miller, “Excitonic effects in coupled quantum wells,” Phys. Rev. B 44, 6231–6242 (1991).
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1990 (2)

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96–99 (1990).
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M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
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1989 (2)

D. A. B. Miller and A. M. Fox, “Excitons in resonant coupling of quantum wells,” Phys. Rev. B 42, 1841–1844 (1989).
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A. Shimizu, “Two-photon absorption in quantum-well structures near half the direct band gap,” Phys. Rev. B 40, 1403–1406 (1989).
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1987 (2)

R. Coehoorn, C. Haas, J. Dijkstra, C. J. F. Flipse, R. A. de Groot, and A. Wold, “Electronic structure of MoSe2, MoS2, and WSe2. I. Band-structure calculations and photoelectron spectroscopy,” Phys. Rev. B 35, 6195–6202 (1987).
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R. Coehoorn, C. Haas, and R. A. de Groot, “Electronic structure of MoSe2, MoS2, and WSe2. II. The nature of the optical band gaps,” Phys. Rev. B 35, 6203–6206 (1987).
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1985 (1)

1984 (1)

1979 (1)

A. R. Beal and H. P. Huges, “Kramers-Kronig analysis of the reflectivity spectra of 2H-MoS2, 2H-MoSe2, and 2H-MoTe2,” J. Phys. C 12, 881–890 (1979).
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1968 (1)

G. D. Mahan, “Theory of two-photon spectroscopy in solids,” Phys. Rev. 170, 825–838 (1968).
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Amand, T.

G. Wang, C. Robert, M. 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, 047401 (2017).
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M. M. Glazov, L. E. Golub, G. Wang, X. Marie, T. Amand, and B. Urbaszek, “Intrinsic exciton-state mixing and nonlinear optical properties in transition metal dichalcogenide monolayers,” Phys. Rev. B 95, 035311 (2017).
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Appling, D.

B. Taheri, H. Liu, B. Jassemnejad, D. Appling, R. C. Powell, and J. J. Song, “Intensity scan and two photon absorption and nonlinear refraction of C60 in toluene,” Appl. Phys. Lett. 68, 1317–1319 (1996).
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Aslan, O. B.

A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, O. B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, “Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2,” Phys. Rev. Lett. 113, 076802 (2014).
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Attaccalite, C.

P. Cudazzo, C. Attaccalite, I. V. Tokatly, and A. Rubio, “Strong charge-transfer excitonic effects and the Bose-Einstein exciton condensate in graphane,” Phys. Rev. Lett. 104, 226804 (2010).
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Baev, A.

G. S. He, Q. Zheng, A. Baev, and P. N. Prasad, “Saturation of multiphoton absorption upon strong and ultrafast infrared laser excitation,” J. Appl. Phys. 101, 083108 (2007).
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Baillargeat, D.

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

Beal, A. R.

A. R. Beal and H. P. Huges, “Kramers-Kronig analysis of the reflectivity spectra of 2H-MoS2, 2H-MoSe2, and 2H-MoTe2,” J. Phys. C 12, 881–890 (1979).
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Berkelbach, T. C.

H. M. Hill, A. F. Rigosi, C. Roquelet, A. Chernikov, T. C. Berkelbach, D. R. Reichman, M. S. Hybertsen, L. E. Brus, and T. F. Heinz, “Observation of excitonic Rydberg states in monolayer MoS2 and WS2 by photoluminescence excitation spectroscopy,” Nano Lett. 15, 2992–2997 (2015).
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T. C. Berkelbach, M. S. Hybertsen, and D. R. Reichman, “Bright and dark singlet excitons via linear and two-photon spectroscopy in monolayer transition-metal dichalcogenides,” Phys. Rev. B 92, 085413 (2015).
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A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, O. B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, “Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2,” Phys. Rev. Lett. 113, 076802 (2014).
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Berner, N. C.

S. F. Zhang, N. N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. X. Li, X. Y. Zhang, Z. H. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9, 7142–7150 (2015).
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Brus, L. E.

H. M. Hill, A. F. Rigosi, C. Roquelet, A. Chernikov, T. C. Berkelbach, D. R. Reichman, M. S. Hybertsen, L. E. Brus, and T. F. Heinz, “Observation of excitonic Rydberg states in monolayer MoS2 and WS2 by photoluminescence excitation spectroscopy,” Nano Lett. 15, 2992–2997 (2015).
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C. G. Lee, H. G. Yan, L. E. Brus, and T. F. Heinz, “Anomalous lattice vibrations of single and few-layer MoS2,” ACS Nano 4, 2695–2700 (2010).
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Cadiz, F.

G. Wang, C. Robert, M. 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, 047401 (2017).
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Cao, T.

Z. Ye, T. Cao, K. O’Brien, H. Zhu, X. Yin, Y. Wang, S. G. Louie, and X. Zhang, “Probing excitonic dark states in single-layer tungsten disulphide,” Nature 513, 214–218 (2014).
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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, 887 (2012).
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Cheiwchanchamnangij, T.

T. Cheiwchanchamnangij and W. R. L. Lambrecht, “Quasiparticle band structure calculation of monolayer, bilayer, and bulk MoS2,” Phys. Rev. B 85, 205302 (2012).
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Chen, X.

B. Zhu, X. Chen, and X. Cui, “Exciton binding energy of monolayer WS2,” Sci. Rep. 5, 9218 (2015).
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Chen, Z. H.

S. F. Zhang, N. N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. X. Li, X. Y. Zhang, Z. H. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9, 7142–7150 (2015).
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Chenet, D. A.

X. B. Yin, Z. L. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344, 488–490 (2014).
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Cheong, H.

H. C. Kim, H. Kim, J. U. Lee, H. B. Lee, D. H. Choi, J. H. Lee, W. H. Lee, S. H. Jhang, B. H. Park, H. Cheong, S. W. Lee, and H. J. Chung, “Engineering optical and electronic properties of WS2 by varying the number of layers,” ACS Nano 9, 6854–6860 (2015).
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Chernikov, A.

H. M. Hill, A. F. Rigosi, C. Roquelet, A. Chernikov, T. C. Berkelbach, D. R. Reichman, M. S. Hybertsen, L. E. Brus, and T. F. Heinz, “Observation of excitonic Rydberg states in monolayer MoS2 and WS2 by photoluminescence excitation spectroscopy,” Nano Lett. 15, 2992–2997 (2015).
[Crossref]

A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, O. B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, “Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2,” Phys. Rev. Lett. 113, 076802 (2014).
[Crossref]

Chim, C. Y.

A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C. Y. Chim, G. Galli, and F. Wang, “Emerging photoluminescence in monolayer MoS2,” Nano Lett. 10, 1271–1275 (2010).
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Choi, D. H.

H. C. Kim, H. Kim, J. U. Lee, H. B. Lee, D. H. Choi, J. H. Lee, W. H. Lee, S. H. Jhang, B. H. Park, H. Cheong, S. W. Lee, and H. J. Chung, “Engineering optical and electronic properties of WS2 by varying the number of layers,” ACS Nano 9, 6854–6860 (2015).
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Choi, J. H.

J. H. Choi, P. Cui, H. P. Lan, and Z. Y. Zhang, “Linear scaling of the exciton binding energy versus the band gap of two-dimensional materials,” Phys. Rev. Lett. 115, 066403 (2015).
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Chung, H. J.

H. C. Kim, H. Kim, J. U. Lee, H. B. Lee, D. H. Choi, J. H. Lee, W. H. Lee, S. H. Jhang, B. H. Park, H. Cheong, S. W. Lee, and H. J. Chung, “Engineering optical and electronic properties of WS2 by varying the number of layers,” ACS Nano 9, 6854–6860 (2015).
[Crossref]

Cirloganu, C. M.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Coehoorn, R.

R. Coehoorn, C. Haas, J. Dijkstra, C. J. F. Flipse, R. A. de Groot, and A. Wold, “Electronic structure of MoSe2, MoS2, and WSe2. I. Band-structure calculations and photoelectron spectroscopy,” Phys. Rev. B 35, 6195–6202 (1987).
[Crossref]

R. Coehoorn, C. Haas, and R. A. de Groot, “Electronic structure of MoSe2, MoS2, and WSe2. II. The nature of the optical band gaps,” Phys. Rev. B 35, 6203–6206 (1987).
[Crossref]

Courtade, E.

G. Wang, C. Robert, M. 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, 047401 (2017).
[Crossref]

Cudazzo, P.

P. Cudazzo, C. Attaccalite, I. V. Tokatly, and A. Rubio, “Strong charge-transfer excitonic effects and the Bose-Einstein exciton condensate in graphane,” Phys. Rev. Lett. 104, 226804 (2010).
[Crossref]

Cui, P.

J. H. Choi, P. Cui, H. P. Lan, and Z. Y. Zhang, “Linear scaling of the exciton binding energy versus the band gap of two-dimensional materials,” Phys. Rev. Lett. 115, 066403 (2015).
[Crossref]

Cui, X.

B. Zhu, X. Chen, and X. Cui, “Exciton binding energy of monolayer WS2,” Sci. Rep. 5, 9218 (2015).
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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, 490–493 (2012).
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Cui, Y.

Currie, M.

G. Kioseoglou, A. T. Hanbicki, M. Currie, A. L. Friedman, D. Gunlycke, and B. T. Jonker, “Valley polarization and intervalley scattering in monolayer MoS2,” Appl. Phys. Lett. 101, 221907 (2012).
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da Jornada, F. H.

D. Y. Qiu, F. H. da Jornada, and S. G. Louie, “Screening and many-body effects in two-dimensional crystals: monolayer MoS2,” Phys. Rev. B 93, 235435 (2016).
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D. Y. Qiu, F. H. da Jornada, and S. G. Louie, “Optical spectrum of MoS2: many-body effects and diversity of exciton states,” Phys. Rev. Lett. 111, 216805 (2013).
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Dai, J.

H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7, 490–493 (2012).
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de Groot, R. A.

R. Coehoorn, C. Haas, and R. A. de Groot, “Electronic structure of MoSe2, MoS2, and WSe2. II. The nature of the optical band gaps,” Phys. Rev. B 35, 6203–6206 (1987).
[Crossref]

R. Coehoorn, C. Haas, J. Dijkstra, C. J. F. Flipse, R. A. de Groot, and A. Wold, “Electronic structure of MoSe2, MoS2, and WSe2. I. Band-structure calculations and photoelectron spectroscopy,” Phys. Rev. B 35, 6195–6202 (1987).
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Deilmann, T.

T. Deilmann and K. S. Thygesen, “Important role of screening the electron-hole exchange interaction for the optical properties of molecules near metal surfaces,” Phys. Rev. B 99, 045133 (2019).
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T. Deilmann and K. S. Thygesen, “Interlayer excitons with large optical amplitudes in layered van der Waals materials,” Nano Lett. 18, 2984–2989 (2018).
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M. Drüppel, T. Deilmann, P. Krüger, and M. Rohlfing, “Diversity of trion states and substrate effects in the optical properties of an MoS2 monolayer,” Nat. Commun. 8, 2117 (2017).
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Dijkstra, J.

R. Coehoorn, C. Haas, J. Dijkstra, C. J. F. Flipse, R. A. de Groot, and A. Wold, “Electronic structure of MoSe2, MoS2, and WSe2. I. Band-structure calculations and photoelectron spectroscopy,” Phys. Rev. B 35, 6195–6202 (1987).
[Crossref]

Dong, N.

N. Dong, Y. Li, S. Zhang, N. McEvoy, R. Gatensby, G. S. Duesberg, and J. Wang, “Saturation of two-photon absorption in layered transition metal dichalcogenides: experiment and theory,” ACS Photon. 5, 1558–1565 (2018).
[Crossref]

N. Dong, Y. Li, S. Zhang, N. McEvoy, X. Zhang, Y. Cui, L. Zhang, G. S. Duesberg, and J. Wang, “Dispersion of nonlinear refractive index in layered WS2 and WSe2 semiconductor films induced by two-photon absorption,” Opt. Lett. 41, 3936–3939 (2016).
[Crossref]

Y. Li, N. Dong, S. Zhang, X. Zhang, Y. Feng, K. Wang, L. Zhang, and J. Wang, “Giant two-photon absorption in monolayer MoS2,” Laser Photon. Rev. 9, 427–434 (2015).
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Dong, N. N.

S. F. Zhang, N. N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. X. Li, X. Y. Zhang, Z. H. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9, 7142–7150 (2015).
[Crossref]

Drüppel, M.

M. Drüppel, T. Deilmann, P. Krüger, and M. Rohlfing, “Diversity of trion states and substrate effects in the optical properties of an MoS2 monolayer,” Nat. Commun. 8, 2117 (2017).
[Crossref]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref]

Duesberg, G. S.

N. Dong, Y. Li, S. Zhang, N. McEvoy, R. Gatensby, G. S. Duesberg, and J. Wang, “Saturation of two-photon absorption in layered transition metal dichalcogenides: experiment and theory,” ACS Photon. 5, 1558–1565 (2018).
[Crossref]

N. Dong, Y. Li, S. Zhang, N. McEvoy, X. Zhang, Y. Cui, L. Zhang, G. S. Duesberg, and J. Wang, “Dispersion of nonlinear refractive index in layered WS2 and WSe2 semiconductor films induced by two-photon absorption,” Opt. Lett. 41, 3936–3939 (2016).
[Crossref]

S. F. Zhang, N. N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. X. Li, X. Y. Zhang, Z. H. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9, 7142–7150 (2015).
[Crossref]

C. Yim, M. O’Brien, N. McEvoy, S. Winters, I. Mirza, J. G. Lunney, and G. S. Duesberg, “Investigation of the optical properties of MoS2 thin films using spectroscopic ellipsometry,” Appl. Phys. Lett. 104, 103114 (2014).
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Edwin, T. H. T.

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

Fan, J. T.

K. P. Wang, J. Wang, and J. T. Fan, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7, 9260–9267 (2013).
[Crossref]

Feng, J.

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, 887 (2012).
[Crossref]

Feng, Y.

Y. Li, N. Dong, S. Zhang, X. Zhang, Y. Feng, K. Wang, L. Zhang, and J. Wang, “Giant two-photon absorption in monolayer MoS2,” Laser Photon. Rev. 9, 427–434 (2015).
[Crossref]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref]

Fishman, D. A.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Flipse, C. J. F.

R. Coehoorn, C. Haas, J. Dijkstra, C. J. F. Flipse, R. A. de Groot, and A. Wold, “Electronic structure of MoSe2, MoS2, and WSe2. I. Band-structure calculations and photoelectron spectroscopy,” Phys. Rev. B 35, 6195–6202 (1987).
[Crossref]

Fox, A. M.

A. M. Fox and D. A. B. Miller, “Excitonic effects in coupled quantum wells,” Phys. Rev. B 44, 6231–6242 (1991).
[Crossref]

D. A. B. Miller and A. M. Fox, “Excitons in resonant coupling of quantum wells,” Phys. Rev. B 42, 1841–1844 (1989).
[Crossref]

Friedman, A. L.

G. Kioseoglou, A. T. Hanbicki, M. Currie, A. L. Friedman, D. Gunlycke, and B. T. Jonker, “Valley polarization and intervalley scattering in monolayer MoS2,” Appl. Phys. Lett. 101, 221907 (2012).
[Crossref]

Galli, G.

A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C. Y. Chim, G. Galli, and F. Wang, “Emerging photoluminescence in monolayer MoS2,” Nano Lett. 10, 1271–1275 (2010).
[Crossref]

Gatensby, R.

N. Dong, Y. Li, S. Zhang, N. McEvoy, R. Gatensby, G. S. Duesberg, and J. Wang, “Saturation of two-photon absorption in layered transition metal dichalcogenides: experiment and theory,” ACS Photon. 5, 1558–1565 (2018).
[Crossref]

Geim, A. K.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref]

Glazov, M. M.

G. Wang, C. Robert, M. 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, 047401 (2017).
[Crossref]

M. M. Glazov, L. E. Golub, G. Wang, X. Marie, T. Amand, and B. Urbaszek, “Intrinsic exciton-state mixing and nonlinear optical properties in transition metal dichalcogenide monolayers,” Phys. Rev. B 95, 035311 (2017).
[Crossref]

Golub, L. E.

M. M. Glazov, L. E. Golub, G. Wang, X. Marie, T. Amand, and B. Urbaszek, “Intrinsic exciton-state mixing and nonlinear optical properties in transition metal dichalcogenide monolayers,” Phys. Rev. B 95, 035311 (2017).
[Crossref]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref]

Gunlycke, D.

G. Kioseoglou, A. T. Hanbicki, M. Currie, A. L. Friedman, D. Gunlycke, and B. T. Jonker, “Valley polarization and intervalley scattering in monolayer MoS2,” Appl. Phys. Lett. 101, 221907 (2012).
[Crossref]

Haas, C.

R. Coehoorn, C. Haas, and R. A. de Groot, “Electronic structure of MoSe2, MoS2, and WSe2. II. The nature of the optical band gaps,” Phys. Rev. B 35, 6203–6206 (1987).
[Crossref]

R. Coehoorn, C. Haas, J. Dijkstra, C. J. F. Flipse, R. A. de Groot, and A. Wold, “Electronic structure of MoSe2, MoS2, and WSe2. I. Band-structure calculations and photoelectron spectroscopy,” Phys. Rev. B 35, 6195–6202 (1987).
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Hagan, D. J.

M. Reichert, A. L. Smirl, G. Salamo, D. J. Hagan, and E. W. Van Stryland, “Observation of nondegenerate two-photon gain in GaAs,” Phys. Rev. Lett. 117, 073602 (2016).
[Crossref]

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96–99 (1990).
[Crossref]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[Crossref]

Han, W.

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, 887 (2012).
[Crossref]

Han, W. P.

X. L. Li, W. P. Han, J. B. Wu, X. F. Qiao, J. Zhang, and P. H. Tan, “Layer-number dependent optical properties of 2D materials and their application for thickness determination,” Adv. Funct. Mater. 27, 1604468 (2017).
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Hanbicki, A. T.

G. Kioseoglou, A. T. Hanbicki, M. Currie, A. L. Friedman, D. Gunlycke, and B. T. Jonker, “Valley polarization and intervalley scattering in monolayer MoS2,” Appl. Phys. Lett. 101, 221907 (2012).
[Crossref]

He, G. S.

G. S. He, Q. Zheng, A. Baev, and P. N. Prasad, “Saturation of multiphoton absorption upon strong and ultrafast infrared laser excitation,” J. Appl. Phys. 101, 083108 (2007).
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Figures (10)

Fig. 1.
Fig. 1. (a) Microscopic images of mechanically exfoliated monolayer (1L), bilayer (2L), and trilayer (3L) of MoS2 nanosheets. (b) AFM image of the monolayer and bilayer, where the boundary is marked by yellow dashed-dotted lines. The height profiles are along the direction of the green dashed line. (c)–(f) PL, Raman, and linear absorption spectra of MoS2 nanosheets with different layers, exhibiting the layer-modulated Raman shift, PL intensity, and one-photon absorption.
Fig. 2.
Fig. 2. (a) Micro-I-scan results for monolayer, few-layer, and multilayer MoS2, which are fitted using the homogeneously broadened TPA model. (b) TPA coefficients of layered MoS2. The green solid circle stands for the TPA coefficients, which can be separated into two parts: the trailing edge (as indicated by the blue solid line) corresponds to the excitonic resonance part, and the following rising edge corresponds to the interband transition part. The orange dashed line indicates the transition of MoS2 from the two-dimensional prototype to the bulk one.
Fig. 3.
Fig. 3. Schematic illustration of a TPA-active exciton at the K point in the Brillouin zone. 1s and 2p (1.88  eV and 2.41  eV in monolayer MoS2) represent ground state and the first excitonic dark state in a 2D non-hydrogen model. (a) In monolayer MoS2, the 2p excitonic dark state is almost in resonance with two-photon energy. (b) In few-layer MoS2, the excitonic resonance detuning increases with layer number. (c) In multilayer MoS2, the red shift of quasiparticle bandgap continues to increase, and the interband TPA occurs.
Fig. 4.
Fig. 4. Shift of the quasiparticle bandgap Eg and the first excited excitonic state (En=2) versus number of layers. As a result, the exciton binding energy (Ebn=1 and Ebn=2) decreases with layer number (bottom inset). The 1s-excitonic state locates at 1.88  eV [obtained from the linear absorption spectra in Fig. 1(e)] and is independent of the layer number. Here, n is the principal quantum number in the non-hydrogen model. Top inset: increase of the dielectric parameter (εn=1, εn=2) with layers. The dashed lines are intended as a visual guide.
Fig. 5.
Fig. 5. Green circles represent the TPA coefficients of 25L MoS2 obtained at different excitation photon energies. The peak at 1.21  eV is ascribed to the sub-band resonance in the conduction band. (Inset: schematic of two-photon resonant transition from valence band to a sub-band in the conduction band.) The dashed-dotted line is intended as a visual guide.
Fig. 6.
Fig. 6. Spectrum of the femtosecond laser pulse in the nonlinear optical measurements.
Fig. 7.
Fig. 7. Identification of the size of laser beam spot in our nonlinear optical measurements; the radius is 5  μm.
Fig. 8.
Fig. 8. AFM images of few-layer and multilayer MoS2.
Fig. 9.
Fig. 9. Complete micro-I-scan fitting results of monolayer, few-layer, and multilayer MoS2, according to the homogeneously broadened TPA model.
Fig. 10.
Fig. 10. Schematic diagram of the setup of micro-intensity scan.

Tables (2)

Tables Icon

Table 1. Complete Parameters of Thickness and NLO Coefficients

Tables Icon

Table 2. Dielectric Parameters (εn=1, εn=2), Quasiparticle Bandgap Eg, Energy Level, and Binding Energy for n=1 and n=2 Excitonic States from Monolayer to Multilayer

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

dI(z)dz=αIβ(I)I2(z).
I(r,t)=I0·exp(2r2wp2)·exp(t2τp2),
β(I)=β01+(I/Isat)2,
Eb(n)=μe422εn2(n12)2=EgEn,
εn=12[1+1+32παμ9n(n1)+3].
β(2ω)=2ωI2W(2ω)=2ωI2W0δ(2ωE2p),
β0=KEpF(2ω/Eg)n02Eg3,
F(2ω/Eg)=(2ω/Eg1)3/2(2ω/Eg)5.
Eb(1)=EgEn=1=2.7591.88=0.879eV,ε1=2.8,
εn=12[1+1+32παμ9n(n1)+3],
Eb(n)=μe422εn2(n12)2.

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