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Exchange-driven intravalley mixing of excitons in monolayer transition metal dichalcogenides

Nature Physics volume 15, pages 228–232 (2019)Cite this article

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Abstract

Monolayer transition metal dichalcogenides (TMDCs) are promising two-dimensional (2D) semiconductors for application in optoelectronics. Their optical properties are dominated by two series of photo-excited exciton states—A (XA) and B (XB)1,2—that are derived from direct interband transitions near the band extrema. These exciton states have large binding energies and strong optical absorption3,4,5,6, and form an ideal system to investigate many-body effects in low dimensions. Because spin–orbit coupling causes a large splitting between bands of opposite spins, XA and XB are usually treated as spin-polarized Ising excitons, each arising from interactions within a specific set of states induced by interband transitions between pairs of either spin-up or spin-down bands (TA or TB). Here, by using monolayer MoS2 as a prototypical system and solving the first-principles Bethe–Salpeter equations, we demonstrate a strong intravalley exchange interaction between TA and TB, indicating that XA and XB are mixed states instead of pure Ising excitons. Using 2D electronic spectroscopy, we observe that an optical excitation of the lower-energy TA induces a population of the higher-energy TB, manifesting the intravalley exchange interaction. This work elucidates the dynamics of exciton formation in monolayer TMDCs, and sheds light on many-body effects in 2D materials.

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Fig. 1: Exciton state mixing from the intravalley exchange interaction.
Fig. 2: 2D electronic spectroscopy measurement of monolayer MoS2.
Fig. 3: Simulation of the rephasing amplitude 2D spectra including the intravalley exchange interaction.

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The data that support the findings of this study are available from the corresponding authors on reasonable request.

References

  1. Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: a new direct-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. Ye, Z. et al. Probing excitonic dark states in single-layer tungsten disulphide. Nature 513, 214–218 (2014).

    Article  ADS  Google Scholar 

  6. Chernikov, A. et al. Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2. Phys. Rev. Lett. 113, 076802 (2014).

    Article  ADS  Google Scholar 

  7. Rossler, U., Jorda, S. & Broido, D. Fine structure of quantum well excitons. Solid State Commun. 73, 209–214 (1990).

    Article  ADS  Google Scholar 

  8. Andreani, L. C. & Bassani, F. Exchange interaction and polariton effects in quantum-well excitons. Phys. Rev. B 41, 7536–7544 (1990).

    Article  ADS  Google Scholar 

  9. Damen, T. C., Via, L., Cunningham, J. E., Shah, J. & Sham, L. J. Subpicosecond spin relaxation dynamics of excitons and free carriers in GaAs quantum wells. Phys. Rev. Lett. 67, 3432–3435 (1991).

    Article  ADS  Google Scholar 

  10. Maialle, M. Z., de Andrada e Silva, E. A. & Sham, L. J. Exciton spin dynamics in quantum wells. Phys. Rev. B 47, 15776–15788 (1993).

    Article  ADS  Google Scholar 

  11. Vinattieri, A. et al. Exciton dynamics in GaAs quantum wells under resonant excitation. Phys. Rev. B 50, 10868–10879 (1994).

    Article  ADS  Google Scholar 

  12. Yu, T. & Wu, M. W. Valley depolarization due to intervalley and intravalley electron–hole exchange interactions in monolayer MoS2. Phys. Rev. B 89, 205303 (2014).

    Article  ADS  Google Scholar 

  13. Jones, A. M. et al. Optical generation of excitonic valley coherence in monolayer WSe2. Nat. Nanotech. 8, 634–638 (2013).

    Article  ADS  Google Scholar 

  14. Hao, K. et al. Direct measurement of exciton valley coherence in monolayer WSe2. Nat. Phys. 12, 677–682 (2016).

    Article  Google Scholar 

  15. Yu, H., Liu, G.-B., Gong, P., Xu, X. & Yao, W. Dirac cones and Dirac saddle points of bright excitons in monolayer transition metal dichalcogenides. Nat. Commun. 5, 3876 (2014).

    Article  Google Scholar 

  16. Qiu, D. Y., Cao, T. & Louie, S. G. Nonanalyticity, valley quantum phases, and lightlike exciton dispersion in monolayer transition metal dichalcogenides: theory and first-principles calculations. Phys. Rev. Lett. 115, 176801 (2015).

    Article  ADS  Google Scholar 

  17. Wu, F., Qu, F. & MacDonald, A. H. Exciton band structure of monolayer MoS2. Phys. Rev. B 91, 075310 (2015).

    Article  ADS  Google Scholar 

  18. Mai, C. et al. Many-body effects in valleytronics: direct measurement of valley lifetimes in single-layer MoS2. Nano Lett. 14, 202–206 (2014).

    Article  ADS  Google Scholar 

  19. Singh, A. et al. Coherent electronic coupling in atomically thin MoSe2. Phys. Rev. Lett. 112, 216804 (2014).

    Article  ADS  Google Scholar 

  20. Hao, K. et al. Coherent and incoherent coupling dynamics between neutral and charged excitons in monolayer MoSe2. Nano Lett. 16, 5109–5113 (2016).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. Brixner, T. et al. Two-dimensional spectroscopy of electronic couplings in photosynthesis. Nature 434, 625–628 (2005).

    Article  ADS  Google Scholar 

  23. Panitchayangkoon, G. et al. Long-lived quantum coherence in photosynthetic complexes at physiological temperature. Proc. Natl Acad. Sci. USA 107, 12766–12770 (2010).

    Article  ADS  Google Scholar 

  24. Li, X., Zhang, T., Borca, C. N. & Cundiff, S. T. Many-body interactions in semiconductors probed by optical two-dimensional Fourier transform spectroscopy. Phys. Rev. Lett. 96, 057406 (2006).

    Article  ADS  Google Scholar 

  25. Graham, M. W., Calhoun, T. R., Green, A. A., Hersam, M. C. & Fleming, G. R. Two-dimensional electronic spectroscopy reveals the dynamics of phonon-mediated excitation pathways in semiconducting single-walled carbon nanotubes. Nano Lett. 12, 813–819 (2012).

    Article  ADS  Google Scholar 

  26. Moody, G. et al. Intrinsic homogeneous linewidth and broadening mechanisms of excitons in monolayer transition metal dichalcogenides. Nat. Commun. 6, 8315 (2015).

    Article  Google Scholar 

  27. Czech, K. J. et al. Measurement of ultrafast excitonic dynamics of few-layer MoS2 using state-selective coherent multidimensional spectroscopy. ACS Nano 9, 12146–12157 (2015).

    Article  Google Scholar 

  28. Jones, A. M. et al. Excitonic luminescence upconversion in a two-dimensional semiconductor. Nat. Phys. 12, 323–327 (2016).

    Article  Google Scholar 

  29. Yang, L. et al. Long-lived nanosecond spin relaxation and spin coherence of electrons in monolayer MoS2 and WS2. Nat. Phys. 11, 830–834 (2015).

    Article  Google Scholar 

  30. Deslippe, J. et al. BerkeleyGW: a massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures. Comput. Phys. Commun. 183, 1269–1289 (2012).

    Article  ADS  Google Scholar 

  31. Giannozzi, P. et al. Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).

    Article  Google Scholar 

  32. Hybertsen, M. S. & Louie, S. G. Electron correlation in semiconductors and insulators: band gaps and quasiparticle energies. Phys. Rev. B 34, 5390–5413 (1986).

    Article  ADS  Google Scholar 

  33. da Jornada, F. H., Qiu, D. Y. & Louie, S. G. Nonuniform sampling schemes of the Brillouin zone for many-electron perturbation-theory calculations in reduced dimensionality. Phys. Rev. B 95, 035109 (2017).

    Article  ADS  Google Scholar 

  34. Deslippe, J., Samsonidze, G., Jain, M., Cohen, M. L. & Louie, S. G. Coulomb-hole summations and energies for GW calculations with limited number of empty orbitals: a modified static remainder approach. Phys. Rev. B 87, 165124 (2013).

    Article  ADS  Google Scholar 

  35. Mostofi, A. A. et al. Wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 178, 685–699 (2008).

    Article  ADS  Google Scholar 

  36. Rohlfing, M. & Louie, S. G. Electron–hole excitations in semiconductors and insulators. Phys. Rev. Lett. 81, 2312–2315 (1998).

    Article  ADS  Google Scholar 

  37. Rohlfing, M. & Louie, S. G. Electron–hole excitations and optical spectra from first principles. Phys. Rev. B 62, 4927–4944 (2000).

    Article  ADS  Google Scholar 

  38. Yu, L. et al. Design, modeling, and fabrication of chemical vapor deposition grown MoS2 circuits with E-mode FETs for large-area electronics. Nano Lett. 16, 6349–6356 (2016).

    Article  ADS  Google Scholar 

  39. Li, H. et al. From bulk to monolayer MoS2: evolution of Raman scattering. Adv. Funct. Mater. 22, 1385–1390 (2012).

    Article  ADS  Google Scholar 

  40. Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: a new direct-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010).

    Article  ADS  Google Scholar 

  41. Cerullo, G., Nisoli, M., Stagira, S. & De Silvestri, S. Sub-8-fs pulses from an ultrabroadband optical parametric amplifier in the visible. Opt. Lett. 23, 1283–1285 (1998).

    Article  ADS  Google Scholar 

  42. Shirakawa, A., Sakane, I. & Kobayashi, T. Pulse-front-matched optical parametric amplification for sub-10-fs pulse generation tunable in the visible and near infrared. Opt. Lett. 23, 1292–1294 (1998).

    Article  ADS  Google Scholar 

  43. Isaienko, O. & Borguet, E. Pulse-front matching of ultrabroadband near-infrared noncollinear optical parametric amplified pulses. J. Opt. Soc. Am. B 26, 965–972 (2009).

    Article  ADS  Google Scholar 

  44. Brixner, T., Mancal, T., Stiopkin, I. V. & Fleming, G. R. Phase-stabilized two-dimensional electronic spectroscopy. J. Chem. Phys. 121, 4221–4236 (2004).

    Article  ADS  Google Scholar 

  45. Guo, L., Monahan, D. M. & Fleming, G. R. Rapid and economical data acquisition in ultrafast frequency-resolved spectroscopy using choppers and a microcontroller. Opt. Express 26, 18126–18132 (2016).

    Article  ADS  Google Scholar 

  46. Monahan, D. M. et al. Room-temperature coherent optical phonon in 2D electronic spectra of CH3NH3PbI3 perovskite as a possible cooling bottleneck. J. Phys. Chem. Lett. 8, 3211–3215 (2017).

    Article  Google Scholar 

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Acknowledgements

We thank G. Moody and K. Hao for helpful discussion. This material is based on work supported by the National Science Foundation under grant no. CHE-1362830, grant no. DMR-1508412 and grant no. EFMA-1542741. D.M.M. received a National Science Foundation Graduate Research Fellowship under grant no. DGE-1106400. Advanced codes were provided by the Center for Computational Study of Excited-State Phenomena in Energy Materials (C2SEPEM) at LBNL, which is funded by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division under contract no. DE-AC02-05CH11231, as part of the Computational Materials Sciences Program. Computational resources were provided by the DOE at Lawrence Berkeley National Laboratory’s NERSC facility and the NSF through XSEDE resources at NICS. Y.-H. L. acknowledges support from the Ministry of Science and Technology (MoST-106-2119-M-007-023-MY3; MoST-105-2112-M-007-032-MY3), the Frontier Research Center on Fundamental and Applied Sciences of Matters, and the Center for Quantum Technology of National Tsing Hua University.

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Author notes

  1. These authors contributed equally: Liang Guo, Meng Wu, Ting Cao, Daniele M. Monahan.

Authors and Affiliations

  1. Department of Chemistry, University of California, Berkeley, CA, USA

    Liang Guo, Daniele M. Monahan & Graham R. Fleming

  2. Kavli Energy Nanoscience Institute at Berkeley, Berkeley, CA, USA

    Liang Guo, Daniele M. Monahan & Graham R. Fleming

  3. Department of Physics, University of California, Berkeley, CA, USA

    Meng Wu, Ting Cao & Steven G. Louie

  4. Material Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Meng Wu, Ting Cao & Steven G. Louie

  5. Material Sciences and Engineering, National Tsing-Hua University, Hsinchu, Taiwan

    Yi-Hsien Lee

  6. Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Graham R. Fleming

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Contributions

L.G., M.W., T.C. and D.M.M. contributed equally to this work. L.G., M.W. and T.C. conceived the concept. Supervised by G.R.F., L.G. and D.M.M. led the experiments by designing the optical system and acquiring the data. M.W. and T.C. performed the theoretical studies under the supervision of S.G.L. Y.-H.L. provided the samples. L.G., M.W. and T.C. wrote the manuscript. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Steven G. Louie or Graham R. Fleming.

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Supplementary Figures 1–11; Supplementary Tables 1–4; Supplementary References 1–24

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Guo, L., Wu, M., Cao, T. et al. Exchange-driven intravalley mixing of excitons in monolayer transition metal dichalcogenides. Nat. Phys. 15, 228–232 (2019). https://doi.org/10.1038/s41567-018-0362-y

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