单层黑磷烯中磁极化子的基态性质

量子电子学报 ›› 2019, Vol. 36 ›› Issue (4): 500-505.

单层黑磷烯中磁极化子的基态性质

刘佳丽¹,赵翠兰²,王龙¹,李大伟³

内蒙古民族大学物理与电子信息学院，内蒙古通辽 028043

收稿日期:2019-05-08 修回日期:2019-05-30 出版日期:2019-07-28 发布日期:2019-07-11
通讯作者: 赵翠兰 E-mail:nmdzcl@163.com
作者简介:刘佳丽（1995-），女，内蒙古通辽人，研究生，从事凝聚态光学性质方面的研究。E-mail：1621665670@qq.com
基金资助:
Supported by National Natural Science Foundation of China (国家自然科学基金，11464034）, Natural Science Foundation of Inner Mogolia Autonomous Region of China(内蒙古自然科学基金，2016MS0119)

Ground state properties of magnetic polaron in monolayer black phosphonene

College of Physics and Electronic Information, Inner Mongolia University for Nationalites, Tongliao 028043, China

Received:2019-05-08 Revised:2019-05-30 Published:2019-07-28 Online:2019-07-11
Contact: 赵翠兰（1962-），女，内蒙古赤峰人，硕士，教授，研究生导师，主要从事凝聚态光学性质和固态量子信息方面的研究 E-mail:nmdzcl@163.com

摘要/Abstract

摘要： 利用Lee-Low-Pines(LLP)幺正变换、线性组合算符和变分方法，推导出均匀磁场中极性基底上单层黑磷烯中极化子的基态能量公式，研究了磁场、基底材料对单层黑磷烯中极化子基态能量的影响。数值计算表明：基底与单层黑磷烯之间的垂直距离和截断波矢保持不变时，极化子基态能量随磁场强度的增大而增大，随基底材料声子频率的增大而减小，不同基底上极化子的基态能量不同，但变化规律一致。当基底与单层黑磷烯之间的垂直距离和磁场强度保持不变时，极化子基态能量随截断波矢的增大而增大。这些结果表明，单层黑磷烯中极化子的基态能量与外磁场和基底材料有关。

关键词: 光电子学, 黑磷烯, 线性组合算符, 极化子, 基态能量, 基底

Abstract: By using the Lee-Low-Pines(LLP) unitary transformation, linear combination operator and variational method, the ground state energy formula of polaron in monolayer black phosphonene on polar substrate in uniform magnetic field is derived, and the effects of magnetic field and substrate material on the ground state energy of the polaron in monolayer black phosene are investigated. The numerical calculation shows that the ground state energy of the polaron increases with the increase of the magnetic field strength when the vertical distance between the substrate and monolayer black phosphonene and the truncated wave vector remain unchanged, and decreases with the increase of the phonon energy of the substrate material. The ground state energy of the polaron on different substrates is different, but the variation law is consistent. When the vertical distance and magnetic field strength remain unchanged, the ground state energy of the polaron increases with the increase of the truncated wave vector. These results indicate that the ground state energy of the polaron in the monolayer black phosphonene is related to the external magnetic field and substrate material.

Key words: optoelectronics, black phosphorene, linear combination operator, polaron, ground state energy, substrate

中图分类号:

0469

刘佳丽赵翠兰王龙李大伟. 单层黑磷烯中磁极化子的基态性质[J]. 量子电子学报, 2019, 36(4): 500-505.

参考文献

[1] Chen Pengfei, Li Neng, Chen Xinzhu, et al. The rising star of 2D black phosphorus beyond graphene: Synthesis,properties and electronic applicatios [J]. 2D Materials, 2018, 5: 014002. [2] Liang Fengxia, Ren Yuhang, Zhang Xiaodong, et al. Electronic properties and optical absorption of a phosphorene quantum dot [J]. Journal of Applied Physics, 2018, 123: 125109. [3] Abdelsalam H, Saroka V A, Lukyanchuk I, et al. Multilayer phosphorene quantum dots in an electric field: Energy levels and optical absorption [J]. Journal of Applied Physics, 2018, 124: 124303. [4] Wang Ke, Wang Hai, Zhang Min, et al. Electrical properties of phosphorene systems doped with fourth-period elements [J]. Applied Physics Letters， 2018, 112: 202101-1-4. [5] Kavoos M, Ziba T, Farzaneh S. Electro/mechanical mutable properties of black phosphorene by electric field and strain engineering [J]. IOP Publishing, 2018, 5: 066307. [6] Li Xiaojing, Yu Jiahan, Luo Kun, et al. Tuning the electrical and optical anisotropy of a monolayer black phosphorus magnetic superlattice [J]. IOP Publishing, 2018, 29: 174001. [7] Margulis VI A, Muryumin E E. Theory for surface polaritons supported by a black-phosphorus monolayer [J]. Physical Review B, 2018, 98: 165305. [8] Zhao Cuilan, Wang Long. Effect of temperature on ground state energy and band bap of monolayer black phosphorus [J]. Chinese Journal of Quantum Electronics（量子电子学报）, 2018, 35(6): 736-742（in Chinese）. [9] Rudenko A N, Katsnelson M I. Quasiparticle band structure and tight-binding model for single- and bilayer black phosphorus [J]. Physical Review B, 2014, 89: 201408-1-6. [10] Rudebko A N, Yuan Shenjun, Katsnelson M I. Toward a realistic description of multilayer black phosphorus: From GW approximation to large-scale tight-binding simulations [J]. Physical Review B, 2015， 92(8): 085419. [11] Rodin A S, Carvalho A, Castro Neto A H. Strain-induced gap modification in black phosphorus [J]. Physical Review Letters, 2014, 112(17): 176801. [12] Pereira Jr J M, Katsnelson M I. Landau levels of single-layer and bilayer phosphorene [J]. Physical Review B, 2015, 92: 075437. [13] Zhou Xiaoying, Zhang Rui, Sun Jianpeng, et al. Landau levels and magneto-transport property of monolayer phosphorene [J]. Scientific Reports, 2015, 5: 12295. [14] Ezawa M, New J. Topological origin of quasi-flat edge band in phosphorene [J]. Physics,2014， 16: 115004. [15] Wang S Q, Mahan G D. Electron scattering from surface excitations [J]. Physical Review B, 1972, 6(12): 4517-4524. [16] Mori N, Ando T. Electron-optical-phonon interaction in single and double structures [J]. Physical Review B, 1989, 40(9): 6175-6188. [17] Sak J. Theory of Surface Polarons [J]. Physical Review B, 1972, 6: 3981-3986. [18] Mogclkoc A, Mogulkoc Y. Polaronic effects in monolayer black phosphorus on polar substrates [J]. Physical Review B, 2016, 93: 085417. [19] Wang Ziwu, Liu Lei, Li Zhiqing. Energy gap induced by the surface optical polaron in grapheme on polar substrates [J]. Applied Physics Letters, 2015, 106: 101601. [20] Konar A, Fang Tian, Jena D. Effect of high-_ gate dielectrics on charge transport in graphene-based field effect transistors [J]. Physical Review B, 2010, 82: 115452.