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Dark exciton-exciton annihilation in monolayer
Phys. Rev. B 104, L241406 – Published 17 December, 2021
DOI: https://doi.org/10.1103/PhysRevB.104.L241406
Abstract
The exceptionally strong Coulomb interaction in semiconducting transition-metal dichalcogenides (TMDs) gives rise to a rich exciton landscape consisting of bright and dark exciton states. At elevated densities, excitons can interact through exciton-exciton annihilation (EEA), an Auger-like recombination process limiting the efficiency of optoelectronic applications. Although EEA is a well-known and particularly important process in atomically thin semiconductors determining exciton lifetimes and affecting transport at elevated densities, its microscopic origin has remained elusive. In this joint theory-experiment study combining microscopic and material-specific theory with time- and temperature-resolved photoluminescence measurements, we demonstrate the key role of dark intervalley states that are found to dominate the EEA rate in monolayer . We reveal an intriguing, characteristic temperature dependence of Auger scattering in this class of materials with an excellent agreement between theory and experiment. Our study provides microscopic insights into the efficiency of technologically relevant Auger scattering channels within the remarkable exciton landscape of atomically thin semiconductors.
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References (72)
- G. Wang, A. Chernikov, M. M. Glazov, T. F. Heinz, X. Marie, T. Amand, and B. Urbaszek, Rev. Mod. Phys. 90, 021001 (2018).
- T. Mueller and E. Malic, npj 2D Mater. Appl. 2, 29 (2018).
- Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Nature (London) 556, 43 (2018).
- P. Merkl, F. Mooshammer, P. Steinleitner, A. Girnghuber, K.-Q. Lin, P. Nagler, J. Holler, C. Schüller, J. M. Lupton, T. Korn et al., Nat. Mater. 18, 691 (2019).
- D. Sun, Y. Rao, G. A. Reider, G. Chen, Y. You, L. Brezin, A. R. Harutyunyan, and T. F. Heinz, Nano Lett. 14, 5625 (2014).
- N. Kumar, Q. Cui, F. Ceballos, D. He, Y. Wang, and H. Zhao, Phys. Rev. B 89, 125427 (2014).
- L. Yuan and L. Huang, Nanoscale 7, 7402 (2015).
- Y. Yu, Y. Yu, C. Xu, A. Barrette, K. Gundogdu, and L. Cao, Phys. Rev. B 93, 201111(R) (2016).
- M. Manca, M. Glazov, C. Robert, F. Cadiz, T. Taniguchi, K. Watanabe, E. Courtade, T. Amand, P. Renucci, X. Marie et al., Nat. Commun. 8, 14927 (2017).
- K.-Q. Lin, C. S. Ong, S. Bange, P. E. Faria Junior, B. Peng, J. D. Ziegler, J. Zipfel, C. Bäuml, N. Paradiso, K. Watanabe et al., Nat. Commun. 12, 5500 (2021).
- K.-Q. Lin, S. Bange, and J. M. Lupton, Nat. Phys. 15, 242 (2019).
- J.-H. Kim, M. R. Bergren, J. C. Park, S. Adhikari, M. Lorke, T. Frauenheim, D.-H. Choe, B. Kim, H. Choi, T. Gregorkiewicz et al., Nat. Commun. 10, 5488 (2019).
- T. Winzer and E. Malić, Phys. Rev. B 85, 241404(R) (2012).
- T. Winzer, A. Knorr, and E. Malic, Nano Lett. 10, 4839 (2010).
- D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo et al., Nat. Commun. 4, 1987 (2013).
- F. Wendler and E. Malic, in Terahertz Emitters, Receivers, and Applications VI (International Society for Optics and Photonics, San Diego, 2015), Vol. 9585, p. 95850D.
- K.-Q. Lin, P. E. F. Junior, J. M. Bauer, B. Peng, B. Monserrat, M. Gmitra, J. Fabian, S. Bange, and J. M. Lupton, Nat. Commun. 12, 1553 (2021).
- B. Han, C. Robert, E. Courtade, M. Manca, S. Shree, T. Amand, P. Renucci, T. Taniguchi, K. Watanabe, X. Marie, L. E. Golub, M. M. Glazov, and B. Urbaszek, Phys. Rev. X 8, 031073 (2018).
- A. Steinhoff, F. Jahnke, and M. Florian, Phys. Rev. B 104, 155416 (2021).
- M. Massicotte, F. Vialla, P. Schmidt, M. B. Lundeberg, S. Latini, S. Haastrup, M. Danovich, D. Davydovskaya, K. Watanabe, T. Taniguchi et al., Nat. Commun. 9, 1633 (2018).
- M. Danovich, V. Zólyomi, V. I. Fal'ko, and I. L. Aleiner, 2D Mater. 3, 035011 (2016).
- Y. Hoshi, T. Kuroda, M. Okada, R. Moriya, S. Masubuchi, K. Watanabe, T. Taniguchi, R. Kitaura, and T. Machida, Phys. Rev. B 95, 241403(R) (2017).
- J. Zipfel, M. Kulig, R. Perea-Causín, S. Brem, J. D. Ziegler, R. Rosati, T. Taniguchi, K. Watanabe, M. M. Glazov, E. Malic, and A. Chernikov, Phys. Rev. B 101, 115430 (2020).
- T. Deilmann and K. S. Thygesen, Phys. Rev. B 96, 201113(R) (2017).
- E. Malic, M. Selig, M. Feierabend, S. Brem, D. Christiansen, F. Wendler, A. Knorr, and G. Berghäuser, Phys. Rev. Mater. 2, 014002 (2018).
- J. Madéo, M. K. Man, C. Sahoo, M. Campbell, V. Pareek, E. L. Wong, A. Al-Mahboob, N. S. Chan, A. Karmakar, B. M. K. Mariserla et al., Science 370, 1199 (2020).
- R. Wallauer, R. Perea-Causin, L. Münster, S. Zajusch, S. Brem, J. Güdde, K. Tanimura, K.-Q. Lin, R. Huber, E. Malic et al., Nano Lett. 21, 5867 (2021).
- S. Brem, A. Ekman, D. Christiansen, F. Katsch, M. Selig, C. Robert, X. Marie, B. Urbaszek, A. Knorr, and E. Malic, Nano Lett. 20, 2849 (2020).
- D. Erkensten, S. Brem, and E. Malic, Phys. Rev. B 103, 045426 (2021).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.104.L241406 for additional details on the temperature- and time-resolved photoluminescence measurements, microscopic modeling (derivation of excitonic Auger matrix elements, exciton-exciton annihilation rates, and exciton binding energies) and ab initio calculations; also see references [48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72] therein.
- H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 2009).
- M. Kira and S. W. Koch, Prog. Quantum. Electron. 30, 155 (2006).
- G. Berghäuser and E. Malic, Phys. Rev. B 89, 125309 (2014).
- A. Kormányos, G. Burkard, M. Gmitra, J. Fabian, V. Zólyomi, N. D. Drummond, and V. Fal'ko, 2D Mater. 2, 022001 (2015).
- Y. P. Varshni, Physica 34, 149 (1967).
- K. O'Donnell and X. Chen, Appl. Phys. Lett. 58, 2924 (1991).
- A. Arora, M. Koperski, K. Nogajewski, J. Marcus, C. Faugeras, and M. Potemski, Nanoscale 7, 10421 (2015).
- A. Arora, K. Nogajewski, M. Molas, M. Koperski, and M. Potemski, Nanoscale 7, 20769 (2015).
- Y. You, X. Zhang, T. C. Berkelbach, M. S. Hybertsen, D. R. Reichman, and T. F. Heinz, Nat. Phys. 11, 477 (2015).
- Z. Ye, L. Waldecker, E. Y. Ma, D. Rhodes, A. Antony, B. Kim, X.-X. Zhang, M. Deng, Y. Jiang, Z. Lu, D. Smirnov, K. Watanabe, T. Taniguchi, J. Hone, and T. F. Heinz, Nat. Commun. 9, 3718 (2018).
- A. Steinhoff, M. Flrian, A. Singh, K. Tran, M. Kolarczik, S. Helmrich, A. W. Achtstein, U. Woggon, N. Owschimikow, F. Jahnke, and X. Li, Nat. Phys. 14, 1199 (2018).
- P. Nagler, M. V. Ballottin, A. A. Mitioglu, M. V. Durnev, T. Taniguchi, K. Watanabe, A. Chernikov, C. Schüller, M. M. Glazov, P. C. M. Christianen, and T. Korn, Phys. Rev. Lett. 121, 057402 (2018).
- K. Wagner, J. Zipfel, R. Rosati, E. Wietek, J. D. Ziegler, S. Brem, R. Perea-Causín, T. Taniguchi, K. Watanabe, M. M. Glazov, E. Malic, and A. Chernikov, Phys. Rev. Lett. 127, 076801 (2021).
- M. Kulig, J. Zipfel, P. Nagler, S. Blanter, C. Schüller, T. Korn, N. Paradiso, M. M. Glazov, and A. Chernikov, Phys. Rev. Lett. 120, 207401 (2018).
- S. Lippert, L. M. Schneider, D. Renaud, K. N. Kang, O. Ajayi, J. Kuhnert, M.-U. Halbich, O. M. Abdulmunem, X. Lin, K. Hassoon et al., 2D Mater. 4, 025045 (2017).
- W.-T. Hsu, J. Quan, C.-Y. Wang, L.-S. Lu, M. Campbell, W.-H. Chang, L.-J. Li, X. Li, and C.-K. Shih, 2D Mater. 6, 025028 (2019).
- L. Waldecker, A. Raja, M. Rösner, C. Steinke, A. Bostwick, R. J. Koch, C. Jozwiak, T. Taniguchi, K. Watanabe, E. Rotenberg, T. O. Wehling, and T. F. Heinz, Phys. Rev. Lett. 123, 206403 (2019).
- P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. D. Corso, S. de Gironcoli, S. Fabris et al., J. Condens. Matter Phys. 21, 395502 (2009).
- A. Marini, C. Hogan, M. Grüning, and D. Varsano, Comput. Phys. Commun. 180, 1392 (2009).
- J. Deslippe, G. Samsonidze, D. A. Strubbe, M. Jain, M. L. Cohen, and S. G. Louie, Comput. Phys. Commun. 183, 1269 (2012).
- S. Grimme, S. Ehrlich, and L. Goerigk, J. Comput. Chem 32, 1456 (2011).
- F. Bruneval and X. Gonze, Phys. Rev. B 78, 085125 (2008).
- D. R. Hamann, Phys. Rev. B 88, 085117 (2013).
- R. Gillen and J. Maultzsch, Phys. Rev. B 97, 165306 (2018).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
- E. Liu, J. van Baren, T. Taniguchi, K. Watanabe, Y.-C. Chang, and C. H. Lui, Phys. Rev. Research 1, 032007(R) (2019).
- L. V. Keldysh, J. Exp. Theor. Phys. 29, 658 (1979).
- E. O. Kane, J. Phys. Chem. Solids 1, 249 (1957).
- J. M. Luttinger and W. Kohn, Phys. Rev. 97, 869 (1955).
- S. Brem, J. Zipfel, M. Selig, A. Raja, L. Waldecker, J. D. Ziegler, T. Taniguchi, K. Watanabe, A. Chernikov, and E. Malic, Nanoscale 11, 12381 (2019).
- M. He, P. Rivera, D. Van Tuan, N. P. Wilson, M. Yang, T. Taniguchi, K. Watanabe, J. Yan, D. G. Mandrus, H. Yu, H. Dery, W. Yao, and X. Xu, Nat. Commun 11, 618 (2020).
- A. L. Ivanov and H. Haug, Phys. Rev. B 48, 1490 (1993).
- P. Cudazzo, I. V. Tokatly, and A. Rubio, Phys. Rev. B 84, 085406 (2011).
- S. Latini, T. Olsen, and K. S. Thygesen, Phys. Rev. B 92, 245123 (2015).
- M. L. Trolle, T. G. Pedersen, and V. Véniard, Sci. Rep. 7, 39844 (2017).
- D. Y. Qiu, F. H. da Jornada, and S. G. Louie, Phys. Rev. B 93, 235435 (2016).
- F. H. da Jornada, D. Y. Qiu, and S. G. Louie, Phys. Rev. B 95, 035109 (2017).
- D. V. Rybkovskiy, I. C. Gerber, and M. V. Durnev, Phys. Rev. B 95, 155406 (2017).
- F. Katsch, M. Selig, A. Carmele, and A. Knorr, Phys. Status Solidi B 255, 1800185 (2018).
- F. Katsch, M. Selig, and A. Knorr, Phys. Rev. Lett. 124, 257402 (2020).
- A. A. Mosto, J. R. Yates, G. Pizzi, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, Comput. Phys. Commun. 185, 2309 (2014).
- A. Raja, L. Waldecker, J. Zipfel, Y. Cho, S. Brem, J. D. Ziegler, M. Kulig, T. Taniguchi, K. Watanabe, E. Malic, T. F. Heinz, T. C. Berkelbach, and A. Chernikov, Nat. Nanotechnol. 14, 832 (2019).