Abstract
Mechanism of exciton appearance and disappearance under isotropic strain in monolayer WS2 is investigated using the non-local van der Waals density functionals theory with taking into account the spin–orbit coupling (SOC). The essential effects such as vertical shift (the shift in the binding energy scale) of the d and p partial orbitals of the W and S atoms, respectively, and the flattening of band valleys caused by strain are explored. The exciton appearance and disappearance in the isotropic strained WS2 are discussed. Thanks to the spin splitting by SOC effect, light and dark excitons are visually shown. Under strain, the flattening of the band valleys may lead to the disappearance of excitons, causing the direct-to-indirect transition of the band gap. Furthermore, the vertical shift of electron orbitals at band edges can result in a notable reduction in the band gap. These findings can open a possible path to manipulate excitons using strain scheme.
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Data Availability Statement
This manuscript has associated data in a data repository. [Authors' comment: The datasets generated and analysed in this manuscript are available upon reasonable request, by contacting the corresponding authors.]
References
C. Ballif, M. Regula, F. Levy, Sol. Energy Mater. Sol. Cells 57, 189 (1999)
S.Y. Chen, C. Zheng, M.S. Fuhrer, J. Yan, Nano Lett. 15, 2526 (2015)
S.K. Srivastava, B.N. Avasthi, J. Mater. Sci. 20, 3801 (1985)
C. Ataca, H. Sahin, S. Ciraci, J. Phys. Chem. C 116, 8983 (2012)
A.B. Kaul, J. Mater. Res. 29, 348 (2014)
Y. Sang, Z. Zhao, M. Zhao, P. Hao, Y. Leng, H. Liu, Adv. Mater. 27, 363 (2015)
H.R. Gutierrez, N. Perea-Lopez, A.L. Elias, A. Berkdemir, B. Wang, R. Lv, F. Lopez-Urias, V.H. Crespi, H. Terrones, M. Terrones, Nano Lett. 13, 3447 (2013)
L. Yuan, L. Huang, Nanoscale 7, 7402 (2015)
M. Pumera, H.L. Adeline, TrAC Trends Anal. Chem. 61, 49 (2014)
E. Bucher, A. Aruchamy, Photoelectrochemistry and Photovoltaics of Layered Semiconductors, vol. 14 (Springer, Netherlands, 1992), p.1
A. Klein, S. Tiefenbacher, V. Eyert, C. Pettenkofer, W. Jaegermann, Phys. Rev. B 64, 205416 (2001)
H.A. Therese, J. Li, U. Kolb, W. Tremel, Solid State Sci. 7, 67 (2005)
P. Zeng, X. Ji, Z. Su, S. Zhang, RSC Adv. 8, 20557 (2018)
R. Roldán, J.A. Silva-Guillén, M.P. López-Sancho, F. Guinea, E. Cappelluti, P. Ordejón, Ann. Phys. 526, 347 (2014)
Z. Fan, Z. Wei-Bing, T. Bi-Yu, Chin. Phys. B 24, 097103 (2015)
S. Tongay, W. Fan, J. Kang, J. Park, U. Koldemir, J. Suh, D.S. Narang, K. Liu, J. Ji, J. Li, R. Sinclair, J. Wu, Nano Lett. 14, 3185 (2014)
M. Hosseini, M. Elahi, M. Pourfath, D. Esseni, IEEE Trans. Electron Devices 62, 3192 (2015)
G. Kresse, D. Joubert, Phys. Rev. B 59, 1758 (1999)
G. Kresse, J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996)
G. Kresse, J. Furthmüller, Phys. Rev. B 54, 11169 (1996)
H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13, 5188 (1976)
J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)
K. Lee, E.D. Murray, L. Kong, B.I. Lundqvist, D.C. Langreth, Phys. Rev. B 82, 081101(R) (2010)
J. Klimeš, D.R. Bowler, A. Michaelides, J. Phys.: Condens. Matter 22, 022201 (2010)
J. Klimeš, D.R. Bowler, A. Michaelides, Phys. Rev. B 83, 195131 (2011)
M. Dion, H. Rydberg, E. Schröder, D.C. Langreth, B.I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)
W.J. Schutte, J.L. de Boer, F. Jellinek, J. Solid State Chem. 70, 207 (1987)
Z. Li, T. Wang, C. Jin, Z. Lu, Z. Lian, Y. Meng, M. Blei, S. Gao, T. Taniguchi, K. Watanabe, T. Ren, S. Tongay, L. Yang, D. Smirnov, T. Cao, S.-F. Shi, Nat. Commun. 10, 1 (2019)
K. Kośmider, W.G. Jhon, J. Fernández-Rossier, Phys. Rev. B 88, 245436 (2013)
Q.F. Yao, J. Cai, W.Y. Tong, S.J. Gong, J.Q. Wang, X. Wan, C.G. Duan, J.H. Chu, Phys. Rev. B 95, 165401 (2017)
K.F. Mak, C. Lee, J. Hone, J. Shan, T.F. Heinz, Phys. Rev. Lett. 105, 136805 (2010)
A. Raja, A. Chaves, Y. Jaeeun, G. Arefe, H.M. Hill, A.F. Rigosi, T.C. Berkelbach, P. Nagler, C. Schüller, T. Korn, C. Nuckolls, J. Hone, L.E. Brus, T.F. Heinz, D.R. Reichman, A. Chernikov, Nat. Commun. 8, 15251 (2017)
Z. Li, T. Wang, C. Jin, L. Zhengguang, Z. Lian, Y. Meng, M. Blei, S. Gao, T. Taniguchi, K. Watanabe, T. Ren, S. Tongay, L. Yang, D. Smirnov, T. Cao, S.-F. Shi, Nat. Commun. 10, 1 (2019)
D. Shin, H. Hübener, U. De Giovannini, H. Jin, A. Rubio, N. Park, Nat. Commun. 9, 1 (2018)
D. Xiao, G. Liu, W. Feng, X. Xu, W. Yao, Phys. Rev. Lett. 108, 196802 (2012)
T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, B. Liu, J. Feng, Nat. Commun. 3, 1 (2012)
G. Berghäuser, I. Bernal-Villamil, R. Schmidt, R. Schneider, I. Niehues, P. Erhart, S.M. de Váconcellos, R. Bratschitsh, A. Knorr, E. Malic, Nat. Commun. 9, 1 (2018)
E. Cappelluti, R. Roldán, J.A. Silva-Guillén, P. Ordejón Guinea, Phys. Rev. B 88, 075409 (2013)
S.J. Kim, K. Choi, B. Lee, Y. Kim, B.H. Hong, Annu. Rev. Mater. Res. 45, 63 (2015)
J. Su, J. He, J. Zhang, Z. Lin, J. Chang, J. Zhang, Y. Hao, Sci. Rep. 9, 3518 (2019)
R.K. Defo, S. Fang, S.N. Shirodkar, G.A. Tritsaris, A. Dimoulas, E. Kaxiras, Phys. Rev. B 94, 155310 (2016)
A. Kumar, P.K. Ahluwalia, Physica B: Condens. Matt. 419, 66 (2013)
J. Feng, X. Qian, C.W. Huang, J. Li, Nat. Photonics 6, 866 (2012)
J. Krustok, R. Kaupmees, R. Jaaniso, V. Kiisk, I. Sildos, B. Li, Y. Gong, AIP Adv. 7, 065005 (2017)
A. Castellanos-Gomez, R. Roldán, E. Cappelluti, M. Buscema, F. Guinea, H.S. van der Zant, G.A. Steele, Nano Lett. 13, 5361 (2013)
A. Chernikov, A.M. Van Der Zande, H.M. Hill, A.F. Rigosi, A. Velauthapillai, J. Hone, T.F. Heinz, Phys. Rev. Lett. 115, 126802 (2015)
Acknowledgements
This research was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 103.01-2018.315. One of the authors (V. A. Dinh) would like to thank Center for Computational Physics, Institute of Physics, Vietnam Academy of Science and Technology for providing the HPC system.
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Tran, Q.H., Tran, T.N., Luong, T.T. et al. Band valley flattening and exciton appearance/disappearance under isotropic strain in monolayer WS2. Eur. Phys. J. Plus 137, 1317 (2022). https://doi.org/10.1140/epjp/s13360-022-03537-2
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DOI: https://doi.org/10.1140/epjp/s13360-022-03537-2