Linear and Nonlinear Magneto-optical Absorption Coefficients and Refractive Index Changes in Wse2 Monolayer
Main Article Content
Abstract
This work studies the linear, the third-order nonlinear, and the total optical absorption coefficients (OACs) and the refractive index changes (RICs) caused by both intra- and inter-band transitions in the WSe2 monolayer. The expression for the OACs and RICs in the presence of a magnetic field as well as the Zeeman and electric fields are found by using the compact density matrix approach. The results show that the spin states strongly affect the OACs and RICs, which display the violet-shift behavior with the increase of the magnetic field. The Zeeman fields do not affect the peak positions but slightly reduce peak intensities. The OACs and RICs due to intra-band transition display only one peak in the THz range, while the inter-band spectra show a series of peaks in the near-infrared optical range, making monolayer WSe2 be a promising candidate for novel optoelectronic applications.
Keywords:
WSe2 monolayer, optical absorption coefficients, refractive index changes, magnetic field.
References
[1] D. Xiao, G. B. Liu, W. Feng, X. Xu, W. Yao, Coupled Spin and Valley Physics in Monolayers of MoS2 and Other Group-VI Dichalcogenides, Phys. Rev. Lett., Vol. 108, 2012, pp. 196802, https://doi.org/10.1103/PhysRevLett.108.196802.
[2] J. Have, G. Catarina, T. G. Pedersen, N. Peres, Monolayer Transition Metal Dichalcogenides in Strong Magnetic Fields: Validating the Wannier Model Using a Microscopic Calculation, Phys. Rev. B, Vol. 99, 2019, pp. 035416, https://doi.org/10.1103/PhysRevB.99.035416.
[3] G. Catarina, J. Have, J. F. Rossier, N. M. Peres, Optical Orientation with Linearly Polarized Light in Transition Metal Dichalcogenides, Phys. Rev. B, Vol. 99, 2019, pp. 125405, https://doi.org/10.1103/PhysRevB.99.125405.
[4] G. B. Liu, W. Y. Shan, Y. Yao, W. Yao, D. Xiao, Three-band Tight-binding Model for Monolayers of Group-VIB Transition Metal Dichalcogenides, Phys. Rev. B, Vol. 88, 2013, pp. 085433, https://doi.org/10.1103/PhysRevB.88.085433.
[5] D. Xiao, G. B. Liu, W. Feng, X. Xu, W. Yao, Coupled Spin and Valley Physics in Monolayers of MoS2 and Other Group-VI Dichalcogenides, Phys. Rev. Lett., Vol. 108, 2012, pp. 196802, https://doi.org/10.1103/PhysRevLett.108.196802.
[6] G. Aivazian, Z. Gong, A. M. Jones, R. L. Chu, J. Yan, D. G. Mandrus, C. Zhang, D. Cobden, W. Yao, X. Xu, Magnetic Control of Valley Pseudospin in Monolayer WSe2, Nat. Phys., Vol. 11, 2015, pp. 148-152, https://doi.org/10.1038/nphys3201.
[7] A. Srivastava, M. Sidler, A. V. Allain, D. S. Lembke, A. Kis, A. Imamoğlu, Valley Zeeman Effect in Elementary Optical Excitations of Monolayer WSe2, Nat. Phys. Vol. 11, 2015, pp. 141-147, https://doi.org/10.1038/nphys3203.
[8] M. Tahir, P. Vasilopoulos, Magneto-optical Transport Properties of Monolayer WSe2, Phys. Rev. B, Vol. 94, 2016, pp. 045415, https://doi.org/10.1103/PhysRevB.101.045424.
[9] C. V. Nguyen, N. N. Hieu, C. A. Duque, D. Q. Khoa, N. V. Hieu, L. V. Tung, H. V. Phuc, Linear and Nonlinear Magneto-optical Properties of Monolayer Phosphorene, J. Appl. Phys., Vol. 121, 2017, pp. 045107, https://doi.org/10.1063/1.4974951.
[10] C. V. Nguyen, N. N. Hieu, D. Muoi, C. A. Duque, E. Feddi, H. V. Nguyen, L. T. Phuong, B. D. Hoi, H. V. Phuc, Linear and Nonlinear Magneto-optical Properties of Monolayer MoS2, J. Appl. Phys., Vol. 123, 2018, pp. 034301, https://doi.org/10.1063/1.5009481.
[11] P. T. Huong, D. Muoi, T. N. Bich, H. V. Phuc, C. Duque, P. T. N. Nguyen, C. V. Nguyen, N. N. Hieu, L. T. Hoa, Intra-and Inter-band Magneto-optical Absorption in Monolayer WS2, Physica E: Low-dimensional Systems and Nanostructures, Vol. 124, 2020, pp. 114315, https://doi.org/10.1016/j.physe.2020.114315.
[12] N. D. Hien, C. V. Nguyen, N. N. Hieu, S. Kubakaddi, C. Duque, M. M. Ramos, L. Dinh, T. N. Bich, H. V. Phuc, Magneto-optical Transport Properties of Monolayer Transition Metal Dichalcogenides, Phys. Rev. B, Vol. 101, 2020, p p. 045424, https://doi.org/10.1103/PhysRevB.101.045424.
[13] A. Kormányos, V. Zólyomi, N. D. Drummond, G. Burkard, Spin-orbit Coupling, Quantum Dots, and Qubits in Monolayer Transition Metal Dichalcogenides, Phys. Rev. X, Vol. 4, 2014, pp. 011034, https://doi.org/10.1103/PhysRevX.4.011034.
[14] Y. Ding, Y. Wang, J. Ni, L. Shi, S. Shi, W. Tang, First Principles Study of Structural, Vibrational and Electronic Properties of Graphene-like MX2 (M= Mo, Nb, W, Ta; X= S, Se, Te) Monolayers, Physica B: Condensed Matter, Vol. 406, 2011, pp. 2254-2260, https://doi.org/10.1016/j.physb.2011.03.044.
[15] G. Rezaei, M. Karimi, A. Keshavarz, Excitonic Effects on the Nonlinear Intersubband Optical Properties of a Semi-parabolic One-dimensional Quantum Dot, Physica E: Low-dimensional Systems and Nanostructures, Vol. 43, 2010, pp. 475-481, https://doi.org/10.1016/j.physe.2010.08.035.
[16] H. L. Liu, C. C. Shen, S. H. Su, C. L. Hsu, M. Y. Li, L. J. Li, Optical Properties of Monolayer Transition Metal Dichalcogenides Probed by Spectroscopic Ellipsometry, Appl. Phys. Lett., Vol. 105, 2014, pp. 201905, https://doi.org/10.1063/1.4901836.
[17] T. Morimoto, Y. Hatsugai, H. Aoki, Optical Hall Conductivity in Ordinary and Graphene Quantum Hall Systems, Phys. Rev. Lett., Vol. 103, 2009, pp. 116803, https://doi.org/10.1103/PhysRevLett.103.116803.
[18] C. J. Tabert, E. J. Nicol, Valley-spin Polarization in The Magneto-optical Response of Silicene and Other Similar 2D Crystals, Phys. Rev. Lett., Vol. 110, 2013, pp. 197402, https://doi.org/10.1103/PhysRevLett.110.197402.
[2] J. Have, G. Catarina, T. G. Pedersen, N. Peres, Monolayer Transition Metal Dichalcogenides in Strong Magnetic Fields: Validating the Wannier Model Using a Microscopic Calculation, Phys. Rev. B, Vol. 99, 2019, pp. 035416, https://doi.org/10.1103/PhysRevB.99.035416.
[3] G. Catarina, J. Have, J. F. Rossier, N. M. Peres, Optical Orientation with Linearly Polarized Light in Transition Metal Dichalcogenides, Phys. Rev. B, Vol. 99, 2019, pp. 125405, https://doi.org/10.1103/PhysRevB.99.125405.
[4] G. B. Liu, W. Y. Shan, Y. Yao, W. Yao, D. Xiao, Three-band Tight-binding Model for Monolayers of Group-VIB Transition Metal Dichalcogenides, Phys. Rev. B, Vol. 88, 2013, pp. 085433, https://doi.org/10.1103/PhysRevB.88.085433.
[5] D. Xiao, G. B. Liu, W. Feng, X. Xu, W. Yao, Coupled Spin and Valley Physics in Monolayers of MoS2 and Other Group-VI Dichalcogenides, Phys. Rev. Lett., Vol. 108, 2012, pp. 196802, https://doi.org/10.1103/PhysRevLett.108.196802.
[6] G. Aivazian, Z. Gong, A. M. Jones, R. L. Chu, J. Yan, D. G. Mandrus, C. Zhang, D. Cobden, W. Yao, X. Xu, Magnetic Control of Valley Pseudospin in Monolayer WSe2, Nat. Phys., Vol. 11, 2015, pp. 148-152, https://doi.org/10.1038/nphys3201.
[7] A. Srivastava, M. Sidler, A. V. Allain, D. S. Lembke, A. Kis, A. Imamoğlu, Valley Zeeman Effect in Elementary Optical Excitations of Monolayer WSe2, Nat. Phys. Vol. 11, 2015, pp. 141-147, https://doi.org/10.1038/nphys3203.
[8] M. Tahir, P. Vasilopoulos, Magneto-optical Transport Properties of Monolayer WSe2, Phys. Rev. B, Vol. 94, 2016, pp. 045415, https://doi.org/10.1103/PhysRevB.101.045424.
[9] C. V. Nguyen, N. N. Hieu, C. A. Duque, D. Q. Khoa, N. V. Hieu, L. V. Tung, H. V. Phuc, Linear and Nonlinear Magneto-optical Properties of Monolayer Phosphorene, J. Appl. Phys., Vol. 121, 2017, pp. 045107, https://doi.org/10.1063/1.4974951.
[10] C. V. Nguyen, N. N. Hieu, D. Muoi, C. A. Duque, E. Feddi, H. V. Nguyen, L. T. Phuong, B. D. Hoi, H. V. Phuc, Linear and Nonlinear Magneto-optical Properties of Monolayer MoS2, J. Appl. Phys., Vol. 123, 2018, pp. 034301, https://doi.org/10.1063/1.5009481.
[11] P. T. Huong, D. Muoi, T. N. Bich, H. V. Phuc, C. Duque, P. T. N. Nguyen, C. V. Nguyen, N. N. Hieu, L. T. Hoa, Intra-and Inter-band Magneto-optical Absorption in Monolayer WS2, Physica E: Low-dimensional Systems and Nanostructures, Vol. 124, 2020, pp. 114315, https://doi.org/10.1016/j.physe.2020.114315.
[12] N. D. Hien, C. V. Nguyen, N. N. Hieu, S. Kubakaddi, C. Duque, M. M. Ramos, L. Dinh, T. N. Bich, H. V. Phuc, Magneto-optical Transport Properties of Monolayer Transition Metal Dichalcogenides, Phys. Rev. B, Vol. 101, 2020, p p. 045424, https://doi.org/10.1103/PhysRevB.101.045424.
[13] A. Kormányos, V. Zólyomi, N. D. Drummond, G. Burkard, Spin-orbit Coupling, Quantum Dots, and Qubits in Monolayer Transition Metal Dichalcogenides, Phys. Rev. X, Vol. 4, 2014, pp. 011034, https://doi.org/10.1103/PhysRevX.4.011034.
[14] Y. Ding, Y. Wang, J. Ni, L. Shi, S. Shi, W. Tang, First Principles Study of Structural, Vibrational and Electronic Properties of Graphene-like MX2 (M= Mo, Nb, W, Ta; X= S, Se, Te) Monolayers, Physica B: Condensed Matter, Vol. 406, 2011, pp. 2254-2260, https://doi.org/10.1016/j.physb.2011.03.044.
[15] G. Rezaei, M. Karimi, A. Keshavarz, Excitonic Effects on the Nonlinear Intersubband Optical Properties of a Semi-parabolic One-dimensional Quantum Dot, Physica E: Low-dimensional Systems and Nanostructures, Vol. 43, 2010, pp. 475-481, https://doi.org/10.1016/j.physe.2010.08.035.
[16] H. L. Liu, C. C. Shen, S. H. Su, C. L. Hsu, M. Y. Li, L. J. Li, Optical Properties of Monolayer Transition Metal Dichalcogenides Probed by Spectroscopic Ellipsometry, Appl. Phys. Lett., Vol. 105, 2014, pp. 201905, https://doi.org/10.1063/1.4901836.
[17] T. Morimoto, Y. Hatsugai, H. Aoki, Optical Hall Conductivity in Ordinary and Graphene Quantum Hall Systems, Phys. Rev. Lett., Vol. 103, 2009, pp. 116803, https://doi.org/10.1103/PhysRevLett.103.116803.
[18] C. J. Tabert, E. J. Nicol, Valley-spin Polarization in The Magneto-optical Response of Silicene and Other Similar 2D Crystals, Phys. Rev. Lett., Vol. 110, 2013, pp. 197402, https://doi.org/10.1103/PhysRevLett.110.197402.