- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Controlling exciton many-body states by the electric-field effect in monolayer MoS2

J. Klein1,2,*, A. Hötger1, M. Florian3, A. Steinhoff3, A. Delhomme4, T. Taniguchi5, K. Watanabe5, F. Jahnke3, A. W. Holleitner1 et al.

M. Potemski4, C. Faugeras4, J. J. Finley1,†, and A. V. Stier1,‡

  • 1Walter Schottky Institut and Physik Department, Technische Universität München, Am Coulombwall 4, 85748 Garching, Germany
  • 2Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 3Institut für Theoretische Physik, Universität Bremen, P.O. Box 330 440, 28334 Bremen, Germany
  • 4Université Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS, LNCMI, 38000 Grenoble, France
  • 5Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

  • *jpklein@mit.edu
  • †finley@wsi.tum.de
  • ‡andreas.stier@wsi.tum.de
PDF

Phys. Rev. Research 3, L022009 – Published 30 April, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L022009

Abstract

We report magneto-optical spectroscopy of gated monolayer MoS2 in high magnetic fields up to 28T and obtain new insights on the many-body interaction of neutral and charged excitons with the resident charges of distinct spin and valley texture. For neutral excitons at low electron doping, we observe a nonlinear valley Zeeman shift due to dipolar spin-interactions that depends sensitively on the local carrier concentration. As the Fermi energy increases to dominate over the other relevant energy scales in the system, the magneto-optical response depends on the occupation of the fully spin-polarized Landau levels (LL) in both K/K′ valleys. This manifests itself in a many-body state. Our experiments demonstrate that the exciton in monolayer semiconductors is only a single particle boson close to charge neutrality. We find that away from charge neutrality it smoothly transitions into polaronic states with a distinct spin-valley flavor that is defined by the LL quantized spin and valley texture.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (67)

  1. P. Massignan, M. Zaccanti, G. M. Bruun, Polarons, dressed molecules and itinerant ferromagnetism in ultracold fermi gases, Rep. Prog. Phys. 77, 034401 (2014).
  2. I. Bloch, J. Dalibard, W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  3. M. Boll, T. A. Hilker, G. Salomon, A. Omran, J. Nespolo, L. Pollet, I. Bloch, and C. Gross, Spin- and density-resolved microscopy of antiferromagnetic correlations in fermi-hubbard chains, Science 353, 1257 (2016).
  4. A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, A cold-atom fermi–hubbard antiferromagnet, Nature 545, 462 (2017).
  5. D. K. Efimkin and A. H. MacDonald, Many-body theory of trion absorption features in two-dimensional semiconductors, Phys. Rev. B 95, 035417 (2017).
  6. J. Koepsell, J. Vijayan, P. Sompet, F. Grusdt, T. A. Hilker, E. Demler, G. Salomon, I. Bloch, and C. Gross, Imaging magnetic polarons in the doped fermi–hubbard model, Nature 572, 358 (2019).
  7. C. Fey, P. Schmelcher, A. Imamoglu, and R. Schmidt, Theory of exciton-electron scattering in atomically thin semiconductors, Phys. Rev. B 101, 195417 (2020).
  8. M. M. Glazov, Optical properties of charged excitons in two-dimensional semiconductors, J. Chem. Phys. 153, 034703 (2020).
  9. W. Chen, M. Fritze, A.V. Nurmikko, D. Ackley, C. Colvard, and H. Lee, Interaction of Magnetoexcitons and Two-Dimensional Electron Gas in the Quantum Hall Regime, Phys. Rev. Lett. 64, 2434 (1990).
  10. B. B. Goldberg, D. Heiman, A. Pinczuk, L. Pfeiffer, and K. West, Optical Investigations of the Integer and Fractional Quantum Hall Effects: Energy Plateaus, Intensity Minima, and Line Splitting in Band-Gap Emission, Phys. Rev. Lett. 65, 641 (1990).
  11. J. Zhu, H. L. Stormer, L. N. Pfeiffer, K. W. Baldwin, and K. W. West, Spin Susceptibility of an Ultra-Low-Density Two-Dimensional Electron System, Phys. Rev. Lett. 90, 056805 (2003).
  12. O. Gunawan, Y.P. Shkolnikov, K. Vakili, T. Gokmen, E.P. DePoortere, and M. Shayegan, Valley Susceptibility of an Interacting Two-Dimensional Electron System, Phys. Rev. Lett. 97, 186404 (2006).
  13. S. D. Sarma, E. H. Hwang, and Q. Li, Valley-dependent many-body effects in two-dimensional semiconductors, Phys. Rev. B 80, 121303(R) (2009).
  14. K. Nomura and A. H. MacDonald, Quantum Hall Ferromagnetism in Graphene, Phys. Rev. Lett. 96, 256602 (2006).
  15. A. F. Young, C. R. Dean, L. Wang, H. Ren, P. Cadden-Zimansky, K. Watanabe, T. Taniguchi, J. Hone, K. L. Shepard, and P. Kim, Spin and valley quantum hall ferromagnetism in graphene, Nat. Phys. 8, 550 (2012).
  16. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden et al., Layer-dependent ferromagnetism in a van der waals crystal down to the monolayer limit, Nature 546, 270 (2017).
  17. Y. Tang, L. Li, T. Li, Y. Xu, S. Liu, K. Barmak, K. Watanabe, T. Taniguchi, A. H. MacDonald, J. Shan et al., Simulation of hubbard model physics in WSe2/WS2 moiré superlattices, Nature 579, 353 (2020).
  18. Y. Shimazaki, I. Schwartz, K. Watanabe, T. Taniguchi, M. Kroner, and A. Imamoğlu, Strongly correlated electrons and hybrid excitons in a moiré heterostructure, Nature 580, 472 (2020).
  19. E. C. Regan, D. Wang, C. Jin, M. I. B. Utama, B. Gao, X. Wei, S. Zhao, W. Zhao, Z. Zhang, K. Yumigeta et al., Mott and generalized wigner crystal states in WSe2/WS2 moiré superlattices, Nature 579, 359 (2020).
  20. 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).
  21. A.V. Stier, N.P. Wilson, K.A. Velizhanin, J. Kono, X. Xu, and S.A. Crooker, Magnetooptics of Exciton Rydberg States in a Monolayer Semiconductor, Phys. Rev. Lett. 120, 057405 (2018).
  22. M. Sidler, P. Back, O. Cotlet, A. Srivastava, T. Fink, M. Kroner, E. Demler, and A. Imamoglu, Fermi polaron-polaritons in charge-tunable atomically thin semiconductors, Nat. Phys. 13, 255 (2016).
  23. S. Ravets, P. Knuppel, S. Faelt, O. Cotlet, M. Kroner, W. Wegscheider, and A. Imamoglu, Polaron Polaritons in the Integer and Fractional Quantum Hall Regimes, Phys. Rev. Lett. 120, 057401 (2018).
  24. Z. Wang, K. F. Mak, and J. Shan, Strongly Interaction-Enhanced Valley Magnetic Response in Monolayer WSe2, Phys. Rev. Lett. 120, 066402 (2018).
  25. T. Smolenski, O. Cotlet, A. Popert, P. Back, Y. Shimazaki, P. Knuppel, N. Dietler, T. Taniguchi, K. Watanabe, M. Kroner, and A. Imamoglu, Interaction-Induced Shubnikov–de Haas Oscillations in Optical Conductivity of Monolayer MoSe2, Phys. Rev. Lett. 123, 097403 (2019).
  26. L.B. Tan, O. Cotlet, A. Bergschneider, R. Schmidt, P. Back, Y. Shimazaki, M. Kroner, and A. Imamoglu, Interacting Polaron-Polaritons, Phys. Rev. X 10, 021011 (2020).
  27. E. Liu, J. vanBaren, T. Taniguchi, K. Watanabe, Y.C. Chang, and C.H. Lui, Landau-Quantized Excitonic Absorption and Luminescence in a Monolayer Valley Semiconductor, Phys. Rev. Lett. 124, 097401 (2020).
  28. R. Pisoni, A. Kormanyos, M. Brooks, Z. Lei, P. Back, M. Eich, H. Overweg, Y. Lee, P. Rickhaus, K. Watanabe, T. Taniguchi, A. Imamoglu, G. Burkard, T. Ihn, and K. Ensslin, Interactions and Magnetotransport Through Spin-Valley Coupled Landau Levels in Monolayer MoS2, Phys. Rev. Lett. 121, 247701 (2018).
  29. H.C.P. Movva, B. Fallahazad, K. Kim, S. Larentis, T. Taniguchi, K. Watanabe, S.K. Banerjee, and E. Tutuc, Density-Dependent Quantum Hall States and Zeeman Splitting in Monolayer and Bilayer WSe2, Phys. Rev. Lett. 118, 247701 (2017).
  30. S. Xu, J. Shen, G. Long, Z. Wu, Z.Q. Bao, C.C. Liu, X. Xiao, T. Han, J. Lin, Y. Wu, H. Lu, J. Hou, L. An, Y. Wang, Y. Cai, K.M. Ho, Y. He, R. Lortz, F. Zhang, and N. Wang, Odd-Integer Quantum Hall States and Giant Spin Susceptibility in p-type Few-Layer WSe2, Phys. Rev. Lett. 118, 067702 (2017).
  31. M. V. Gustafsson, M. Yankowitz, C. Forsythe, D. Rhodes, K. Watanabe, T. Taniguchi, J. Hone, X. Zhu, and C. R. Dean, Ambipolar landau levels and strong band-selective carrier interactions in monolayer WSe2, Nat. Mater. 17, 411 (2018).
  32. S. Larentis, H.C.P. Movva, B. Fallahazad, K. Kim, A. Behroozi, T. Taniguchi, K. Watanabe, S.K. Banerjee, and E. Tutuc, Large effective mass and interaction-enhanced zeeman splitting of k-valley electrons in MoSe2, Phys. Rev. B 97 201407 (2018).
  33. B. Fallahazad, H.C.P. Movva, K. Kim, S. Larentis, T. Taniguchi, K. Watanabe, S.K. Banerjee, and E. Tutuc, Shubnikov–de Haas Oscillations of High-Mobility Holes in Monolayer and Bilayer WSe2: Landau Level Degeneracy, Effective Mass, and Negative Compressibility, Phys. Rev. Lett. 116, 086601 (2016).
  34. J. L. Lin, T. Han, B. A. Piot, Z. Wu, S. Xu, G. Long, L. An, P. Cheung, P.-P. Zheng, P. Plochocka et al., Determining interaction enhanced valley susceptibility in spin-valley-locked MoS2, Nano Lett. 19, 1736 (2019).
  35. J. Li, M. Goryca, N.P. Wilson, A.V. Stier, X. Xu, and S.A. Crooker, Spontaneous Valley Polarization of Interacting Carriers in a Monolayer Semiconductor, Phys. Rev. Lett. 125, 147602 (2020).
  36. 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 65tesla, Nat. Commun. 7, 10643 (2016).
  37. A.A. Mitioglu, K. Galkowski, A. Surrente, L. Klopotowski, D. Dumcenco, A. Kis, D.K. Maude, and P. Plochocka, Magnetoexcitons in large area CVD-grown monolayer MoS2 and MoSe2 on sapphire, Phys. Rev. B 93 165412 (2016).
  38. F. Cadiz, E. Courtade, C. Robert, G. Wang, Y. Shen, H. Cai, T. Taniguchi, K. Watanabe, H. Carrere, D. Lagarde, M. Manca, T. Amand, P. Renucci, S. Tongay, X. Marie, and B. Urbaszek, Excitonic Linewidth Approaching the Homogeneous Limit in MoS2-Based Van Der Waals Heterostructures, Phys. Rev. X 7, 021026 (2017).
  39. M. Goryca, J. Li, A. V. Stier, T. Taniguchi, K. Watanabe, E. Courtade, S. Shree, C. Robert, B. Urbaszek, X. Marie et al., Revealing exciton masses and dielectric properties of monolayer semiconductors with high magnetic fields, Nat. Commun. 10, 4172 (2019).
  40. J. Jadczak, J. Kutrowska-Girzycka, M. Bieniek, T. Kazimierczuk, P. Kossacki, J. Schindler, J. Debus, K. Watanabe, T. Taniguchi, C.-H. Ho et al., Fine structure of negatively charged and neutral excitons in monolayer MoS2, arXiv:2001.07929.
  41. G. Aivazian, Z. Gong, A. M. Jones, R.-L. Chu, J. Yan, D. G. Mandrus, C. Zhang, D. Cobden, W. Yao, and X. Xu, Magnetic control of valley pseudospin in monolayer WSe2, Nat. Phys. 11, 148 (2015).
  42. A. Srivastava, M. Sidler, A. V. Allain, D. S. Lembke, A. Kis, and A. Imamoğlu, Valley zeeman effect in elementary optical excitations of monolayer WSe2, Nat. Phys. 11, 141 (2015).
  43. D. MacNeill, C. Heikes, K.F. Mak, Z. Anderson, A. Kormanyos, V. Zolyomi, J. Park, and D.C. Ralph, Breaking of Valley Degeneracy by Magnetic Field in Monolayer MoSe2, Phys. Rev. Lett. 114, 037401 (2015).
  44. Y. Li, J. Ludwig, T. Low, A. Chernikov, X. Cui, G. Arefe, Y.D. Kim, A.M. vanderZande, A. Rigosi, H.M. Hill, S.H. Kim, J. Hone, Z. Li, D. Smirnov, and T.F. Heinz, Valley Splitting and Polarization by the Zeeman Effect in Monolayer MoSe2, Phys. Rev. Lett. 113, 266804 (2014).
  45. Z. Wang, J. Shan, and K. F. Mak, Valley- and spin-polarized landau levels in monolayer WSe2, Nat. Nanotechnol. 12, 144 (2016).
  46. A. V. Stier, N. P. Wilson, G. Clark, X. Xu, and S. A. Crooker, Probing the influence of dielectric environment on excitons in monolayer WSe2: Insight from high magnetic fields, Nano Lett. 16, 7054 (2016).
  47. T. P. Lyons, S. Dufferwiel, M. Brooks, F. Withers, T. Taniguchi, K. Watanabe, K. S. Novoselov, G. Burkard, and A. I. Tartakovskii, The valley zeeman effect in inter- and intravalley trions in monolayer WSe2, Nat. Commun. 10, 2330 (2019).
  48. T. Wang, Z. Li, Z. Lu, Y. Li, S. Miao, Z. Lian, Y. Meng, M. Blei, T. Taniguchi, K. Watanabe, S. Tongay, W. Yao, D. Smirnov, C. Zhang, and S. F. Shi, Observation of Quantized Exciton Energies in Monolayer WSe2 Under a Strong Magnetic Field, Phys. Rev. X 10, 021024 (2020).
  49. 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).
  50. F. Volmer, M. Ersfeld, L. Rathmann, M. Heithoff, L. Kotewitz, M. Lohmann, B. Yang, K. Watanabe, T. Taniguchi, L. Bartels et al., How photoinduced gate screening and leakage currents dynamically change the fermi level in 2d materials, Phys. Status Solidi, RRL, 14, 2000298 (2020).
  51. J. Klein, A. Kerelsky, M. Lorke, M. Florian, F. Sigger, J. Kiemle, M. C. Reuter, T. Taniguchi, K. Watanabe, J. J. Finley et al., Impact of substrate induced band tail states on the electronic and optical properties of MoS2, Appl. Phys. Lett. 115, 261603 (2019).
  52. J. Wierzbowski, J. Klein, F. Sigger, C. Straubinger, M. Kremser, T. Taniguchi, K. Watanabe, U. Wurstbauer, A. W. Holleitner, M. Kaniber et al., Direct exciton emission from atomically thin transition metal dichalcogenide heterostructures near the lifetime limit, Sci. Rep. 7, 12383 (2017).
  53. M. Florian, M. Hartmann, A. Steinhoff, J. Klein, A. W. Holleitner, J. J. Finley, T. O. Wehling, M. Kaniber, and C. Gies, The dielectric impact of layer distances on exciton and trion binding energies in van der waals heterostructures, Nano Lett. 18, 2725 (2018).
  54. J.G. Roch, D. Miserev, G. Froehlicher, N. Leisgang, L. Sponfeldner, K. Watanabe, T. Taniguchi, J. Klinovaja, D. Loss, R.J. Warburton, First-Order Magnetic Phase Transition of Mobile Electrons in Monolayer MoS2, Phys. Rev. Lett. 124, 187602 (2020).
  55. M. Barbone, A. R.-P. Montblanch, D. M. Kara, C. Palacios-Berraquero, A. R. Cadore, D. De Fazio, B. Pingault, E. Mostaani, H. Li, B. Chen et al., Charge-tuneable biexciton complexes in monolayer WSe2, Nat. Commun. 9, 3721 (2018).
  56. D. V. Tuan, B. Scharf, I. Žutić and H. Dery, Marrying Excitons and Plasmons in Monolayer Transition-Metal Dichalcogenides, Phys. Rev. X 7, 041040 (2017).
  57. T. Deilmann and K. S. Thygesen, Dark excitations in monolayer transition metal dichalcogenides, Phys. Rev. B 96, 201113 (2017).
  58. C. Robert, B. Han, P. Kapuscinski, A. Delhomme, C. Faugeras, T. Amand, M. R. Molas, M. Bartos, K. Watanabe, T. Taniguchi et al., Measurement of the spin-forbidden dark excitons in MoS2 and MoSe2 monolayers, Nat. Commun. 11, 4037 (2020).
  59. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L022009 for device preparation and electrical device characterization, magnetic field and carrier density-dependent PL data, carrier density-dependent valley Zeeman shifts, calculation of the quantized spin-valley texture, theoretical considerations to the magnetic moment, as well as magnetic field and carrier density-dependent valley polarization data.
  60. X. Xu, W. Yao, D. Xiao, and T. F. Heinz, Spin and pseudospins in layered transition metal dichalcogenides, Nat. Phys. 10, 343 (2014).
  61. G. Wang, L. Bouet, M. M. Glazov, T. Amand, E. L. Ivchenko, E. Palleau, X. Marie, and B. Urbaszek, Magneto-optics in transition metal diselenide monolayers, 2D Mater. 2, 034002 (2015).
  62. T. Deilmann, P. Krüger, and M. Rohlfing, Ab Initio Studies of Exciton g Factors: Monolayer Transition Metal Dichalcogenides in Magnetic Fields, Phys. Rev. Lett. 124, 226402 (2020).
  63. T. Woźniak, P. E. F. Junior, G. Seifert, A. Chaves, and J. Kunstmann, Exciton g factors of van der waals heterostructures from first-principles calculations, Phys. Rev. B 101, 235408 (2020).
  64. V. Jovanov, T. Eissfeller, S. Kapfinger, E.C. Clark, F. Klotz, M. Bichler, J.G. Keizer, P. Koenraad, G. Abstreiter, and J.J. Finley, Observation and explanation of strong electrically tunable exciton g-factors in composition engineered In(Ga)As quantum dots, Phys. Rev. B 83, 161303(R) (2011).
  65. J. K. Furdyna, Diluted magnetic semiconductors, J. Appl. Phys. 64, R29 (1988).
  66. C. Latta, F. Haupt, M. Hanl, A. Weichselbaum, M. Claassen, W. Wuester, P. Fallahi, S. Faelt, L. Glazman, J. von Delft, H. E. Türeci, and A. Imamoglu, Quantum quench of kondo correlations in optical absorption, Nature 474, 627 (2011).
  67. A. Steinhoff, M. Florian, M. Rösner, G. Schönhoff, T. O. Wehling, and F. Jahnke, Exciton fission in monolayer transition metal dichalcogenide semiconductors, Nat. Commun. 8, 1166 (2017).

Outline

Information

Phys. Rev. Research 3, L022009– Published 30 April, 2021
  • Received 28 July 2020
  • Accepted 2 April 2021
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation