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Optical signature of bipolaron in monolayer transition metal dichalcogenides: all coupling approach

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Abstract

We studied the optical signature of bipolaron and its effects on the bandgap modulation in the single-layer Transition Metal Dichalcogenides (TMDs) under magnetic field. Using the Huybrecht method, we derived the ground state energies in the modified zero Landau levels for all Fröhlich coupling constants. We take into account both intrinsic longitudinal optical phonon modes and surface optical phonon modes induced by the polar substrate. We observed that the higher the coupling strength, the stronger is the magnetic field effect. The highest amplitude of the bandgap modulation is obtained for the MoS2 monolayer and the lowest with the WSe2 monolayer. We also found that the bipolaron is stable in TMDs. It is seen that the optical absorption presents the threshold values and respectively increases for WSe2, MoSe2, WS2 and MoS2.

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References

  • Arora, A., Nogajewski, K., Molas, M., Koperski, M., Potemski, M.: Exciton band structure in layered MoSe2: from a monolayer to the bulk limit. Nanoscale 7, 20769–20775 (2015)

    ADS  Google Scholar 

  • Berman, O.L., Roman, Y.K.: Towards superfluidity of dipolar excitons in a transition metal dichalcogenide double layer. Phys. Rev. B 96, 094502 (2017)

    ADS  Google Scholar 

  • Brosens, F., Devreese, J.T.: Stability of bipolarons in the presence of a magnetic field. Phys. Rev. B 54, 9792–9808 (1996)

    ADS  Google Scholar 

  • Chen, C., Avila, J., Wang, S., Wang, Y., Shen, C., Yang, R., Nosarzewski, B., Devereaux, T.P., Zhang, G., Asensio, M.C.: Emergence of interfacial polarons from electron–phonon coupling in graphene/h-BN van der waals heterostructures. Nano. Lett. 18, 1082–1087 (2018)

    ADS  Google Scholar 

  • Chen, C., Avila, J., Wang, S., Wang, Y., Mucha-Kruczyński, M., Shen, C., Asensio, M.C.: Emergence of Frohlich polaron from interlayer electron-phonon coupling in van der Waals heterostructure. arXiv preprint, http://arxiv.org/abs/1707.00184 (2017)

  • Choi, W., Chaudhary, N., Han, G.H., Park, J., Akinwande, D., Lee, Y.H.: Recent development of two-dimensional transition metal dichalcogenides and their applications. Mater. Today 20, 116–130 (2017)

    Google Scholar 

  • Chow, C.M., Yu, H., Jones, A.M., Yan, J., Mandrus, D.G., Taniguchi, T., Xu, X.: Unusual exciton–phonon interactions at van der Waals engineered interfaces. Nano. Lett. 17, 1194–1199 (2017)

    ADS  Google Scholar 

  • Devreese, J.T., Huybrechts, W., Lemmeks, L.: On the optical absorption of free polarons at weak coupling. Physica Status Solidi (B) 48, 77–86 (1971)

    ADS  Google Scholar 

  • Devreese, J.T.: Fröhlich polarons from 0D to 3D: concepts and recent developments. J. Phys. Cond. Mater. 19, 255201 (2007)

    ADS  Google Scholar 

  • Devreese, J.T., Alexandre, S.A.: Fröhlich polaron and bipolaron: recent developments. Rep. Prog. Phys. 72, 066501 (2009)

    ADS  Google Scholar 

  • Devreese, J.T.: Fröhlich Polarons. Lecture course including detailed theoretical derivations. arXiv preprint: http://arxiv.org/abs/1611.06122 (2016)

  • Emin, D.: Barrier to recombination of oppositely charged large polarons. J. Appl. Phys. 123, 055105 (2018)

    ADS  Google Scholar 

  • Fobasso, M.F.C., Kenfack-Sadem, C., Baloitcha, E., Fotué, A.J., Fai, L.C.: Lifetime and dynamics of polaron and bipolaron in graphene nanoribbon under laser. Eur. Phys. J. Plus 135, 1–18 (2020)

    Google Scholar 

  • Gordon, R.A., Yang, D., Crozier, E.D., Jiang, D.T., Frindt, R.F.: Structures of exfoliated single layers of WS2, MoS2, and MoSe2 in aqueous suspension. Phys. Rev. B 65, 125407 (2002)

    ADS  Google Scholar 

  • Hien, N.D., Nguyen, C.V., Hieu, N.N., Kubakaddi, S.S., Duque, C.A., Mora-Ramos, M.E., Phuc, H.V.: Magneto-optical transport properties of monolayer transition metal dichalcogenides. Phys. Rev. B 101, 045424 (2020)

    ADS  Google Scholar 

  • Kaasbjerg, K.K., Thygesen, S., Jacobsen, K.W.: Phonon-limited mobility in n-type single-layer MoS2 from first principles. Phys. Rev. B 85, 115317 (2012)

    ADS  Google Scholar 

  • Kaasbjerg, K.K., Bhargavi, K.S., Kubakaddi, S.S.: Hot-electron cooling by acoustic and optical phonons in monolayers of MoS2 and other transition-metal dichalcogenides. Phys. Rev. B 90, 165436 (2014)

    ADS  Google Scholar 

  • Kandemir, B.S., Akay, D.: The effect of electron-phonon coupling in spin–orbit-coupled graphene. Philosop. Mag. 97, 2225–2235 (2017)

    ADS  Google Scholar 

  • Kang, M., Kim, B., Ryu, S.H., Jung, S.W., Kim, J., Moreschini, L., Kim, K.S.: Universal mechanism of band-gap engineering in transition-metal dichalcogenides. Nano. Lett. 17, 1610–1615 (2017)

    ADS  Google Scholar 

  • Kenfack-Sadem, C., Ekengoue, C.M., Danga, J.E., Fobasso, F.M.C., Nguepnang, J.V., Fotue, A.J., Fai, L.C.: Laser control of magneto-polaron in transition metal dichalcogenides triangular quantum well. Phys. Lett. A 384, 126662 (2020)

    MathSciNet  Google Scholar 

  • Klimin, S.N., Devreese, J.T.: Optical conductivity of a strong-coupling Fröhlich polaron. Phys. Rev. B 89, 035201 (2014)

    ADS  Google Scholar 

  • Kormányos, A., Burkard, G., Gmitra, M., Fabian, J., Zólyomi, V., Drummond, N.D., Fal’ko, V.: k-p theory for two-dimensional transition metal dichalcogenide semiconductors. 2D. Mater. 2. 022001 (2015)

  • Koschorreck, M., Pertot, D., Vogt, E., Fröhlich, B., Feld, M., Köhl, M.: Attractive and repulsive Fermi polarons in two dimensions. Nature 485, 619–622 (2012)

    ADS  Google Scholar 

  • Kuc, A., Zibouche, N., Heine, T.: Influence of quantum confinement on the electronic structure of the transition metal sulfide TS2. Phys. Rev. B 83, 245213 (2011)

    ADS  Google Scholar 

  • Landau, L.D.: Electron motion in crystal lattices. Phys. Z. Sowjetunion 3, 664–666 (1993)

  • Lee, C.S., Jin, G., Seo, S.Y., Kim, J., Han, C., Park, M.Y., Jo, M.H.: Programmed band-gap modulation within van der Waals semiconductor monolayers by metalorganic vapor-phase epitaxy. Chem. Mater. 32, 5084–5090 (2020)

    Google Scholar 

  • Lee, H.S., Min, S.W., Chang, Y.G., Park, M.K., Nam, T., Kim, H., Kim, J.H., Ryu, S., Im, S.: MoS2 nanosheet phototransistors with thickness-modulated optical energy gap. Nano. Lett. 12, 3695–3700 (2012)

    ADS  Google Scholar 

  • Lee, J., Huang, J., Sumpter, B.G., Yoon, M.: Strain-engineered optoelectronic properties of 2D transition metal dichalcogenide lateral heterostructures. 2D. Mater. 4, 021016 (2017)

  • Li, P.-F., Wang, Z.-W.: Optical absorption of Fröhlich polaron in monolayer transition metal dichalcogenides. J. Appl. Phys. 123, 204308 (2018)

    ADS  Google Scholar 

  • Lin, I.-T., Liu, J.-M.: Surface polar optical phonon scattering of carriers in graphene on various substrates. Appl. Phys. Lett. 103, 081606 (2013)

    ADS  Google Scholar 

  • Liu, B., Zhao, W., Ding, Z., Verzhbitskiy, I., Li, L., Lu, J., Loh, K.P.: Engineering bandgaps of monolayer MoS2 and WS2 on fluoropolymer substrates by electrostatically tuned many-body effects. Adv. Mater. 28, 6457–6464 (2016)

    Google Scholar 

  • Liu, G.-B., Pang, H., Yao, Y., Yao, W.: Intervalley coupling by quantum dot confinement potentials in monolayer transition metal dichalcogenides. News J. Phys. 16, 105011 (2014)

    Google Scholar 

  • Liu, B., Niu, W., Ruan, X., Zhu, C., Wang, X., He, L., Xu, Y.: Observation of Small Polaron and Acoustic Phonon Coupling in Ultrathin La0. 7Sr0. 3MnO3/SrTiO3 Structures. physica status solidi (RRL)–Rapid Research Letters, 13, 1800657(2019)

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

    ADS  Google Scholar 

  • Nguepnang, J.V., Teguimfouet, A.K., Kenfack-Sadem, C., Kenfack-Jiotsa, A.: Polaron dynamic and decoherence in transition metal dichalcogenides under electric field. Indian J. Phys. (2021). https://doi.org/10.1007/s12648-021-02158-2

    Article  Google Scholar 

  • Ni, Z., Liu, Q., Tang, K., Zheng, J., Zhou, J., Qin, R., Lu, J.: Tunable bandgap in silicene and germanene. Nano. Lett. 12, 113–118 (2012)

    ADS  Google Scholar 

  • Raja, A., Chaves, A., Yu, J., Arefe, G., Hill, H.M., Rigosi, A.F., Nuckolls, C.: Coulomb engineering of the bandgap and excitons in two-dimensional materials. Nat. Comm. 8, 1–7 (2017)

    Google Scholar 

  • Ruan, Y.-H., Chen, Q.-H.: Ground and excited states of bipolarons in two and three dimensions. Comm. Theor. Phys. 48, 169 (2007)

    ADS  Google Scholar 

  • Ryou, J., Kim, Y.S., Kc, S., Cho, K.: Monolayer MoS2 bandgap modulation by dielectric environments and tunable bandgap transistors. Sci. Rep. 6, 1–8 (2016)

    Google Scholar 

  • Sezen, H., Shang, H., Bebensee, F., Yang, C., Buchholz, M., Nefedov, A., Wöll, C.: Evidence for photogenerated intermediate hole polarons in ZnO. Nat. Comm. 6, 1–5 (2015)

    Google Scholar 

  • Sohier, T., Gibertini, M., Calandra, M., Mauri, F., Marzari, N.: Breakdown of optical phonons’ splitting in two-dimensional materials. Nano. Lett. 17, 3758–3763 (2017)

    ADS  Google Scholar 

  • Sohier, T., Calandra, M., Mauri, F.: Two-dimensional Fröhlich interaction in transition-metal dichalcogenide monolayers: Theoretical modeling and first-principles calculations. Phys. Rev. B 94, 085415 (2016)

    ADS  Google Scholar 

  • Thilagam, A.: Exciton formation assisted by longitudinal optical phonons in transition metal dichalcogenides. J. Appl. Phys. 120, 124306–124314 (2016)

    ADS  Google Scholar 

  • Thygesen, K.S.: Calculating excitons, plasmons, and quasiparticles in 2D materials and van der Waals heterostructures. 2D. Mater. 4, 022004 (2017)

  • Tongay, S., Zhou, J., Ataca, C., Lo, K., Matthews, T.S., Li, J., Grossman, J.C., Wu, J.: Thermally driven crossover from indirect toward direct bandgap in 2D semiconductors: MoSe2 versus MoS2. Nano. Lett. 12, 5576–5580 (2012)

    ADS  Google Scholar 

  • Trolle, M.L., Pedersen, T.G., Véniard, V.: Model dielectric function for 2D semiconductors including substrate screening. Sci. Rep. 7, 39844 (2017)

    ADS  Google Scholar 

  • Ugeda, M.M., Bradley, A.J., Shi, S.F., da Jornada, F.H., Zhang, Y., Qiu, D.Y., Ruan, W., Mo, S.K., Hussain, Z., Shen, Z.X., Wang, F., Louie, S.G., Crommie, M.F.: Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor. Nat. Mater. 13, 1091–1095 (2014)

    ADS  Google Scholar 

  • Wang, Z.-W., Lei, L., Li, Z.-Q.: Energy gap induced by the surface optical polaron in graphene on polar substrates. Appl. Phys. Lett. 106, 101601 (2015)

    ADS  Google Scholar 

  • Withers, F., Del Pozo-Zamudio, O., Mishchenko, A., Rooney, A.P., Gholinia, A., Watanabe, K., Novoselov, K.S.: Light-emitting diodes by band-structure engineering in van der Waals heterostructures. Nat. Mater. 14, 301–306 (2015)

    ADS  Google Scholar 

  • Xiao, Y., Li, Z.Q., Wang, Z.W.: Polaron effect on the bandgap modulation in monolayer transition metal dichalcogenides. J. Phys. Cond. Matter. 29, 485001 (2017)

    Google Scholar 

  • Xin-Ran, W., Yi, S., Rong, Z.: Field-effect transistors based on two-dimensional materials for logic applications. Chineese Phys. B 22, 098505 (2013)

    ADS  Google Scholar 

  • Yin, Z., Li, H., Jiang, L., Shi, Y., Sun, Y., Lu, G., Zhang, Q., Chen, X., Zhang, H.: Single-layer MoS2 phototransistors. ACS. Nano. 6, 74–80 (2012)

    Google Scholar 

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Nguepnang, J.V., Kenfack-Sadem, C., Kenfack-Jiotsa, A. et al. Optical signature of bipolaron in monolayer transition metal dichalcogenides: all coupling approach. Opt Quant Electron 53, 728 (2021). https://doi.org/10.1007/s11082-021-03365-1

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