Skip to main content
SpringerLink
Log in

Lennard-Jones-Like Potential of 2D Excitons in Monolayer WS2

  • Chapter
  • First Online:
Coherent Light-Matter Interactions in Monolayer Transition-Metal Dichalcogenides

Part of the book series: Springer Theses ((Springer Theses))

  • 1517 Accesses

Abstract

In this chapter, we report a rare atom-like interaction between excitons in monolayer WS2, measured using ultrafast absorption spectroscopy. At increasing excitation density, the exciton resonance energy exhibits a pronounced redshift followed by an anomalous blueshift. Using both material-realistic computation and phenomenological modeling, we attribute this observation to plasma effects and an attraction-repulsion crossover of the exciton-exciton interaction that mimics the Lennard-Jones potential between atoms. Our experiment demonstrates a strong analogy between excitons and atoms with respect to inter-particle interaction, which holds promise to pursue the predicted liquid and crystalline phases of excitons in two-dimensional materials.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. J.E. Jones, On the determination of molecular fields. II. From the equation of state of a gas. Proc. R. Soc. A: Math. Phys. Eng. Sci. 106, 463–477 (1924)

    Article  ADS  Google Scholar 

  2. J.E. Lennard-Jones, Cohesion. Proc. Phys. Soc. 43, 461–482 (1931)

    Article  ADS  MATH  Google Scholar 

  3. J.B. Mock, G.A. Thomas, M. Combescot, Entropy ionization of an exciton gas. Solid State Commun. 25, 279–282 (1978)

    Article  ADS  Google Scholar 

  4. D. Semkat et al., Ionization equilibrium in an excited semiconductor: Mott transition versus Bose-Einstein condensation. Phys. Rev. B 80, 155201 (2009)

    Article  ADS  Google Scholar 

  5. A. Steinhoff, M. Rosner, F. Jahnke, T.O. Wehling, C. Gies, Influence of excited carriers on the optical and electronic properties of MoS2. Nano Lett. 14, 3743–3748 (2014)

    Article  ADS  Google Scholar 

  6. R. Zimmermann, Dynamical T-matrix theory for high-density excitons in coupled quantum wells. Phys. Status Solidi B 243, 2358–2362 (2006)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. M.M. Ugeda 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 

  9. H.M. Hill et al., Observation of Excitonic Rydberg states in monolayer MoS2 and WS2 by photoluminescence excitation spectroscopy. Nano Lett. 15, 2992–2997 (2015)

    Article  ADS  Google Scholar 

  10. A.R. Klots et al., Probing excitonic states in suspended two-dimensional semiconductors by photocurrent spectroscopy. Sci. Rep. 4, 6608 (2014)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  12. A. Chernikov, C. Ruppert, H.M. Hill, A.F. Rigosi, T.F. Heinz, Population inversion and giant bandgap renormalization in atomically thin WS2 layers. Nat. Photonics 9, 466–470 (2015)

    Article  ADS  Google Scholar 

  13. E.A. Pogna et al., Photo-induced bandgap renormalization governs the ultrafast response of single-layer MoS2. ACS Nano 10, 1182–1188 (2016)

    Article  Google Scholar 

  14. E.J. Sie, A.J. Frenzel, Y.-H. Lee, J. Kong, N. Gedik, Intervalley biexcitons and many-body effects in monolayer MoS2. Phys. Rev. B 92, 125417 (2015)

    Article  ADS  Google Scholar 

  15. C. Mai 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 

  16. R. Schmidt et al., Ultrafast coulomb-induced intervalley coupling in atomically thin WS2. Nano Lett. 16, 2945–2950 (2016)

    Article  ADS  Google Scholar 

  17. C. Ruppert, A. Chernikov, H.M. Hill, A.F. Rigosi, T.F. Heinz, The role of electronic and Phononic excitation in the optical response of monolayer WS2 after ultrafast excitation. Nano Lett. 17, 644–651 (2017)

    Article  ADS  Google Scholar 

  18. D.R. Wake, H.W. Yoon, J.P. Wolfe, H. Morkoç, Response of excitonic absorption spectra to photoexcited carriers in GaAs quantum wells. Phys. Rev. B 46, 13452–13460 (1992)

    Article  ADS  Google Scholar 

  19. N. Peyghambarian et al., Blue shift of the exciton resonance due to exciton-exciton interactions in a multiple-quantum-well structure. Phys. Rev. Lett. 53, 2433–2436 (1984)

    Article  ADS  Google Scholar 

  20. D. Hulin et al., Well-size dependence of exciton blue shift in GaAs multiple-quantum-well structures. Phys. Rev. B 33, 4389–4391 (1986)

    Article  ADS  Google Scholar 

  21. K.H. Schlaad et al., Many-particle effects and nonlinear optical properties of GaAs/(Al,Ga)As multiple-quantum-well structures under quasistationary excitation conditions. Phys. Rev. B 43, 4268–4275 (1991)

    Article  ADS  Google Scholar 

  22. S. Schmitt-Rink, D. Chemla, D. Miller, Theory of transient excitonic optical nonlinearities in semiconductor quantum-well structures. Phys. Rev. B 32, 6601–6609 (1985)

    Article  ADS  Google Scholar 

  23. Y.H. Lee et al., Synthesis of large-area MoS2 atomic layers with chemical vapor deposition. Adv. Mater. 24, 2320–2325 (2012)

    Article  Google Scholar 

  24. Y.H. Lee et al., Synthesis and transfer of single-layer transition metal disulfides on diverse surfaces. Nano Lett. 13, 1852–1857 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. Y. Li et al., Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2. Phys. Rev. B 90, 205422 (2014)

    Article  ADS  Google Scholar 

  27. Y. Yu et al., Fundamental limits of exciton-exciton annihilation for light emission in transition metal dichalcogenide monolayers. Phys. Rev. B 93, 201111 (2016)

    Article  ADS  Google Scholar 

  28. D. Sun et al., Observation of rapid exciton-exciton annihilation in monolayer molybdenum disulfide. Nano Lett. 14, 5625–5629 (2014)

    Article  ADS  Google Scholar 

  29. Y. Chen et al., Temperature-dependent photoluminescence emission and Raman scattering from Mo1-x Wx S2 monolayers. Nanotechnology 27, 445705 (2016)

    Article  Google Scholar 

  30. M. Rösner, E. Şaşıoğlu, C. Friedrich, S. Blügel, T.O. Wehling, Wannier function approach to realistic Coulomb interactions in layered materials and heterostructures. Phys. Rev. B 92, 085102 (2015)

    Article  ADS  Google Scholar 

  31. K. Kośmider, J.W. González, J. Fernández-Rossier, Large spin splitting in the conduction band of transition metal dichalcogenide monolayers. Phys. Rev. B 88, 245436 (2013)

    Article  ADS  Google Scholar 

  32. A. Kormányos et al., k·p theory for two-dimensional transition metal dichalcogenide semiconductors. 2D Mater. 2, 022001 (2015)

    Article  Google Scholar 

  33. L. Yuan, L. Huang, Exciton dynamics and annihilation in WS2 2D semiconductors. Nanoscale 7, 7402–7408 (2015)

    Article  ADS  Google Scholar 

  34. P.D. Cunningham, K.M. McCreary, B.T. Jonker, Auger recombination in chemical vapor deposition-grown monolayer WS2. J. Phys. Chem. Lett. 7, 5242–5246 (2016)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  36. T.C. Berkelbach, M.S. Hybertsen, D.R. Reichman, Theory of neutral and charged excitons in monolayer transition metal dichalcogenides. Phys. Rev. B 88, 045318 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  38. J.S. Ross et al., Electrical control of neutral and charged excitons in a monolayer semiconductor. Nat. Commun. 4, 1474 (2013)

    Article  Google Scholar 

  39. C.H. Lui et al., Trion-induced negative photoconductivity in monolayer MoS2. Phys. Rev. Lett. 113, 166801 (2014)

    Article  ADS  Google Scholar 

  40. J. Shang et al., Observation of excitonic fine structure in a 2D transition-metal dichalcogenide semiconductor. ACS Nano 9, 647–655 (2015)

    Article  Google Scholar 

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

    Article  Google Scholar 

  42. C. Schindler, R. Zimmermann, Analysis of the exciton-exciton interaction in semiconductor quantum wells. Phys. Rev. B 78, 045313 (2008)

    Article  ADS  Google Scholar 

  43. P. Steinleitner et al., Direct observation of ultrafast exciton formation in a monolayer of WSe2. Nano Lett. 17, 1455–1460 (2017)

    Article  ADS  Google Scholar 

  44. F. Ceballos, Q. Cui, M.Z. Bellus, H. Zhao, Exciton formation in monolayer transition metal dichalcogenides. Nanoscale 8, 11681–11688 (2016)

    Article  ADS  Google Scholar 

  45. B. Gao et al., Studies of intrinsic hot phonon dynamics in suspended graphene by transient absorption microscopy. Nano Lett. 11, 3184–3189 (2011)

    Article  ADS  Google Scholar 

  46. P.H. Handel, C. Kittel, Proc. Nat. Acad. Sci. USA 68, 3120–3121 (1971)

    Article  ADS  Google Scholar 

  47. A.L. Ivanov, H. Haug, Existence of exciton crystals in quantum wires. Phys. Rev. Lett. 71, 3182–3185 (1993)

    Article  ADS  Google Scholar 

  48. J. Böning, A. Filinov, M. Bonitz, Crystallization of an exciton superfluid. Phys. Rev. B 84, 075130 (2011)

    Article  ADS  Google Scholar 

  49. C. Friedrich, S. Blügel, A. Schindlmayr, Efficient implementation of the GW approximation within the all-electron FLAPW method. Phys. Rev. B 81, 125102 (2010)

    Article  ADS  Google Scholar 

  50. A.A. Mostofi et al., An updated version of wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 185, 2309–2310 (2014)

    Article  ADS  MATH  Google Scholar 

  51. G.B. Liu, W.Y. Shan, Y.G. Yao, W. Yao, D. Xiao, Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides. Phys. Rev. B 88, 085433 (2013)

    Article  ADS  Google Scholar 

  52. A. Ramasubramaniam, Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides. Phys. Rev. B 86, 115409 (2012)

    Article  ADS  Google Scholar 

  53. A. Molina-Sánchez, L. Wirtz, Phonons in single-layer and few-layer MoS2 and WS2. Phys. Rev. B 84, 155413 (2011)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Stanford University, Stanford, CA, USA

    Edbert Jarvis Sie

Authors
  1. Edbert Jarvis Sie
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Sie, E.J. (2018). Lennard-Jones-Like Potential of 2D Excitons in Monolayer WS2 . In: Coherent Light-Matter Interactions in Monolayer Transition-Metal Dichalcogenides. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-69554-9_7

Download citation

Publish with us

Policies and ethics

Search

Navigation