温度对单层黑磷烯基态能量及带隙的影响?

量子电子学报

温度对单层黑磷烯基态能量及带隙的影响?

赵翠兰，王龙

内蒙古民族大学物理与电子信息学院，内蒙古通辽 028000

出版日期:2018-11-28 发布日期:2018-11-14
通讯作者: 赵翠兰（1962-），女，内蒙古赤峰人，硕士，教授，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
作者简介:赵翠兰（1962-），女，内蒙古赤峰人，硕士，教授，主要从事凝聚态光学性质和固态量子信息方面的研究。
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）

Effect of temperature on ground state energy and band bap of monolayer black phosphorus

ZHAO Cuilan, WANG Long

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

Published:2018-11-28 Online:2018-11-14
Supported by:

摘要/Abstract

摘要： 黑磷烯与石墨烯相比具有直接带隙和较高的载流子迁移率，与硅烯相比具有较高的稳定性，这些优越的物理性质使其在新型量子器件的设计中具有巨大的潜在应用价值。采用幺正变换和变分相结合的方法，推导出极性基底上单层黑磷烯中极化子、空穴-声子相互作用体系的基态能量以及带隙的能量公式，研究了温度对极化子、空穴与声子相互作用体系的能量和带隙的影响。对典型极性基底上黑磷烯的数值计算结果表明：极化子（或空穴-声子体系）的能量及带隙均随温度升高或截断波矢的增大而增大，随声子频率的增大而减小，这说明黑磷烯中极化子的能量及带隙与基底材料直接相关，且温度对其性质的影响不可忽略。

关键词: 光电子学, 黑磷烯, 幺正变换, 极化子, 带隙, 温度

Abstract: Compared with graphene, black phosphorene has direct band gap and higher carrier mobility, and has higher stability compared with siliconene. These superior physical properties make it a huge potential application value in the design of new quantum devices. By combining the unitary transformation with variational method, the ground-state energy formula of hole-phonon interaction system in monolayer black phosphorus on a polar substrate is deduced, and the band gap formula is obtained. The influence of temperature on the energy and band gap of polaron, hole and hole-phonon interaction system is studied. Numerical calculation for black phosphorus on typical polar substrates shows that the energy and band gap of polaron (or hole-phonon system) increase with the increase of temperature or truncated wave vector, and decrease with the increase of phonon frequency, which indicates that the energy and band gap of polaron in black phosphene are directly related to the substrate material, and the influence of temperature on the properties of the substrate can’t be ignored.

Key words: optoelectronics, black phosphorene, unitary transformation, polaron, band gap, temperature

中图分类号:

赵翠兰，王龙. 温度对单层黑磷烯基态能量及带隙的影响?[J]. 量子电子学报.

ZHAO Cuilan, WANG Long. Effect of temperature on ground state energy and band bap of monolayer black phosphorus[J]. Chinese Journal of Quantum Electronics.

参考文献

[1] Li Likai，Yu Yijun，Ye Guo Jun，et al. Black phosphorus field-effect transistors[J]. Nature Nanotechnology，2014, 9: 372-377. [2] Liu H，Neal A T，Zhu Z，et al. Phosphorene: An unexplored 2D semiconductor with a high hole mobility [J]. ACS Nano, 2014，8(4): 4033–4041. [3] Xia Fengnian，Wang Han，Jia Yichen. Rediscovering black phosphorus: A unique anisotropic 2D material for optoelectronics and electronics[J]. Nature Communication，2014，5: 44581-44586. [4] Castellanos-Gomez A，Vicarelli L，Prada E，et al. Isolation and characterization of few-layer black phosphorus[J].2D Materials，2014,1(2): 025001. [5] Qiao Jingsi，Kong Xianghua，Hu Zhixin, et al. High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus[J]. Nature Communication，2014, 5: 44751-44757. [6] Ling Xi，Wang Han，Huang Shengxi，et al. The renaissance of black phosphorus[J]. Proceedings of the National Academy of Sciences of the United States of America, 2014, 112: 4523-4530. [7] Tran V，Soklaski R，Liang Yufeng，et al. Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus[J].Physical Review B, 2014, 89(23): 235319. [8] Tran V，Fei Ruixiang，Yang Li. Quasiparticle energies, excitons, and optical spectra of few-layer black phosphorus[J]. 2D Materials，2015，2(4): 044014. [9] Li Xibo，Guo Pan，Cao Tengfei，et al. Structures, stabilities, and electronic properties of defects in monolayer black phosphorus[J].Scientific Reports，2015, 5: 10848. [10] Li Likai，Yang Fangyuan，Ye Guo Jun，et al. Quantum Hall effect in black phosphorus two-dimensional electron system[J]. Nature Nanotechnology，2016, 11: 593-597. [11] Li Likai，Kim Jonghwan，Jin Chenhao，et al. Direct observation of the layer-dependent electronic structure in phosphorene[J]. Nature Nanotechnology，2017,12: 21-25. [12]Surrente A，Mitioglu A A，Galkowski K，et al. Excitons in atomically thin black phosphorus[J]. Physical Review B ，2016，93(12): 121405. [13] Mogulkoc A，Mogulkoc Y，Rudenko A N，et al. Polaronic effects in monolayer black phosphorus on polar substrates[J]. Physical Review B，2016, 93(8)：085417. [14]Zhao Cuilan，XuEnhui. Properties of polaron in nanotubes[J]. Chinese Journal of Quantum Electronics(量子电子学报)，2017，34（2）：247-251(in Chinese). [15] Gao Kuanyun，Xing Haifeng. Mean number of phonons of strong-coupled polaron in a parabolic quantum well[J]. Chinese Journal of Quantum Electronics(量子电子学报)，2016，33（5）: 635-640(in Chinese). [16] Yang Hongtao, Ji Wenhui, Feng Youliang, et al. Influence of phonon dispersion on average optical phonon number of weak-coupling polaron in aparabolic quantum dot[J]. Chinese Journal of Quantum Electronics(量子电子学报)，2016，33（1）: 106-110(in Chinese). [17] Pereira Jr J M，Katsnelson M I. Landau levels of single-layer and bilayer phosphorene[J]. Physical Review B，2015,92(7): 075437. [18] Wang Ziwu, Liu Lei, Li Zhiqing. Energy gap induced by the surface optical polaron in graphene on polar substrates[J]. Applied Physics Letters, 2015, 106(10): 101601. [19] Konar A, Fang T, Jena D. Effect of high- gate dielectrics on charge transport in graphene-based field effect transistors[J]. Physical Review B, 2010, 82(11): 115452.