Abstract

Cooperative effects allow for fascinating characteristics in light–matter interacting systems. Here, we study naturally occurring superradiant coupling in a class of quasi–two-dimensional, layered semiconductor systems. We perform optical absorption experiments of the lowest exciton for transition-metal dichalcogenides with different numbers of atomic layers. We examine two representative materials, MoSe2 and WSe2, using incoherent broadband white light. The measured transmission at the A exciton resonance does not saturate for optically thick samples consisting of hundreds of atomic layers, and the transmission varies nonmonotonously with the layer number. A self-consistent microscopic calculation reproduces the experimental observations, clearly identifying superradiant coupling effects as the origin of this unexpected behavior.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. M. Ye, D. Winslow, D. Zhang, R. Pandey, and Y. K. Yap, “Recent advancement on the optical properties of two-dimensional molybdenum disulfide (MoS2) thin films,” Photonics 2, 288–307 (2015).
    [Crossref]
  2. A. Arora, M. Drüppel, R. Schmidt, T. Deilmann, R. Schneider, M. R. Molas, P. Marauhn, S. Michaelis de Vasconcellos, M. Potemski, M. Rohlfing, and R. Bratschitsch, “Interlayer excitons in a bulk van der Waals semiconductor,” Nat. Commun. 8, 639 (2017).
    [Crossref]
  3. J. Horng, T. Stroucken, L. Zhang, E. Y. Paik, H. Deng, and S. W. Koch, “Observation of inter-layer excitons in MoSe2 single crystals,” arXiv:1712.04485 (2017).
  4. R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954).
    [Crossref]
  5. J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112, 1555–1567 (1958).
    [Crossref]
  6. L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–645 (1991).
    [Crossref]
  7. D. Citrin, “Homogeneous-linewidth effects on radiative lifetimes of excitons in quantum wells,” Solid State Commun. 84, 281–284 (1992).
    [Crossref]
  8. E. Ivchenko, A. Nesvizhskii, and S. Jorda, “Resonant Bragg reflection from quantum-well structures,” Superlattices Microstruct. 16, 17–20 (1994).
    [Crossref]
  9. T. Stroucken, A. Knorr, P. Thomas, and S. W. Koch, “Coherent dynamics of radiatively coupled quantum-well excitons,” Phys. Rev. B 53, 2026–2033 (1996).
    [Crossref]
  10. M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
    [Crossref]
  11. 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]
  12. P. Back, S. Zeytinoglu, A. Ijaz, M. Kroner, and A. Imamoğlu, “Realization of an electrically tunable narrow-bandwidth atomically thin mirror using monolayer MoSe2,” Phys. Rev. Lett. 120, 037401 (2018).
    [Crossref]
  13. G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride,” Phys. Rev. Lett. 120, 037402 (2018).
    [Crossref]
  14. A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Magnetoreflection spectroscopy of monolayer transition-metal dichalcogenide semiconductors in pulsed magnetic fields,” J. Vac. Sci. Technol. B 34, 04J102 (2016).
    [Crossref]
  15. A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Exciton diamagnetic shifts and valley Zeeman effects in monolayer WS2 and MoS2 to 65 Tesla,” Nat. Commun. 7, 10643 (2016).
    [Crossref]
  16. L. Meckbach, T. Stroucken, and S. W. Koch, “Influence of the effective layer thickness on the ground-state and excitonic properties of transition-metal dichalcogenide systems,” Phys. Rev. B 97, 035425 (2018).
    [Crossref]
  17. D. Xiao, G.-B. 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, 196802 (2012).
    [Crossref]
  18. R. K. Ghosh and S. Mahapatra, “Monolayer transition metal dichalcogenide channel-based tunnel transistor,” IEEE J. Electron Devices Soc. 1, 175–180 (2013).
    [Crossref]
  19. Q. Ouyang, S. Zeng, L. Jiang, L. Hong, G. Xu, X.-Q. Dinh, J. Qian, S. He, J. Qu, P. Coquet, and K.-T. Yong, “Sensitivity enhancement of transition metal dichalcogenides silicon nanostructure-based surface plasmon resonance biosensor,” Sci. Rep. 6, 28190 (2016).
    [Crossref]
  20. J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
    [Crossref]

2018 (3)

P. Back, S. Zeytinoglu, A. Ijaz, M. Kroner, and A. Imamoğlu, “Realization of an electrically tunable narrow-bandwidth atomically thin mirror using monolayer MoSe2,” Phys. Rev. Lett. 120, 037401 (2018).
[Crossref]

G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride,” Phys. Rev. Lett. 120, 037402 (2018).
[Crossref]

L. Meckbach, T. Stroucken, and S. W. Koch, “Influence of the effective layer thickness on the ground-state and excitonic properties of transition-metal dichalcogenide systems,” Phys. Rev. B 97, 035425 (2018).
[Crossref]

2017 (1)

A. Arora, M. Drüppel, R. Schmidt, T. Deilmann, R. Schneider, M. R. Molas, P. Marauhn, S. Michaelis de Vasconcellos, M. Potemski, M. Rohlfing, and R. Bratschitsch, “Interlayer excitons in a bulk van der Waals semiconductor,” Nat. Commun. 8, 639 (2017).
[Crossref]

2016 (3)

A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Magnetoreflection spectroscopy of monolayer transition-metal dichalcogenide semiconductors in pulsed magnetic fields,” J. Vac. Sci. Technol. B 34, 04J102 (2016).
[Crossref]

A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Exciton diamagnetic shifts and valley Zeeman effects in monolayer WS2 and MoS2 to 65 Tesla,” Nat. Commun. 7, 10643 (2016).
[Crossref]

Q. Ouyang, S. Zeng, L. Jiang, L. Hong, G. Xu, X.-Q. Dinh, J. Qian, S. He, J. Qu, P. Coquet, and K.-T. Yong, “Sensitivity enhancement of transition metal dichalcogenides silicon nanostructure-based surface plasmon resonance biosensor,” Sci. Rep. 6, 28190 (2016).
[Crossref]

2015 (1)

M. Ye, D. Winslow, D. Zhang, R. Pandey, and Y. K. Yap, “Recent advancement on the optical properties of two-dimensional molybdenum disulfide (MoS2) thin films,” Photonics 2, 288–307 (2015).
[Crossref]

2014 (1)

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

2013 (1)

R. K. Ghosh and S. Mahapatra, “Monolayer transition metal dichalcogenide channel-based tunnel transistor,” IEEE J. Electron Devices Soc. 1, 175–180 (2013).
[Crossref]

2012 (1)

D. Xiao, G.-B. 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, 196802 (2012).
[Crossref]

2010 (1)

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]

1996 (2)

T. Stroucken, A. Knorr, P. Thomas, and S. W. Koch, “Coherent dynamics of radiatively coupled quantum-well excitons,” Phys. Rev. B 53, 2026–2033 (1996).
[Crossref]

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref]

1994 (1)

E. Ivchenko, A. Nesvizhskii, and S. Jorda, “Resonant Bragg reflection from quantum-well structures,” Superlattices Microstruct. 16, 17–20 (1994).
[Crossref]

1992 (1)

D. Citrin, “Homogeneous-linewidth effects on radiative lifetimes of excitons in quantum wells,” Solid State Commun. 84, 281–284 (1992).
[Crossref]

1991 (1)

L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–645 (1991).
[Crossref]

1958 (1)

J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112, 1555–1567 (1958).
[Crossref]

1954 (1)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954).
[Crossref]

Andreani, L. C.

L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–645 (1991).
[Crossref]

Arora, A.

A. Arora, M. Drüppel, R. Schmidt, T. Deilmann, R. Schneider, M. R. Molas, P. Marauhn, S. Michaelis de Vasconcellos, M. Potemski, M. Rohlfing, and R. Bratschitsch, “Interlayer excitons in a bulk van der Waals semiconductor,” Nat. Commun. 8, 639 (2017).
[Crossref]

Back, P.

P. Back, S. Zeytinoglu, A. Ijaz, M. Kroner, and A. Imamoğlu, “Realization of an electrically tunable narrow-bandwidth atomically thin mirror using monolayer MoSe2,” Phys. Rev. Lett. 120, 037401 (2018).
[Crossref]

Bahramy, M. S.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

Balasubramanian, T.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

Bassani, F.

L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–645 (1991).
[Crossref]

Bawden, L.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

Bratschitsch, R.

A. Arora, M. Drüppel, R. Schmidt, T. Deilmann, R. Schneider, M. R. Molas, P. Marauhn, S. Michaelis de Vasconcellos, M. Potemski, M. Rohlfing, and R. Bratschitsch, “Interlayer excitons in a bulk van der Waals semiconductor,” Nat. Commun. 8, 639 (2017).
[Crossref]

Citrin, D.

D. Citrin, “Homogeneous-linewidth effects on radiative lifetimes of excitons in quantum wells,” Solid State Commun. 84, 281–284 (1992).
[Crossref]

Coquet, P.

Q. Ouyang, S. Zeng, L. Jiang, L. Hong, G. Xu, X.-Q. Dinh, J. Qian, S. He, J. Qu, P. Coquet, and K.-T. Yong, “Sensitivity enhancement of transition metal dichalcogenides silicon nanostructure-based surface plasmon resonance biosensor,” Sci. Rep. 6, 28190 (2016).
[Crossref]

Crooker, S. A.

A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Magnetoreflection spectroscopy of monolayer transition-metal dichalcogenide semiconductors in pulsed magnetic fields,” J. Vac. Sci. Technol. B 34, 04J102 (2016).
[Crossref]

A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Exciton diamagnetic shifts and valley Zeeman effects in monolayer WS2 and MoS2 to 65 Tesla,” Nat. Commun. 7, 10643 (2016).
[Crossref]

De Greve, K.

G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride,” Phys. Rev. Lett. 120, 037402 (2018).
[Crossref]

Deilmann, T.

A. Arora, M. Drüppel, R. Schmidt, T. Deilmann, R. Schneider, M. R. Molas, P. Marauhn, S. Michaelis de Vasconcellos, M. Potemski, M. Rohlfing, and R. Bratschitsch, “Interlayer excitons in a bulk van der Waals semiconductor,” Nat. Commun. 8, 639 (2017).
[Crossref]

Dendzik, M.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

Deng, H.

J. Horng, T. Stroucken, L. Zhang, E. Y. Paik, H. Deng, and S. W. Koch, “Observation of inter-layer excitons in MoSe2 single crystals,” arXiv:1712.04485 (2017).

Dicke, R. H.

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954).
[Crossref]

Dinh, X.-Q.

Q. Ouyang, S. Zeng, L. Jiang, L. Hong, G. Xu, X.-Q. Dinh, J. Qian, S. He, J. Qu, P. Coquet, and K.-T. Yong, “Sensitivity enhancement of transition metal dichalcogenides silicon nanostructure-based surface plasmon resonance biosensor,” Sci. Rep. 6, 28190 (2016).
[Crossref]

Drüppel, M.

A. Arora, M. Drüppel, R. Schmidt, T. Deilmann, R. Schneider, M. R. Molas, P. Marauhn, S. Michaelis de Vasconcellos, M. Potemski, M. Rohlfing, and R. Bratschitsch, “Interlayer excitons in a bulk van der Waals semiconductor,” Nat. Commun. 8, 639 (2017).
[Crossref]

Feng, W.

D. Xiao, G.-B. 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, 196802 (2012).
[Crossref]

Ghosh, R. K.

R. K. Ghosh and S. Mahapatra, “Monolayer transition metal dichalcogenide channel-based tunnel transistor,” IEEE J. Electron Devices Soc. 1, 175–180 (2013).
[Crossref]

Granerod, C.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

He, S.

Q. Ouyang, S. Zeng, L. Jiang, L. Hong, G. Xu, X.-Q. Dinh, J. Qian, S. He, J. Qu, P. Coquet, and K.-T. Yong, “Sensitivity enhancement of transition metal dichalcogenides silicon nanostructure-based surface plasmon resonance biosensor,” Sci. Rep. 6, 28190 (2016).
[Crossref]

Heinz, T. F.

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]

Hey, R.

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref]

High, A. A.

G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride,” Phys. Rev. Lett. 120, 037402 (2018).
[Crossref]

Hoesch, M.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

Hofmann, P.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

Hone, J.

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]

Hong, L.

Q. Ouyang, S. Zeng, L. Jiang, L. Hong, G. Xu, X.-Q. Dinh, J. Qian, S. He, J. Qu, P. Coquet, and K.-T. Yong, “Sensitivity enhancement of transition metal dichalcogenides silicon nanostructure-based surface plasmon resonance biosensor,” Sci. Rep. 6, 28190 (2016).
[Crossref]

Hopfield, J. J.

J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112, 1555–1567 (1958).
[Crossref]

Horng, J.

J. Horng, T. Stroucken, L. Zhang, E. Y. Paik, H. Deng, and S. W. Koch, “Observation of inter-layer excitons in MoSe2 single crystals,” arXiv:1712.04485 (2017).

Hübner, M.

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref]

Ijaz, A.

P. Back, S. Zeytinoglu, A. Ijaz, M. Kroner, and A. Imamoğlu, “Realization of an electrically tunable narrow-bandwidth atomically thin mirror using monolayer MoSe2,” Phys. Rev. Lett. 120, 037401 (2018).
[Crossref]

Imamoglu, A.

P. Back, S. Zeytinoglu, A. Ijaz, M. Kroner, and A. Imamoğlu, “Realization of an electrically tunable narrow-bandwidth atomically thin mirror using monolayer MoSe2,” Phys. Rev. Lett. 120, 037401 (2018).
[Crossref]

Ivchenko, E.

E. Ivchenko, A. Nesvizhskii, and S. Jorda, “Resonant Bragg reflection from quantum-well structures,” Superlattices Microstruct. 16, 17–20 (1994).
[Crossref]

Jauregui, L. A.

G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride,” Phys. Rev. Lett. 120, 037402 (2018).
[Crossref]

Jiang, L.

Q. Ouyang, S. Zeng, L. Jiang, L. Hong, G. Xu, X.-Q. Dinh, J. Qian, S. He, J. Qu, P. Coquet, and K.-T. Yong, “Sensitivity enhancement of transition metal dichalcogenides silicon nanostructure-based surface plasmon resonance biosensor,” Sci. Rep. 6, 28190 (2016).
[Crossref]

Jonker, B. T.

A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Exciton diamagnetic shifts and valley Zeeman effects in monolayer WS2 and MoS2 to 65 Tesla,” Nat. Commun. 7, 10643 (2016).
[Crossref]

A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Magnetoreflection spectroscopy of monolayer transition-metal dichalcogenide semiconductors in pulsed magnetic fields,” J. Vac. Sci. Technol. B 34, 04J102 (2016).
[Crossref]

Jorda, S.

E. Ivchenko, A. Nesvizhskii, and S. Jorda, “Resonant Bragg reflection from quantum-well structures,” Superlattices Microstruct. 16, 17–20 (1994).
[Crossref]

Kim, P.

G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride,” Phys. Rev. Lett. 120, 037402 (2018).
[Crossref]

Kim, T. K.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

King, P. D. C.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

Knorr, A.

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref]

T. Stroucken, A. Knorr, P. Thomas, and S. W. Koch, “Coherent dynamics of radiatively coupled quantum-well excitons,” Phys. Rev. B 53, 2026–2033 (1996).
[Crossref]

Koch, S. W.

L. Meckbach, T. Stroucken, and S. W. Koch, “Influence of the effective layer thickness on the ground-state and excitonic properties of transition-metal dichalcogenide systems,” Phys. Rev. B 97, 035425 (2018).
[Crossref]

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref]

T. Stroucken, A. Knorr, P. Thomas, and S. W. Koch, “Coherent dynamics of radiatively coupled quantum-well excitons,” Phys. Rev. B 53, 2026–2033 (1996).
[Crossref]

J. Horng, T. Stroucken, L. Zhang, E. Y. Paik, H. Deng, and S. W. Koch, “Observation of inter-layer excitons in MoSe2 single crystals,” arXiv:1712.04485 (2017).

Kono, J.

A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Magnetoreflection spectroscopy of monolayer transition-metal dichalcogenide semiconductors in pulsed magnetic fields,” J. Vac. Sci. Technol. B 34, 04J102 (2016).
[Crossref]

A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Exciton diamagnetic shifts and valley Zeeman effects in monolayer WS2 and MoS2 to 65 Tesla,” Nat. Commun. 7, 10643 (2016).
[Crossref]

Kroner, M.

P. Back, S. Zeytinoglu, A. Ijaz, M. Kroner, and A. Imamoğlu, “Realization of an electrically tunable narrow-bandwidth atomically thin mirror using monolayer MoSe2,” Phys. Rev. Lett. 120, 037401 (2018).
[Crossref]

Kuhl, J.

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref]

Leandersson, M.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

Lee, C.

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]

Liu, G.-B.

D. Xiao, G.-B. 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, 196802 (2012).
[Crossref]

Lukin, M. D.

G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride,” Phys. Rev. Lett. 120, 037402 (2018).
[Crossref]

Mahapatra, S.

R. K. Ghosh and S. Mahapatra, “Monolayer transition metal dichalcogenide channel-based tunnel transistor,” IEEE J. Electron Devices Soc. 1, 175–180 (2013).
[Crossref]

Mak, K. F.

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]

Marauhn, P.

A. Arora, M. Drüppel, R. Schmidt, T. Deilmann, R. Schneider, M. R. Molas, P. Marauhn, S. Michaelis de Vasconcellos, M. Potemski, M. Rohlfing, and R. Bratschitsch, “Interlayer excitons in a bulk van der Waals semiconductor,” Nat. Commun. 8, 639 (2017).
[Crossref]

Mazzola, F.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

McCreary, K. M.

A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Magnetoreflection spectroscopy of monolayer transition-metal dichalcogenide semiconductors in pulsed magnetic fields,” J. Vac. Sci. Technol. B 34, 04J102 (2016).
[Crossref]

A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Exciton diamagnetic shifts and valley Zeeman effects in monolayer WS2 and MoS2 to 65 Tesla,” Nat. Commun. 7, 10643 (2016).
[Crossref]

Meckbach, L.

L. Meckbach, T. Stroucken, and S. W. Koch, “Influence of the effective layer thickness on the ground-state and excitonic properties of transition-metal dichalcogenide systems,” Phys. Rev. B 97, 035425 (2018).
[Crossref]

Meevasana, W.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

Michaelis de Vasconcellos, S.

A. Arora, M. Drüppel, R. Schmidt, T. Deilmann, R. Schneider, M. R. Molas, P. Marauhn, S. Michaelis de Vasconcellos, M. Potemski, M. Rohlfing, and R. Bratschitsch, “Interlayer excitons in a bulk van der Waals semiconductor,” Nat. Commun. 8, 639 (2017).
[Crossref]

Michiardi, M.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

Molas, M. R.

A. Arora, M. Drüppel, R. Schmidt, T. Deilmann, R. Schneider, M. R. Molas, P. Marauhn, S. Michaelis de Vasconcellos, M. Potemski, M. Rohlfing, and R. Bratschitsch, “Interlayer excitons in a bulk van der Waals semiconductor,” Nat. Commun. 8, 639 (2017).
[Crossref]

Nesvizhskii, A.

E. Ivchenko, A. Nesvizhskii, and S. Jorda, “Resonant Bragg reflection from quantum-well structures,” Superlattices Microstruct. 16, 17–20 (1994).
[Crossref]

Ouyang, Q.

Q. Ouyang, S. Zeng, L. Jiang, L. Hong, G. Xu, X.-Q. Dinh, J. Qian, S. He, J. Qu, P. Coquet, and K.-T. Yong, “Sensitivity enhancement of transition metal dichalcogenides silicon nanostructure-based surface plasmon resonance biosensor,” Sci. Rep. 6, 28190 (2016).
[Crossref]

Paik, E. Y.

J. Horng, T. Stroucken, L. Zhang, E. Y. Paik, H. Deng, and S. W. Koch, “Observation of inter-layer excitons in MoSe2 single crystals,” arXiv:1712.04485 (2017).

Pandey, R.

M. Ye, D. Winslow, D. Zhang, R. Pandey, and Y. K. Yap, “Recent advancement on the optical properties of two-dimensional molybdenum disulfide (MoS2) thin films,” Photonics 2, 288–307 (2015).
[Crossref]

Park, H.

G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride,” Phys. Rev. Lett. 120, 037402 (2018).
[Crossref]

Ploog, K.

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref]

Potemski, M.

A. Arora, M. Drüppel, R. Schmidt, T. Deilmann, R. Schneider, M. R. Molas, P. Marauhn, S. Michaelis de Vasconcellos, M. Potemski, M. Rohlfing, and R. Bratschitsch, “Interlayer excitons in a bulk van der Waals semiconductor,” Nat. Commun. 8, 639 (2017).
[Crossref]

Qian, J.

Q. Ouyang, S. Zeng, L. Jiang, L. Hong, G. Xu, X.-Q. Dinh, J. Qian, S. He, J. Qu, P. Coquet, and K.-T. Yong, “Sensitivity enhancement of transition metal dichalcogenides silicon nanostructure-based surface plasmon resonance biosensor,” Sci. Rep. 6, 28190 (2016).
[Crossref]

Qu, J.

Q. Ouyang, S. Zeng, L. Jiang, L. Hong, G. Xu, X.-Q. Dinh, J. Qian, S. He, J. Qu, P. Coquet, and K.-T. Yong, “Sensitivity enhancement of transition metal dichalcogenides silicon nanostructure-based surface plasmon resonance biosensor,” Sci. Rep. 6, 28190 (2016).
[Crossref]

Riley, J. M.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

Rohlfing, M.

A. Arora, M. Drüppel, R. Schmidt, T. Deilmann, R. Schneider, M. R. Molas, P. Marauhn, S. Michaelis de Vasconcellos, M. Potemski, M. Rohlfing, and R. Bratschitsch, “Interlayer excitons in a bulk van der Waals semiconductor,” Nat. Commun. 8, 639 (2017).
[Crossref]

Schmidt, R.

A. Arora, M. Drüppel, R. Schmidt, T. Deilmann, R. Schneider, M. R. Molas, P. Marauhn, S. Michaelis de Vasconcellos, M. Potemski, M. Rohlfing, and R. Bratschitsch, “Interlayer excitons in a bulk van der Waals semiconductor,” Nat. Commun. 8, 639 (2017).
[Crossref]

Schneider, R.

A. Arora, M. Drüppel, R. Schmidt, T. Deilmann, R. Schneider, M. R. Molas, P. Marauhn, S. Michaelis de Vasconcellos, M. Potemski, M. Rohlfing, and R. Bratschitsch, “Interlayer excitons in a bulk van der Waals semiconductor,” Nat. Commun. 8, 639 (2017).
[Crossref]

Scuri, G.

G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride,” Phys. Rev. Lett. 120, 037402 (2018).
[Crossref]

Shan, J.

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]

Shu, C.

G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride,” Phys. Rev. Lett. 120, 037402 (2018).
[Crossref]

Stier, A. V.

A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Magnetoreflection spectroscopy of monolayer transition-metal dichalcogenide semiconductors in pulsed magnetic fields,” J. Vac. Sci. Technol. B 34, 04J102 (2016).
[Crossref]

A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Exciton diamagnetic shifts and valley Zeeman effects in monolayer WS2 and MoS2 to 65 Tesla,” Nat. Commun. 7, 10643 (2016).
[Crossref]

Stroucken, T.

L. Meckbach, T. Stroucken, and S. W. Koch, “Influence of the effective layer thickness on the ground-state and excitonic properties of transition-metal dichalcogenide systems,” Phys. Rev. B 97, 035425 (2018).
[Crossref]

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref]

T. Stroucken, A. Knorr, P. Thomas, and S. W. Koch, “Coherent dynamics of radiatively coupled quantum-well excitons,” Phys. Rev. B 53, 2026–2033 (1996).
[Crossref]

J. Horng, T. Stroucken, L. Zhang, E. Y. Paik, H. Deng, and S. W. Koch, “Observation of inter-layer excitons in MoSe2 single crystals,” arXiv:1712.04485 (2017).

Takagi, H.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

Takayama, T.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

Taniguchi, T.

G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride,” Phys. Rev. Lett. 120, 037402 (2018).
[Crossref]

Tassone, F.

L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–645 (1991).
[Crossref]

Thomas, P.

T. Stroucken, A. Knorr, P. Thomas, and S. W. Koch, “Coherent dynamics of radiatively coupled quantum-well excitons,” Phys. Rev. B 53, 2026–2033 (1996).
[Crossref]

Watanabe, K.

G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride,” Phys. Rev. Lett. 120, 037402 (2018).
[Crossref]

Wells, J. W.

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

Wild, D. S.

G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride,” Phys. Rev. Lett. 120, 037402 (2018).
[Crossref]

Winslow, D.

M. Ye, D. Winslow, D. Zhang, R. Pandey, and Y. K. Yap, “Recent advancement on the optical properties of two-dimensional molybdenum disulfide (MoS2) thin films,” Photonics 2, 288–307 (2015).
[Crossref]

Xiao, D.

D. Xiao, G.-B. 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, 196802 (2012).
[Crossref]

Xu, G.

Q. Ouyang, S. Zeng, L. Jiang, L. Hong, G. Xu, X.-Q. Dinh, J. Qian, S. He, J. Qu, P. Coquet, and K.-T. Yong, “Sensitivity enhancement of transition metal dichalcogenides silicon nanostructure-based surface plasmon resonance biosensor,” Sci. Rep. 6, 28190 (2016).
[Crossref]

Xu, X.

D. Xiao, G.-B. 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, 196802 (2012).
[Crossref]

Yao, W.

D. Xiao, G.-B. 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, 196802 (2012).
[Crossref]

Yap, Y. K.

M. Ye, D. Winslow, D. Zhang, R. Pandey, and Y. K. Yap, “Recent advancement on the optical properties of two-dimensional molybdenum disulfide (MoS2) thin films,” Photonics 2, 288–307 (2015).
[Crossref]

Ye, M.

M. Ye, D. Winslow, D. Zhang, R. Pandey, and Y. K. Yap, “Recent advancement on the optical properties of two-dimensional molybdenum disulfide (MoS2) thin films,” Photonics 2, 288–307 (2015).
[Crossref]

Yong, K.-T.

Q. Ouyang, S. Zeng, L. Jiang, L. Hong, G. Xu, X.-Q. Dinh, J. Qian, S. He, J. Qu, P. Coquet, and K.-T. Yong, “Sensitivity enhancement of transition metal dichalcogenides silicon nanostructure-based surface plasmon resonance biosensor,” Sci. Rep. 6, 28190 (2016).
[Crossref]

Zeng, S.

Q. Ouyang, S. Zeng, L. Jiang, L. Hong, G. Xu, X.-Q. Dinh, J. Qian, S. He, J. Qu, P. Coquet, and K.-T. Yong, “Sensitivity enhancement of transition metal dichalcogenides silicon nanostructure-based surface plasmon resonance biosensor,” Sci. Rep. 6, 28190 (2016).
[Crossref]

Zeytinoglu, S.

P. Back, S. Zeytinoglu, A. Ijaz, M. Kroner, and A. Imamoğlu, “Realization of an electrically tunable narrow-bandwidth atomically thin mirror using monolayer MoSe2,” Phys. Rev. Lett. 120, 037401 (2018).
[Crossref]

Zhang, D.

M. Ye, D. Winslow, D. Zhang, R. Pandey, and Y. K. Yap, “Recent advancement on the optical properties of two-dimensional molybdenum disulfide (MoS2) thin films,” Photonics 2, 288–307 (2015).
[Crossref]

Zhang, L.

J. Horng, T. Stroucken, L. Zhang, E. Y. Paik, H. Deng, and S. W. Koch, “Observation of inter-layer excitons in MoSe2 single crystals,” arXiv:1712.04485 (2017).

Zhou, Y.

G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride,” Phys. Rev. Lett. 120, 037402 (2018).
[Crossref]

IEEE J. Electron Devices Soc. (1)

R. K. Ghosh and S. Mahapatra, “Monolayer transition metal dichalcogenide channel-based tunnel transistor,” IEEE J. Electron Devices Soc. 1, 175–180 (2013).
[Crossref]

J. Vac. Sci. Technol. B (1)

A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Magnetoreflection spectroscopy of monolayer transition-metal dichalcogenide semiconductors in pulsed magnetic fields,” J. Vac. Sci. Technol. B 34, 04J102 (2016).
[Crossref]

Nat. Commun. (2)

A. V. Stier, K. M. McCreary, B. T. Jonker, J. Kono, and S. A. Crooker, “Exciton diamagnetic shifts and valley Zeeman effects in monolayer WS2 and MoS2 to 65 Tesla,” Nat. Commun. 7, 10643 (2016).
[Crossref]

A. Arora, M. Drüppel, R. Schmidt, T. Deilmann, R. Schneider, M. R. Molas, P. Marauhn, S. Michaelis de Vasconcellos, M. Potemski, M. Rohlfing, and R. Bratschitsch, “Interlayer excitons in a bulk van der Waals semiconductor,” Nat. Commun. 8, 639 (2017).
[Crossref]

Nat. Phys. (1)

J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Granerod, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, “Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor,” Nat. Phys. 10, 835–839 (2014).
[Crossref]

Photonics (1)

M. Ye, D. Winslow, D. Zhang, R. Pandey, and Y. K. Yap, “Recent advancement on the optical properties of two-dimensional molybdenum disulfide (MoS2) thin films,” Photonics 2, 288–307 (2015).
[Crossref]

Phys. Rev. (2)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954).
[Crossref]

J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112, 1555–1567 (1958).
[Crossref]

Phys. Rev. B (2)

T. Stroucken, A. Knorr, P. Thomas, and S. W. Koch, “Coherent dynamics of radiatively coupled quantum-well excitons,” Phys. Rev. B 53, 2026–2033 (1996).
[Crossref]

L. Meckbach, T. Stroucken, and S. W. Koch, “Influence of the effective layer thickness on the ground-state and excitonic properties of transition-metal dichalcogenide systems,” Phys. Rev. B 97, 035425 (2018).
[Crossref]

Phys. Rev. Lett. (5)

D. Xiao, G.-B. 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, 196802 (2012).
[Crossref]

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref]

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]

P. Back, S. Zeytinoglu, A. Ijaz, M. Kroner, and A. Imamoğlu, “Realization of an electrically tunable narrow-bandwidth atomically thin mirror using monolayer MoSe2,” Phys. Rev. Lett. 120, 037401 (2018).
[Crossref]

G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, “Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride,” Phys. Rev. Lett. 120, 037402 (2018).
[Crossref]

Sci. Rep. (1)

Q. Ouyang, S. Zeng, L. Jiang, L. Hong, G. Xu, X.-Q. Dinh, J. Qian, S. He, J. Qu, P. Coquet, and K.-T. Yong, “Sensitivity enhancement of transition metal dichalcogenides silicon nanostructure-based surface plasmon resonance biosensor,” Sci. Rep. 6, 28190 (2016).
[Crossref]

Solid State Commun. (2)

L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–645 (1991).
[Crossref]

D. Citrin, “Homogeneous-linewidth effects on radiative lifetimes of excitons in quantum wells,” Solid State Commun. 84, 281–284 (1992).
[Crossref]

Superlattices Microstruct. (1)

E. Ivchenko, A. Nesvizhskii, and S. Jorda, “Resonant Bragg reflection from quantum-well structures,” Superlattices Microstruct. 16, 17–20 (1994).
[Crossref]

Other (1)

J. Horng, T. Stroucken, L. Zhang, E. Y. Paik, H. Deng, and S. W. Koch, “Observation of inter-layer excitons in MoSe2 single crystals,” arXiv:1712.04485 (2017).

Supplementary Material (1)

NameDescription
» Supplement 1       All the atomic force microscopy (AFM) measurements, thickness measurements, and all the transmission, reflection, and absorption spectra for both materials (experiment and theory).

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Figures (5)

Fig. 1.
Fig. 1. (a) Experimental setup. The exfoliated samples are held at 5 K inside a cryostat designed for simultaneous measurement of the transmitted and reflected light. The broadband white light is focused on the sample via a 50× microscope objective and collected on the other side by a second microscope objective. The reflected and transmitted light are dispersed by the spectrometer and collected by the CCD detector. A flip mirror is used to switch between the transmitted and reflected light paths. (b) Schematic of the light propagation through the samples.
Fig. 2.
Fig. 2. Quantitative optical density at the exciton absorption energy for (Top) MoSe2 and (Bottom) WSe2 as a function of the number of layers. The blue circles are the measured optical density values. The green solid lines show the theoretically computed peak absorptions for the full geometry, and the red dashed lines show the absorption in a superradiant (SR) geometry where the interlayer spacing has been artificially set to zero. The blue dashed-dotted lines show the extinction of the transmitted intensity (1-peak transmission). For comparison, we also show the expected extinction of the transmitted intensity assuming Beer’s law, once based on monolayer extinction on a quartz substrate (short-dashed) and once based on the extinction of a monolayer embedded in a dielectric with the dielectric constant of the parent bulk material. Radiative coupling is needed in the theoretical calculations (green solid line) in order to reproduce the experimentally observed light propagation as a function of layer thickness, which deviates drastically from the curves calculated using Beer’s law (dark yellow and brown dashed lines).
Fig. 3.
Fig. 3. (a) Calculated transmission of a single MoSe2 layer embedded in bulk (blue curve) and of a monolayer with the same linear susceptibility on a BK7 substrate. (b) Comparison of the absorption per layer to the layer absorption in a superradiant geometry for different sample thicknesses. The solid lines show the calculated layer absorption of MoSe2 on a BK7 substrate, computed for the full geometry. The dashed lines show the corresponding results in a superradiant geometry, i.e., neglecting the spacing between different layers in the wave equation. All spectra have been calculated using a nonradiative homogenous linewidth of 15 meV for the A exciton series and 25 meV for the B exciton series.
Fig. 4.
Fig. 4. (a) Energy position of the A exciton in WSe2 as a function of magnetic field strength up +60  T (blue squares) and up to 60  T esla (red squares). (b) Obtained diamagnetic shift for the A exciton in WSe2 (yellow squares). The dashed line is a quadratic fitting. (c) Energy position of the A exciton in MoSe2 as a function of magnetic field strength up +60  T (blue squares) and up to 60  T (red squares). (d) Obtained diamagnetic shift for the A exciton in MoSe2 (yellow squares). The dashed line is a quadratic fitting.
Fig. 5.
Fig. 5. Experimental and calculated absorption spectra for (Left) MoSe2 and (Right) WSe2 for different sample thicknesses (number of layers).

Equations (9)

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D=εE+εEzez+4πP,
(z2ε(z)ω2c2)ET(z,ω)=4πω2c2PT(ω),
(εz2+εq2)ϕ(q,z)=4π(ρ·PL),
P=nPnδ(zzn),
ET(zn,ω)=Ein(zn,ω)+4πω2c2mG0(zn,zm,ω)PmT(ω),
t(ω)=nT(nT+nB)/22πiωcχ(ω),r(ω)=t(ω)1.
α(ω)=4πnTωcIm[χT(ω)]|(nT+nB)/22πiωcχT(ω)|2.
kz2=ω2c2(ε+4πχT(ω)/d),
I(ω,z)=I0(ω)eα(ω)z