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

Abstract

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

CLC Number:

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

References

[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.