Abstract
We theoretically study the temperature dependence of the excitonic spectra of monolayer transition metal dichalcogenides using the O′Donnell equation, \({E_g}(T) = {E_g}(0) - S\langle \hbar \omega \rangle [cloth(\frac{{\hbar \omega }}{{2{k_B}T}} - 1)]\) . We develop a theoretical model for the quantitative estimation of the Huang–Rhys factor S and average phonon energy \(\langle \hbar \omega \rangle \) based on exciton coupling with longitudinal optical and acoustic phonons in the Fröhlich and deformation potential mechanisms, respectively. We present reasonable explanations for the fitted values of the Huang–Rhys factor and average phonon energy adopted in experiments. Comparison with experimental results reveals that the temperature dependence of the peak position in the excitonic spectra can be well reproduced by modulating the polarization parameter and deformation potential constant.
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References
H. Y. Yu, X. D. Cui, X. D. Xu, and W. Yao, Valley excitons in two-dimensional semiconductors, Natl. Sci. Rev. 2(1), 57 (2015)
A. V. Kolobov and J. Tominaga, Two-dimensional transition-metal dichalcogenides, Springer Series in Materials Science 239, 321 (2016)
S. Tongay, J. Zhou, C. Ataca, K. Lo, T. S. Matthews, J. Li, J. C. Grossman, and J. Wu, Thermally driven crossover from indirect toward direct bandgap in 2D semiconductors: MoSe2 versus MoS2, Nano Lett. 12(11), 5576 (2012)
J. S. Ross, S. F. Wu, H. Y. Yu, N J. Ghimire, A. M. Jones, G. Aivazian, J. Q. Yan, D. G. Mandrus, D. Xiao, W. Yao, and X. D. Xu, Electrical control of neutral and charged excitons in a monolayer semiconductor, Nature Commun. 4, 1474 (2013)
A. P. S. Gaur, S. Sahoo, J. F. Scott, and R. S. Katiyar, Electron–phonon interaction and double-resonance raman studies in monolayer WS2, J. Phys. Chem. C 119(9), 5146 (2015)
A. Arora, M. Koperski, K. Nogajewski, J. Marcus, C. Faugeras, and M. Potemski, Excitonic resonances in thin films of WSe2: From monolayer to bulk material, Nanoscale 7(23), 10421 (2015)
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(16), 165412 (2016)
P. Dey, J. Paul, Z. Wang, C. E. Stevens, C. Liu, A. H. Romero, J. Shan, D. J. Hilton, and D. Karaiskaj, Optical coherence in atomic-monolayer transition-metal dichalcogenides limited by electron-phonon interactions, Phys. Rev. Lett. 116(12), 127402 (2016)
J. W. Christopher, B. B. Goldberg, and A. K. Swan, Long tailed trions in monolayer MoS2: Temperature dependent asymmetry and resulting red-shift of trion photoluminescence spectra, Sci. Rep. 7(1), 14062 (2017)
K. P. O’Donnell and X. Chen, Temperature dependence of semiconductor band gaps, Appl. Phys. Lett. 58(25), 2924 (1991)
K. L. He, N. Kumar, L. Zhao, Z. F. Wang, K. F. Mak, H. Zhao, and J. Shan, Tightly bound excitons in monolayer WSe2, Phys. Rev. Lett. 113(2), 026803 (2014)
A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. L. 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(7), 076802 (2014)
T. Olsen, S. Latini, F. Rasmussen, and K. S. Thygesen, Simple screened hydrogen model of excitons in twodimensional materials, Phys. Rev. Lett. 116(5), 056401 (2016)
K. Kaasbjerg, K. S. Thygesen, and K. W. Jacobsen, Phonon-limited mobility in n-type single-layer MoS2 from first principles, Phys. Rev. B 85(11), 115317 (2012)
K. Kaasbjerg, K. S. Bhargavi, and S. S. Kubakaddi, Hot-electron cooling by acoustic and optical phonons in monolayers of MoS2 and other transition-metal dichalcogenides, Phys. Rev. B 90(16), 165436 (2014)
A. Ramasubramaniam, Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides, Phys. Rev. B 86(11), 115409 (2012)
A. Thilagam, Ultrafast exciton relaxation in monolayer transition metal dichalcogenides, J. Appl. Phys. 119(16), 164306 (2016)
A. Thilagam, Exciton formation assisted by longitudinal optical phonons in monolayer transition metal dichalcogenides, J. Appl. Phys. 120(12), 124306 (2016)
M. C. Klein, F. Hache, D. Ricard, and C. Flytzanis, Size dependence of electron-phonon coupling in semiconductor nanospheres: The case of CdSe, Phys. Rev. B 42(17), 11123 (1990)
T. Sohier, M. Calandra, and F. Mauri, Two-dimensional Fröhlich interaction in transition-metal dichalcogenide monolayers: Theoretical modeling and first-principles calculations, Phys. Rev. B 94(8), 085415 (2016)
C. Jin, J. Kim, J. Suh, Z. Shi, B. Chen, X. Fan, M. Kam, K. Watanabe, T. Taniguchi, S. Tongay, A. Zettl, J. Q. Wu, and F. Wang, Interlayer electron-phonon coupling in WSe2/hBN heterostructures, Nat. Phys. 13, 127 (2017)
C. M. Chow, H. Y. Yu, A. M. Jones, J. Q. Yan, D. G. Mandrus, T. Taniguchi, K. Watanabe, W. Yao, and X. D. Xu, Unusual exciton–phonon interactions at van der Waals engineered interfaces, Nano Lett. 17(2), 1194 (2017)
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This work was supported by the National Natural Science Foundation of China (Grant No. 11674241) and Young Core Instructor of Peiyang (Grant No. 11303267).
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Wang, ZW., Li, RZ., Dong, XY. et al. Temperature dependence of the excitonic spectra of monolayer transition metal dichalcogenides. Front. Phys. 13, 137305 (2018). https://doi.org/10.1007/s11467-018-0786-y
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DOI: https://doi.org/10.1007/s11467-018-0786-y