The Influence of an External Magnetic Field on Multi-photon Non-linear Absorption Coefficient of a Strong Electromagnetic Wave in Two-dimensional Graphene
Main Article Content
Abstract
Based on the quantum kinetic equation for electrons, we theoretically studied the Quantum Multi-photon Nonlinear Absorption of a Strong Electromagnetic Wave (EMW) in two-dimensional graphene with electron-optical phonon scattering mechanism. The general multi-photon absorption coefficient was presented as a function of the temperature, the external magnetic field, the photon energy, and the amplitude of external EMW. The results show that in the presence of the magnetic field, absorption spectral lines appear consistent with the magneto-phonon resonance conditions. In which, the effect of multi-photon absorption is stronger than that of mono-photon absorption. Besides, the quantum multi-photon nonlinear absorption phenomenon has been studied from low to temperatures. This transcends the limits of the classical Boltzmann kinetic equation which is studied in the high-temperature domain. The computational results show that the dependence of Multi-photon Nonlinear Absorption Coefficient (MNAC) on the above quantities is consistent with the previous theoretical investigation. Another novel feature of this work is that the general analytic expression for MNAC shows the Half Width at Half Maximum (HWHM) dependence on the magnetic field which is in good agreement with the previous experimental observations. Thus, our estimation might give a critical prediction for future experimental observations in graphene.
References
[2] S. D. Sarma, S. Adam, E. H. Hwang, E. Rossi, Electronic Transport in Two-Dimensional Graphene, Reviews of Modern Physics, Vol. 83, No. 2, 2011, pp. 407-470, https://doi.org/10.1103/RevModPhys.83.407.
[3] T. Ando, Magnetic Oscillation of Optical Phonon in Graphene, Journal of the Physical Society of Japan, Vol. 76, No. 2, 2007, pp. 024712(1-7), https://doi.org/10.1143/jpsj.76.024712.
[4] N. Mori and T. Ando, Magnetophonon Resonance in Monolayer Graphene, Journal of the Physical Society of Japan, Vol. 80, No. 4, 2011, pp. 044-706, https://doi.org/10.1143/JPSJ.80.044706.
[5] E. Tiras, S. Ardali, T. Tiras, E. Arslan, S. Cakmakyapan, O. Kazar, J. Hassan, E. Janzen, E. Ozbay, Effective mass of Electron in Monolayer Graphene: Electron-phonon Interaction, Journal of Applied Physics, Vol. 113, No. 4, 2013, pp. 043-708, https://doi.org/10.1063/1.4789385.
[6] N. Nishiguchi, Resonant Acoustic-Phonon Modes in A Quantum Wire, Physical Review B, Vol. 52, No. 7, 1995, pp. 52-79, https://doi.org/10.1103/PhysRevB.52.5279.
[7] H. Dakhlaoui, Linear and Nonlinear Optical Absorption Coefficients and Refractive Index Changes in Gan/Alxga(1−X)N Double Quantum Wells Operating at 1.55 μm , Journal of Applied Physics, Vol. 117, No. 13, 2015, pp. 135-705, https://doi.org/10.1063/1.4916752.
[8] N. Q. Bau, D. M. Hung, Calculation of the Nonlinear Absorption Coefficient of A Strong Electromagnetic Wave by Confined Electrons in Doping Superlatices, Progress in Electromagnetics Research B, Vol. 25, 2010, pp. 39-52, https://doi.org/10.2528/PIERB10062902.
[9] B. D. Hoi, L. T. T. Phuong, T. C. Phong, Magneto-optical Absorption and Cyclotron–phonon Resonance in Graphene Monolayer, Journal of Applied Physics, Vol. 123, No. 9, 2018, pp. 094-303, https://doi.org/10.1063/1.5020746.
[10] H. V. Phuc and N. N. Hieu, Nonlinear Optical Absorption in Graphene Via Two-Photon Absorption Process, Optics Communications, Vol. 344, 2015, pp. 12-16, https://doi.org/10.1016/j.optcom.2014.12.086.
[11] S. V. Kryuchkov, E. I. Kukhar', D. V. Zav'yalov, Conductivity of the Graphene in the Transversal Magnetic Field: Relaxation Time Approximation with Monte-Carlo method, Physica E: Low-dimensional Systems and Nanostructures, Vol. 53, 2013, pp. 124-129, https://doi.org/10.1016/j.physe.2013.05.004.
[12] N. Q. Bau, D. M. Hung, N. B. Ngoc, The Nonlinear Absorption Coefficient of A Strong Electromagnetic Wave Caused by Confined Electrons in Quantum Wells, Journal of the Korean Physical Society, Vol. 54, No. 2, 2009, pp. 765-773, https://doi.org/10.3938/jkps.54.765.
[13] H. D. Trien, N. Q. Bau, The Nonlinear Absorption Coefficient of Strong Electromagnetic Waves Caused by Electrons Confined in Quantum Wires, Journal of the Korean Physical Society, Vol. 56, No. 1, 2010, pp. 120-127, https://doi.org/10.3938/jkps.56.120.
[14] N. Ma, S. Zhang, D. Liu, Mechanical Control Over Valley Magnetotransport in Strained Graphene, Physics Letters A, Vol. 380, No. 21, 2016, pp. 1884-1890, https://doi.org/10.1016/j.physleta.2016.03.039.
[15] M. P. Chaubey, C. M. V. Vliet, Transverse Magnetoconductivity of Quasi-Two-Dimensional Semiconductor Layers in the Presence of Phonon Scattering, Physical Review B, Vol. 33, No. 8, 1986, pp. 5617-5622, https://doi.org/10.1103/PhysRevB.33.5617.
[16] Z. Jiang, E. A. Henriksen, L. C. Tung, Y. J. Wang, M. E. Schwartz, M. Y. Han, H. L. Stormer, Infrared Spectroscopy of Landau Levels of Graphene, Physical Review Letters, Vol. 98, No. 19, 2007, pp. 197403-197407, https://doi.org/10.1103/PhysRevLett.98.197403 .
[17] N. V. Nhan, T. A. Tuan, H. G. Linh, N. D. Nam, N. Q. Bau, Investigation of Nonlinear Absorption of Strong Electromagnetic Wave in Two - Dimensional Graphene by Using Quantum Kinetic Equation Method, Journal of Hanoi Metropolitan University, Vol. 53, 2021, pp. 44-52.