Abstract
We study theoretically the variations of interlayer exciton binding energy caused by the exciton–optical phonons coupling in van der Waals heterostructures composed of double-layer black phosphorus (BP), where both the longitudinal optical phonon modes and the surface optical phonon modes induced by the inserted h-BN layer are taken into account. We find that the strength of exciton–phonon coupling depends on the anisotropy of the effective mass of interlayer exciton, which plays a crucial rule in adjusting the binding energies of interlayer excitons. Moreover, the modulation effects of interlayer distance between two layers as well as the internal distance between BP layer and the inserted h-BN layer on the binding energies are analyzed quantitatively. These results provide theoretical insight when modulating interlayer excitons in two-dimensional van der Waals heterostructures in experiments.
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References
Ankit, J., McGaughey, J.H.: Strongly anisotropic in-plane thermal transport in single-layer black phosphorene. Sci. Rep. 5, 8501 (2015)
Berman, O.L., Gumbs, G., Kezerashvili, R.Y.: Bose–Einstein condensation and superfluidity of dipolar excitons in a phosphorene double layer. Phys. Rev. B 96, 014505 (2017)
Butov, L.V.: Excitonic devices. Superlattices Microstruct. 108, 2–26 (2017)
Chao, X., Zheng, J.X., Su, Y.T., Li, S.K., Zhang, B.K., Feng, Y.C., Pan, F.: Few-layer tin sulfide: a new black-phosphorus-analogue 2D material with a sizeable band gap, odd-even quantum confinement effect, and high carrier mobility. J. Phys. Chem. C 120, 22663–22669 (2016)
Chen, Y.F., Quek, S.Y.: Tunable bright interlayer excitons in few-layer black phosphorus based van der Waals heterostructures. 2D Mater. 5, 045031 (2018)
Chen, Y., Quek, S.Y.: Tunable bright interlayer excitons in few-layer black phosphorus based van der Waals heterostructures. 2D Mater. 5, 045031 (2018)
Devreese, J.T., Alexandrov, A.S.: Frohlich polaron and bipolaron: recent developments. Rep. Prog. Phys. 72, 066501 (2009)
Dong, X.Y., Li, R.Z., Deng, J.P., Wang, Z.W.: Interlayer exciton-polaron effect in transition metal dichalcogenides van der Waals heterostructures. J. Phys. Chem. Solids 134, 1–4 (2019)
Fang, H., Battaglia, C., Carraro, C., Nemsak, S., Ozdol, B., Kang, J.S., Bechtel, H.A., Desai, S.B., Kronast, F., Unal, A.A., Conti, G., Conlon, C., Palsson, G.K., Martin, M.C., Minor, A.M., Fadley, C.S., Yablonovitch, E., Maboudian, R., Javey, A.: Strong interlayer coupling in van der Waals heterostructures built from single-layer chalcogenides. Proc. Natl. Acad. Sci. 111, 6198–61202 (2014)
Gomez, A.C., Vicarelli, L., Prada, E., Island, J.O., Acharya, K.L.N., Blanter, S.I., Groenendijk, D.J., Buscema, M., Steele, G.A., Alvarez, J.V., Zandbergen, H.W., Palacios, J.J., Zant, H.S.J.: Isolation and characterization of few-layer black phosphorus. 2D Mater. 1, 025001 (2014)
High, A.A., Hammack, A.T., Butov, L.V., Hanson, A., Gossard, A.C.: Exciton optoelectronic transistor. Opt. Lett. 32, 2466 (2007)
Hu, H., Shi, Z., Khan, K., Cao, R., Liang, W., Tareen, A.K., Zhang, Y., Huang, W., Guo, Z., Luo, X., Zhang, H.: Recent advances in doping engineering of black phosphorus. J. Mater. Chem. A 8, 5421–5441 (2020)
Jose, P.S., Parente, V., Guinea, F., Roldan, R., Prada, E.: Inverse funnel effect of excitons in strained black phosphorus. Phys. Rev. X 6, 031046 (2016)
Kaasbjerg, K., Thygesen, K.S., Jacobsen, K.W.: Phonon-limited mobility in n-type single-layer MoS2 from first principles. Phys. Rev. B 85, 115317 (2012)
Lee, T.D., Low, F.E., Pines, D.: The motion of slow electrons in a polar crystal. Phys. Rev. 90, 291 (1953)
Lin, I.T., Liu, J.M.: Surface polar optical phonon scattering of carriers in graphene on various substrates. Appl. Phys. Lett. 103, 081606 (2013)
Liu, H., Neal, A.T., Zhu, Z., Luo, Z., Xu, X., Tománek, D., Ye, P.D.: Phosphorene: an unexplored 2D semiconductor with a high hole mobility. ACS Nano 8, 4033 (2014)
Mogulkoc, A., Mogulkoc, Y., Rudenko, A.N., Katsnelson, M.I.: Polaronic effects in monolayer black phosphorus on polar substrates. Phys. Rev. B 93, 085417 (2016)
Pereira, J.M., Katsnelson, M.I.: Landau levels of single-layer and bilayer phosphorene. Phys. Rev. B 92, 075437 (2015)
Pouya, S.S., Vazifehshenas, T., Salavati-fard, T., Farmanbar, M.: Anisotropic hybrid excitation modes in monolayer and double-layer phosphorene on polar substrates. Phys. Rev. B 96, 115402 (2017)
Qiao, J.S., Kong, X.H., Hu, Z.X., Yang, F., Ji, W.: High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus. Nat. Commun. 5, 4475 (2014)
Rengel, R., Pascual, E., Martín, M.J.: Influence of the substrate on the diffusion coefficient and the momentum relaxation in graphene: the role of surface polar phonons. Appl. Phys. Lett. 104, 233107 (2014)
Rudenko, A.N., Brener, S., Katsnelson, M.I.: Intrinsic charge carrier mobility in single-layer black phosphorus. Phys. Rev. Lett. 116, 246401 (2016)
Shi, C.S., Sun, N., Wu, Z.B., Chen, J.S., Ahnsir, T., Alshehri, S.M., Ma, D.G.: Managing excitons for high performance hybrid white organic light-emitting diodes by using a simple planar heterojunction interlayer. Appl. Phys. Lett. 112, 023301 (2018)
Shukla, V., Grigoriev, A., Ahuja, R.: Rectifying behavior in twisted bilayer black phosphorus nanojunctions mediated through intrinsic anisotropy. Nanoscale Adv. 2, 1493–1501 (2020)
Sun, Y.R., Giebink, N.C., Kanno, H., Ma, B.W., Thompson, M.E., Forrest, S.R.: Management of singlet and triplet excitons for efficient white organic light-emitting devices. Nature 440, 908–912 (2006)
Tran, V., Ryan, S., Liang, Y.F., Yang, L.: Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus. Phys. Rev. B 89, 235319 (2014)
Tran, V., Fei, R.X., Yang, L.: Quasiparticle energies, excitons, and optical spectra of few-layer black phosphorus. 2D Mater. 2, 044014 (2015)
Tsuji, T., Naka, S., Okada, H., Onnagawa, H.: Nondoped-type white organic electroluminescent devices utilizing complementary color and exciton diffusion. Appl. Phys. Lett. 81, 3329 (2002)
Wang, C.X., Zhang, C., Jiang, J.W., Park, H.S., Rabczuk, T.: Mechanical strain effects on black phosphorus nanoresonators. Nanoscale 8, 901 (2016)
Wang, Z.W., Li, W.P., Xiao, Y., Li, R.Z., Li, Z.Q.: Influence of exciton–phonons coupling on the exciton binding energy in monolayer transition metal dichalcogenides. Appl. Phys. Lett. 110, 231603 (2017)
Wang, Z.W., Dong, X.Y., Li, R.Z., Xiao, Y., Li, Z.Q.: Effect of exciton–phonon coupling on the interlayer excitons in transition metal dichalcogenides double layers. Phys. Status Solid RLL 12, 1800306 (2018)
Withers, F., Zamudio, O.D.P., Mishchenko, A., Rooney, A.P., Gholinia, A., Watanabe, K., Taniguchi, T., Haigh, S.J., Geim, A.K., Tartakovskii, A.I., Novoselov, K.S.: Light-emitting diodes by band-structure engineering in van der Waals heterostructures. Nat. Mater. 14, 301–306 (2015)
Xiao, J., Zhao, M., Wang, Y., Zhang, X.: Excitons in atomically thin 2D semiconductors and their applications. Nanophotonics 6, 1309–1328 (2017)
Zhang, G.W., Chaves, A., Huang, S.Y., Wang, F.J.: Determination of layer-dependent exciton binding energies in few-layer black phosphorus. Sci. Adv. 4, eaap9977 (2018)
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Li, J. Anisotropic interlayer exciton in black phosphorus van der Waals heterostructures. Opt Quant Electron 52, 392 (2020). https://doi.org/10.1007/s11082-020-02504-4
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DOI: https://doi.org/10.1007/s11082-020-02504-4