Comparative Study of Strain and In-plane Electric Field Effects on Valley Polarization in the Magneto-optical Absorption Spectrum of a Borophene Monolayer
Main Article Content
Abstract
Borophene allotropes possess a variety of captivating physical properties, making them promising for numerous applications in practical devices. In this study, we theoretically explore the magneto-optical absorption of an borophene monolayer subjected to an optical field and a perpendicular static magnetic field considering the combined effect of an in-plane electric field and mechanical strain. The magneto-optical absorption coefficient is calculated using perturbation theory, assuming a degenerate electron gas at low temperatures. The results indicate that valley polarization in the optical absorption coefficient can only be achieved when the in-plane electric field and/or strain is applied to the system. The valley polarization varies gradually with the electric field and becomes significant only at high electric field strengths. On the other hand, the valley polarization is highly sensitive to strain. For the valley, the absorption spectrum shows a red (blue) shift, with the intensity of the absorption peaks increasing (decreasing) as the strain becomes stronger. Additionally, the valley polarization strongly depends on the external magnetic field and the incident photon energy. For the given values of electric field and strain, as the external magnetic field increases, the polarization weakens. The above observations suggest that the combined effects of the factors on the valley polarization need to be considered systematically. The present results are significant for the application of strain and electric field engineering in valleytronics and flexible optoelectronic devices.
References
[2] A. Hirohata, K. Yamada, Y. Nakatani, I. L. Prejbeanu, B. Diény, P. Pirro, B. Hillebrands, Review on spintronics: Principles and device applications, Journal of Magnetism and Magnetic Materials, Vol. 509, 2020, pp. 166711, https://doi.org/10.1016/j.jmmm.2020.166711.
[3] V. K. Joshi, Spintronics: A Contemporary Review of Emerging Electronics Devices, Engineering Science and Technology, Vol. 19, No. 3, 2016, pp. 1503-1513, https://doi.org/10.1016/j.jestch.2016.05.002.
[4] G. Yaqin, Z. Xu, H. Zhi, C. Jinyan, L. Zijun, Z. Jing, L. Jingfeng, Z. Zhaowei, Z. Jinkui, H. Xiufeng, W. Hao, Quantum Materials for Spintronic Applications, Npj Spintronics, Vol. 2, No. 1, 2024, pp. 2948-2119, https://doi.org/ 10.1038/s44306-024-00038-z.
[5] R. Priti, J. Bhandari, U. Sheetal, W. Girish, A Review on—Spintronics an Emerging Technology, Silicon,
Vol. 14, No. 15, 2022, pp. 9195-9210, https://doi.org/10.1007/s12633-021-01643-x.
[6] S. John, R. Yu, H. Clark, G. Rivera, P. R. Jason, S. Kyle, L. Yao, X. Xiaodong, Transport Signatures of Anisotropic Tilted Dirac Cones in 8-Pmmn Borophene, The European Physical Journal B, Vol. 1, No. 11, 2016, pp. 16055, https://doi.org/10.1038/natrevmats.2016.55.
[7] J. Schaibley, Chapter 10 - Valleytronics in 2D Semiconductors, 2D Materials for Photonic and Optoelectronic Applications, Woodhead Publishing, 2020, pp. 281-302, https://www.sciencedirect.com /B978008102637300003.
[8] X. Rui, Z. Zhiguo, L. Jia, Z. Hanyu, Valleytronics: Fundamental Challenges and Materials Beyond Transition Metal Chalcogenides, Nano micro Small, 2024, pp. 2402139, https://doi.org/10.1002/smll.202402139.
[9] V. A. Steven, N. Daniel, V. O. Joseph, K. Philip, G. Nuh, J. H. Pablo, X. Di, R. Mordechai, Valleytronics: Opportunities, Challenges, and Paths Forward, Small, Vol. 14, No. 38, 2018, pp. 1801483, https://doi.org/10.1002/smll.201801483.
[10] K. Jayakrishna, O. Babita, D. Samal, Valleytronics, Resonance, Vol. 28, No. 4, 2023, pp. 537-546, https://doi.org/10.1007/s12045-023-1581-9.
[11] N. Rohling, G. Burkard, Universal Quantum Computing with Spin and Valley States, New Journal of Physics, Vol. 14, No. 8, 2012, pp. 083008, https://dx.doi.org/10.1088/1367-2630/14/8/083008.
[12] E. A. L. Kuemmeth, G. Steele, K. G. Rasmussen, J. Nygård, K. Flensberg, L. P. A. Kouwenhoven, Valley–spin Qubit in A Carbon Nanotube, Nature Nanotechnology, Vol. 8, No. 8, 2013, pp. 565-568, https://doi.org/10.1038/nnano.2013.140.
[13] D. Culcer, A. L. Saraiva, B. Koiller, X. Hu, S. Das Sarma, Valley-based Noise-resistant Quantum Computation Using Si Quantum Dots, Physical Review Letters, Vol. 108, No. 12, 2012, pp. 126804, https://link.aps.org/doi/10.1103/PhysRevLett.108.126804.
[14] Y. S. Ang, S. A. Yang, C. Zhang, Z. Ma, L. K. Ang, Valleytronics in Merging Dirac Cones: All-electric-Controlled Valley Filter, Valve, and Universal Reversible Logic Gate, Physical Review B, Vol. 96, No. 24, 2017, pp. 245410, https://link.aps.org/doi/10.1103/PhysRevB.96.245410.
[15] A. Rycerz, J. Tworzydło, C. W. J. Beenakker, Valley Filter and Valley Valve in Graphene, Nature Physics,
Vol. 3, No. 3, 2007, pp. 172-175, https://doi.org/10.1038/nphys547.
[16] M. S. Mrudul, A. J. Galán, M. Ivanov, G. Dixit, Light-induced Valleytronics in Pristine Graphene, Optica, Vol. 8, No. 3, 2021, pp. 422-427, https://opg.optica.org/optica/abstract.cfm?URI=optica-8-3-422.
[17] X. Zhou, J. Zheng, F. Zhai, Anisotropic and Valley-resolved Beam-splitter Based on a Tilted Dirac System, Communications in Theoretical Physics, Vol. 74, No. 22, 2022, pp. 075701, https://dx.doi.org/10.1088/1572-9494/ac6fc2.
[18] A. Wild, E. Mariani, M. E. Portnoi, Optical Valley Separation in Two-Dimensional Semimetals with Tilted Dirac Cones, Scientific Reports, Vol. 13, No. 1, 2023, pp. 19211, https://doi.org/10.1038/s41598-023-45940-4.
[19] S. H. Zhang, D. F. Shao, Z. A. Wang, J. Yang, W. Yang, E. Y. Tsymbal, Tunneling Valley Hall Effect Driven by Tilted Dirac fermions, Physical Review Letters, Vol. 131, No. 24, 2023, pp. 246301, https://link.aps.org/doi/10.1103/PhysRevLett.131.246301.
[20] N. Rana, G. Dixit, All-optical Ultrafast Valley Switching in Two-Dimensional Materials, Physical Review Applied, Vol. 19, No. 3, 2023, pp. 034056, https://link.aps.org/doi/10.1103/PhysRevApplied.19.034056.
[21] F. Ussolotti, H. Kawai, Z. E. Ooi, V. Chellappan, D. Thian, A. L. C. Pang, K. E. J. Goh, Roadmap on Finding Chiral Valleys: Screening 2D Materials for Valleytronics, Nano Futures, Vol. 2, No. 3, 2018, pp. 032001, https://dx.doi.org/10.1088/2399-1984/aac9d7.
[22] X. F. Zhou, X. Dong, A. R. Oganov, Q. Zhu, Y. Tian, H. T. Wang, Semimetallic Two-dimensional Boron Allotrope with Massless Dirac Fermions, Physical Review Letters, Vol. 112, No. 8, 2014, pp. 085502, https://link.aps.org/doi/10.1103/PhysRevLett.112.085502.
[23] A. L. Bezanilla, P. B. Littlewood, Electronic Properties of 8–Pmmn Borophene, Physical Review B, Vol. 93,
No. 24, 2016, pp. 241405, https://link.aps.org/doi/10.1103/PhysRevB.93.241405.
[24] J. Carrete, W. Li, D. A. Broido, L. J. Gallego, N. Mingo, Physically Founded Phonon Dispersions of Few-layer Materials and the Case of Borophene, Materials Research Letters, Vol. 4, No. 4, 2016, pp. 204–211, https://doi.org/10.1080/21663831.2016.1174163.
[25] A. D. Zabolotskiy, Y. E. Lozovik, Strain-induced Pseudomagnetic Field in the Dirac Semimetal Borophene, Physical Review B, Vol. 94, No. 16, 2016, pp. 165403, https://link.aps.org/doi/10.1103/PhysRevB.94.165403.
[26] S. K. F. Islam, Magnetotransport Properties of 8–Pmmn Borophene: Effects of Hall Field and Strain, Journal of Physics: Condensed Matter, Vol. 30, No. 27, 2018, pp. 275301, https://dx.doi.org/10.1088/1361-648X/aac8b3.
[27] S. A. Herrera, G. G. Naumis, Kubo Conductivity for Anisotropic Tilted Dirac Semimetals and Its Application t8–Pmmn Borophene: Role of Frequency, Temperature, and Scattering Limits, Physical Review B, Vol. 100, No. 19, 2019, pp. 195420, https://link.aps.org/doi/10.1103/PhysRevB.100.195420.
[28] B. D. Napitu, Charge and Heat Transport of Doped 8–Pmmn Borophene with and Without Relaxation Time Approximation, Physical Review B, Vol. 107, No. 15, 2023, pp. 155435, https://link.aps.org/doi/10.1103/PhysRevB.107.155435.
[29] S. K. F. Islam, A. M. Jayannavar, Signature of Tilted Dirac Cones in Weiss Oscillations of 8–Pmmn Borophene, Physical Review B, Vol. 96, No. 23, 2017, pp. 235405, https://link.aps.org/doi/10.1103/PhysRevB.96.235405.
[30] B. D. Napitu, Photoinduced Hall Effect and Transport Properties of Irradiated 8–Pmmn Borophene Monolayer, Journal of Applied Physics, Vol. 127, No. 3, 2020, pp. 034303, https://doi.org/10.1063/1.5130025.
[31] T. Cheng, H. Lang, Z. Li, Z. Liu, L. Zhirong, Anisotropic Carrier Mobility in Two-Dimensional Materials with Tilted Dirac Cones: Theory and Application, Physical Chemistry Chemical Physics, Vol. 19, No. 35, 2017,
pp. 23942–23950, http://dx.doi.org/10.1039/C7CP03736H.
[32] L. Jing, S. Yanmei, W. Meimei, H. Pan, Novel Electric Field Effects on Magneto-Optical Conductivity in Eight–Pmmn Borophene, Journal of Physics: Condensed Matter, Vol. 33, No. 18, 2021, pp. 185501, https://dx.doi.org/10.1088/1361-648X/abf19e.
[33] V. A. Margulis, E. E. Muryumin, Optical Properties of Two-Dimensional Materials with Tilted Anisotropic Dirac Cones: Theoretical Modeling with Application to Doped 8–Pmmn Borophene, Journal of Optics, Vol. 24, No. 1, 2021, pp. 014002, https://dx.doi.org/10.1088/2040-8986/ac3c31.
[34] N. U. Wahab, Y. Abdullah, Transport Signatures of Anisotropic Tilted Dirac Cones in 8–Pmmn Borophene, The European Physical Journal B, Vol. 95, No. 8, 2022, pp. 123, https://doi.org/10.1140/epjb/s10051-022-00389-8.
[35] T. T. Tho, N. N. Hieu, D. M. Quang, N. Q. Bau, B. D. Hoi, Effects of Tilted Dirac Cones and In-plane Electric Field on the Valley-dependent Magneto-optical Absorption Spectra in Monolayer 8–pmmn Borophene, Physics Letters A, Vol. 457, 2023, pp. 128578, https://doi.org/10.1016/j.physleta.2022.128578.
[36] N. Levy, S. A. Burke, K. L. Meaker, M. Panlasigui, A. Zettl, F. Guinea, A. H. C. Neto, M. F. Crommie, Strain-Induced Pseudo–magnetic Fields Greater Than 300 Tesla in Graphene Nanobubbles, Science, Vol. 329,
No. 5991, 2010, pp. 544-547, https://www.science.org/doi/abs/10.1126/science.1191700.
[37] V. M. Pereira, A. H. Castro Neto, Strain engineering of graphene’s electronic structure, Physical Review Letters, Vol. 103, No. 4, 2009, pp. 046801, https://link.aps.org/doi/10.1103/PhysRevLett.103.046801.
[38] B. Roy, H. Z. Xiang, K. Yang, Theory of Unconventional Quantum Hall Effect in Strained Graphene, Physical Review B, Vol. 87, No. 12, 2013, pp. 121408, https://link.aps.org/doi/10.1103/PhysRevB.87.121408.
[39] D. I. Pikulin, A. Chen, M. Franz, Chiral Anomaly from Strain-Induced Gauge Fields in Dirac and Weyl Semimetals, Physical Review X, Vol. 6, No. 4, 2016, pp. 041021, https://link.aps.org/doi/10.1103/PhysRevX.6.041021.
[40] S. Yadav, A. Ptok, Landau Levels in Weyl Semimetal Under Uniaxial Strain, Physica B: Condensed Matter,
Vol. 698, 2025, pp. 416730, https://doi.org/10.1016/j.physb.2024.416730.
[41] V. A. Margulis, V. V. Karpunin, Resonant Absorption of Electromagnetic Radiation in A Quantum Channel Due to the Scattering of Electrons by Impurities, Optics and Spectroscopy, Vol. 122, No. 7, 2017, pp. 979, https://doi.org/10.1134/S0030400X17060108.
[42] V. A. Margulis, V. V. Karpunin, Resonance Absorption of Electromagnetic Radiation in A Phosphorene Single Layer, Semiconductors, Vol. 53, No. 4, 2019, pp. 458, https://doi.org/ 10.1134/S1063782619040134.
[43] N. G. Galkin, A. V. Shorokhov, V. A. Margulis, Intraband Absorption of Electromagnetic Radiation by Quantum Nanostructures with Parabolic Confinement Potential, Physics of the Solid State, Vol. 43, No. 3, 2001, pp. 530, https://doi.org/10.1134/1.1356134.
[44] W. Zawadzki, S. Klahn, U. Merkt, Semirelativistic Behavior of Electrons in Insb in Crossed Magnetic and Electric Fields, Physical Review Letters, Vol. 55, No. 9, 1985, pp. 983-986, https://link.aps.org/doi/10.1103/PhysRevLett.55.983.
[45] V. Ariel, Effective Mass and Energy-Mass Relationship, arXiv Preprint, arXiv, 1205.3995, 2012, https://arxiv.org/abs/1205.3995 (accessed on: April 1st, 2025).
[46] K. Seeger, Semiconductor Physics: An Introduction, Springer Series in Solid-State Sciences, Springer-Verlag, 9783540114215, 1985, https://books.google.com.vn/books?id=gvl9AAAAIAA (accessed on: April 1st, 2025).