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Biexcitonic optical Stark effects in monolayer molybdenum diselenide


Floquet states, where a periodic optical field coherently drives electrons in solids1,2,3, can enable novel quantum states of matter4,5,6. A prominent approach to realize Floquet states is based on the optical Stark effect. Previous studies on the optical Stark effect often treated the excited state in solids as free quasi-particles3,7,8,9,10,11,12. However, exciton–exciton interactions can be sizeably enhanced in low-dimensional systems and may lead to light–matter interactions that are qualitatively different from those in the non-interacting picture. Here we use monolayer molybdenum diselenide (MoSe2) as a model system to demonstrate that the driving optical field can couple a hierarchy of excitonic states, and the many-body inter-valley biexciton state plays a dominant role in the optical Stark effect. Specifically, the exciton–biexciton coupling in monolayer MoSe2 breaks down the valley selection rules based on the non-interacting exciton picture. The photon-dressed excitonic states exhibit an energy redshift, splitting or blueshift as the driving photon frequency varies below the exciton transition. We determine a binding energy of 21 meV for the inter-valley biexciton and a transition dipole moment of 9.3 debye for the exciton–biexciton transition. Our study reveals the crucial role of many-body effects in coherent light–matter interaction in atomically thin two-dimensional materials.

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Fig. 1: Schematic diagrams of optical transition in MoSe2.
Fig. 2: Valley-dependent optical Stark effects.
Fig. 3: Biexcitonic coherent optical Stark effects.
Fig. 4: Anomalous optical Stark shift in the Kʹ valley.


  1. Shirley, J. H. Solution of the Schrödinger equation with a Hamiltonian periodic in time. Phys. Rev. 138, B979–B987 (1965).

    ADS  Article  Google Scholar 

  2. Autler, S. H. & Townes, C. H. Stark effect in rapidly varying fields. Phys. Rev. 100, 703–722 (1955).

    ADS  Article  Google Scholar 

  3. Galitskii, V. M., Goreslavskii, S. P. & Elesin, V. F. Electric and magnetic properties of a semiconductor in the field of a strong electromagnetic wave. J. Exp. Theor. Phys. 30, 117–122 (1970).

    ADS  Google Scholar 

  4. Gupta, J. A., Knobel, R., Samarth, N. & Awschalom, D. D. Ultrafast manipulation of electron spin coherence. Science 292, 2458–2461 (2001).

    ADS  Article  Google Scholar 

  5. Lindner, N. H., Refael, G. & Galitski, V. Floquet topological insulator in semiconductor quantum wells. Nat. Phys. 7, 490–495 (2011).

    Article  Google Scholar 

  6. Berezovsky, J., Mikkelsen, M. H., Stoltz, N. G., Coldren, L. A. & Awschalom, D. D. Picosecond coherent optical manipulation of a single electron spin in a quantum dot. Science 320, 349–352 (2008).

    ADS  Article  Google Scholar 

  7. Sie, E. J. et al. Valley-selective optical Stark effect in monolayer WS2. Nat. Mater. 14, 290–294 (2015).

    ADS  Article  Google Scholar 

  8. Kim, J. et al. Ultrafast generation of pseudo-magnetic field for valley excitons in WSe2 monolayers. Science 346, 1205–1208 (2014).

    ADS  Article  Google Scholar 

  9. Von Lehmen, A., Chemla, D. S., Heritage, J. P. & Zucker, J. E. Optical Stark effect on excitons in GaAs quantum wells. Opt. Lett. 11, 609–611 (1986).

    ADS  Article  Google Scholar 

  10. Cohen-Tannoudji, C. & Reynaud, S. Dressed-atom description of resonance fluorescence and absorption spectra of a multi-level atom in an intense laser beam. J. Phys. B 10, 345–363 (1977).

    ADS  Article  Google Scholar 

  11. De Giovannini, U., Hübener, H. & Rubio, A. Monitoring electron–photon dressing in WSe2. Nano Lett. 16, 7993–7998 (2016).

    ADS  Article  Google Scholar 

  12. Sie, E. J. et al. Large, valley-exclusive Bloch–Siegert shift in monolayer WS2. Science 355, 1066–1069 (2017).

    ADS  Article  Google Scholar 

  13. Cao, T. et al. Valley-selective circular dichroism of monolayer molybdenum disulphide. Nat. Commun. 3, 887–891 (2012).

    Article  Google Scholar 

  14. Xiao, D., Liu, G.-B., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics in monolayers of MoS2 and other Group-VI dichalcogenides. Phys. Rev. Lett. 108, 196802 (2012).

    ADS  Article  Google Scholar 

  15. Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys. 10, 343–350 (2014).

    Article  Google Scholar 

  16. Splendiani, A. et al. Emerging photoluminescence in monolayer MoS2. Nano Lett. 10, 1271–1275 (2010).

    ADS  Article  Google Scholar 

  17. Ugeda, M. M. et al. Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor. Nat. Mater. 13, 1091–1095 (2014).

    ADS  Article  Google Scholar 

  18. Zhang, D. K., Kidd, D. W. & Varga, K. Excited biexcitons in transition metal dichalcogenides. Nano Lett. 15, 7002–7005 (2015).

    ADS  Article  Google Scholar 

  19. Kylänpää, I. & Komsa, H.-P. Binding energies of exciton complexes in transition metal dichalcogenide monolayers and effect of dielectric environment. Phys. Rev. B 92, 205418 (2015).

    ADS  Article  Google Scholar 

  20. Mak, K. F., He, K., Shan, J. & Heinz, T. F. Control of valley polarization in monolayer MoS2 by optical helicity. Nat. Nanotechnol. 7, 494–498 (2012).

    ADS  Article  Google Scholar 

  21. Chernikov, A. et al. Electrical tuning of exciton binding energies in monolayer WS2. Phys. Rev. Lett. 115, 126802 (2015).

    ADS  Article  Google Scholar 

  22. Ye, Z., Sun, D. & Heinz, T. F. Optical manipulation of valley pseudospin. Nat. Phys. 13, 26–29 (2017).

    Article  Google Scholar 

  23. Mak, K. F., McGill, K. L., Park, J. & McEuen, P. L. The valley Hall effect in MoS2 transistors. Science 344, 1489–1492 (2014).

    ADS  Article  Google Scholar 

  24. Rivera, P. et al. Valley-polarized exciton dynamics in a 2D semiconductor heterostructure. Science 351, 688–691 (2016).

    ADS  MathSciNet  Article  Google Scholar 

  25. Claassen, M., Jia, C., Moritz, B. & Devereaux, T. All-optical materials design of chiral edge modes in transition-metal dichalcogenides. Nat. Commun. 7, 13074 (2016).

    ADS  Article  Google Scholar 

  26. Mak, K. F. et al. Tightly bound trions in monolayer MoS2. Nat. Mater. 12, 207–211 (2013).

    ADS  Article  Google Scholar 

  27. You, Y. et al. Observation of biexcitons in monolayer WSe2. Nat. Phys. 11, 477–481 (2015).

    Article  Google Scholar 

  28. Hao, K. et al. Neutral and charged inter-valley biexcitons in monolayer MoSe2. Nat. Commun. 8, 15552 (2017).

    ADS  Article  Google Scholar 

  29. Sie, E. J., Lui, C. H., Lee, Y.-H., Kong, J. & Gedik, N. Observation of intervalley biexcitonic optical Stark effect in monolayer WS2. Nano Lett. 16, 7421–7426 (2016).

    ADS  Article  Google Scholar 

  30. Moody, G. et al. Intrinsic homogeneous linewidth and broadening mechanisms of excitons in monolayer transition metal dichalcogenides. Nat. Commun. 6, 8315 (2017).

    Article  Google Scholar 

  31. Jin, C. et al. Interlayer electron–phonon coupling in WSe2/hBN heterostructures. Nat. Phys. 13, 127–131 (2017).

    Article  Google Scholar 

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This work was primarily supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under contract no. DE-AC02-05-CH11231 (Van der Waals Heterostructures program KCWF16). Preparation of the hBN-encapsulated monolayer MoSe2 is supported by the National Science Foundation EFRI programme (EFMA-1542741). Growth of hBN crystals was supported by the Elemental Strategy Initiative conducted by the MEXT, Japan and JSPS KAKENHI grant numbers JP15K21722 and JP25106006. S.T. acknowledges the support from NSF DMR 1552220 NSF CAREER award.

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C.-K.Y. and F.W. conceived the research. C.-K.Y. carried out optical measurements, assisted by J.H. and C.-S.Y. C.-K.Y., F.W. and J.H. analysed the data and performed theoretical analysis. J.H. fabricated the devices, assisted by A.W., C.-K.L. and S.Z. Y.S, H.C. and S.T. synthesized MoSe2 crystals. K.W. and T.T. synthesized hBN crystals. C.-K.Y. and F.W. wrote the manuscript, with input from all authors.

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Correspondence to Chaw-Keong Yong or Feng Wang.

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Yong, CK., Horng, J., Shen, Y. et al. Biexcitonic optical Stark effects in monolayer molybdenum diselenide. Nature Phys 14, 1092–1096 (2018).

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