Isotropic or anisotropic screening in black phosphorous: Can doping tip the balance?
Zhi-Min Liu, Ye Yang, Yue-Shao Zheng, Qin-Jun Chen, Ye-Xin Feng()
Hunan Provincial Key Laboratory of Low-Dimensional Structural Physics & Devices, School of Physics and Electronics, Hunan University, Changsha 410082, China
Black phosphorus (BP), a layered van der Waals (vdW) crystal, has unique in-plane band anisotropy and many resulting anisotropy properties such as the effective mass, electron mobility, optical absorption, thermal conductivity and plasmonic dispersion. However, whether anisotropic or isotropic charge screening exist in BP remains a controversial issue. Based on first-principles calculations, we study the screening properties in both of single-layer and bulk BP, especially concerning the role of doping. Without charge doping, the single-layer and bulk-phase BP show slight anisotropic screening. Electron and hole doping can increase the charge screening of BP and significantly change the relative static dielectric tensor elements along two different in-plane directions. We further study the charge density change induced by potassium (K) adatom near the BP surface, under different levels of charge doping. The calculated two-dimensional (2D) charge redistribution patterns also confirm that doping can greatly affect the screening feature and tip the balance between isotropic and anisotropic screening. We corroborate that screening in BP exhibits slight intrinsic anisotropy and doping has significant influence on its screening property.
. [J]. Frontiers of Physics, 2020, 15(5): 53501.
Zhi-Min Liu, Ye Yang, Yue-Shao Zheng, Qin-Jun Chen, Ye-Xin Feng. Isotropic or anisotropic screening in black phosphorous: Can doping tip the balance?. Front. Phys. , 2020, 15(5): 53501.
L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, Black phosphorus field-effect transistors, Nat. Nanotechnol. 9(5), 372 (2014) https://doi.org/10.1038/nnano.2014.35
2
X. Wang, A. M. Jones, K. L. Seyler, V. Tran, Y. Jia, H. Zhao, H. Wang, L. Yang, X. Xu, and F. Xia, Highly anisotropic and robust excitons in monolayer black phosphorus, Nat. Nanotechnol. 10(6), 517 (2015) https://doi.org/10.1038/nnano.2015.71
3
R. A. Doganov, S. P. Koenig, Y. Yeo, K. Watanabe, T. Taniguchi, and B. Özyilmaz, Transport properties of ultrathin black phosphorus on hexagonal boron nitride, Appl. Phys. Lett. 106(8), 083505 (2015) https://doi.org/10.1063/1.4913419
4
S. W. Kim, H. Jung, H. J. Kim, J. H. Choi, S. H. Wei, and J. H. Cho, Microscopic mechanism of the tunable band gap in potassium-doped few-layer black phosphorus, Phys. Rev. B 96(7), 075416 (2017) https://doi.org/10.1103/PhysRevB.96.075416
5
A. Chaves, T. Low, P. Avouris, D. Çakır, and F. M. Peeters, Anisotropic exciton Stark shift in black phosphorus, Phys. Rev. B 91(15), 155311 (2015) https://doi.org/10.1103/PhysRevB.91.155311
6
X. Ling, H. Wang, S. Huang, F. Xia, and M. S. Dresselhaus, The renaissance of black phosphorus, Proc. Natl. Acad. Sci. 112(15), 4523 (2015) https://doi.org/10.1073/pnas.1416581112
7
F. Xia, H. Wang, and Y. Jia, Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics, Nat. Commun. 5, 4458 (2014) https://doi.org/10.1038/ncomms5458
8
R. Wang, X. Ren, Z. Yan, W. E. I. Sha, L. J. Jiang, and G. C. Shan, Graphene based functional devices: A short review, Front. Phys. 14(1), 13603 (2019) https://doi.org/10.1007/s11467-018-0859-y
9
K. S. Novoselov, D. Andreeva, W. Ren, and G. Shan, Graphene and other two-dimensional materials, Front. Phys. 14(1), 13301 (2019) https://doi.org/10.1007/s11467-018-0835-6
10
H. Yuan and Z. Li, Interfacial properties of black phosphorus/ transition metal carbide van der Waals heterostructures, Front. Phys. 13(3), 138103 (2018) https://doi.org/10.1007/s11467-018-0759-1
11
M. Hu, N. Zhang, G. Shan, J. Gao, J. Liu, and R. K. Y. Li, Two-dimensional materials: Emerging toolkit for construction of ultrathin high-efficiency microwave shield and absorber, Front. Phys. 13(4), 138113 (2018) https://doi.org/10.1007/s11467-018-0809-8
12
Z. Ma, J. Zhuang, X. Zhang, and Z. Zhou, SiP monolayers: New 2D structures of group IV–V compounds for visible-light photohydrolytic catalysts, Front. Phys. 13(3), 138104 (2018) https://doi.org/10.1007/s11467-018-0760-8
13
S. P. Koenig, R. A. Doganov, H. Schmidt, A. H. C. Neto, and B. Özyilmaz, Electric field effect in ultrathin black phosphorus, Appl. Phys. Lett. 104(10), 103106 (2014) https://doi.org/10.1063/1.4868132
14
X. Liu, C. R. Ryder, S. A. Wells, and M. C. Hersam, Resolving the in-plane anisotropic properties of black phosphorus, Small Methods 1(6), 1700143 (2017) https://doi.org/10.1002/smtd.201700143
15
H. Tian, J. Tice, R. Fei, V. Tran, X. Yan, L. Yang, and H. Wang, Low-symmetry two-dimensional materials for electronic and photonic applications, Nano Today 11(6), 763 (2016) https://doi.org/10.1016/j.nantod.2016.10.003
16
Z. Tian, Y. Gan, T. Zhang, B. Wang, H. Ji, Y. Feng, and J. Xue, Isotropic charge screening of anisotropic black phosphorus revealed by potassium adatoms, Phys. Rev. B 100(8), 085440 (2019) https://doi.org/10.1103/PhysRevB.100.085440
17
T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, Plasmons and screening in monolayer and multilayer black phosphorus, Phys. Rev. Lett. 113(10), 106802 (2014) https://doi.org/10.1103/PhysRevLett.113.106802
18
B. Smith, B. Vermeersch, J. Carrete, E. Ou, J. Kim, N. Mingo, D. Akinwande, and L. Shi, Temperature and thickness dependences of the anisotropic in-plane thermal conductivity of black phosphorus, Adv. Mater. 29(5), 1603756 (2017) https://doi.org/10.1002/adma.201603756
19
X. J. Li, J. H. Yu, Z. H. Wu, and W. Yang, Tuning the electrical and optical anisotropy of a monolayer black phosphorus magnetic superlattice, Nanotechnology 29(17), 174001 (2018) https://doi.org/10.1088/1361-6528/aaaf0f
20
Y. M. Qing, H. F. Ma, and T. J. Cui, Strong coupling between magnetic plasmons and surface plasmons in a black phosphorus-spacer-metallic grating hybrid system, Opt. Lett. 43(20), 4985 (2018) https://doi.org/10.1364/OL.43.004985
21
Q. Fo, L. Pan, X. Chen, Q. Xu, C. Ouyang, X. Zhang, Z. Tian, J. Gu, L. Liu, J. Han, and W. Zhang, Anisotropic plasmonic response of black phosphorus nanostrips in terahertz metamaterials, IEEE Photonics J. 10(3), 1 (2018) https://doi.org/10.1109/JPHOT.2018.2842059
22
Y. Abate, S. Gamage, L. Zhen, S. B. Cronin, H. Wang, V. Babicheva, M. H. Javani, and M. I. Stockman, Nanoscopy reveals surface-metallic black phosphorus, Light Sci. Appl. 5(10), e16162 (2016) https://doi.org/10.1038/lsa.2016.162
23
D. A. Prishchenko, V. G. Mazurenko, M. I. Katsnelson, and A. N. Rudenko, Coulomb interactions and screening effects in few-layer black phosphorus: A tight-binding consideration beyond the long-wavelength limit, 2D Mater. 4, 025064 (2017) https://doi.org/10.1088/2053-1583/aa676b
24
B. Kiraly, E. J. Knol, K. Volckaert, D. Biswas, A. N. Rudenko, D. A. Prishchenko, V. G. Mazurenko, M. I. Katsnelson, P. Hofmann, D. Wegner, and A. A. Khajetoorians, Anisotropic two-dimensional screening at the surface of black phosphorus, Phys. Rev. Lett. 123(21), 216403 (2019) https://doi.org/10.1103/PhysRevLett.123.216403
25
K. Postava, H. Sueki, M. Aoyama, T. Yamaguchi, K. Murakami, and Y. Igasaki, Doping effects on optical propert ies of epitaxial ZnO layers determined by spectroscopic ellipsometry, Appl. Surf. Sci. 175–176, 543 (2001) https://doi.org/10.1016/S0169-4332(01)00145-3
26
P. Gava, M. Lazzeri, A. M. Saitta, and F. Mauri, Ab initio study of gap opening and screening effects in gated bilayer graphene, Phys. Rev. B 79(16), 165431 (2009) https://doi.org/10.1103/PhysRevB.79.165431
27
P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, QUANTUM ESPRESSO: a modular and opensource software project for quantum simulations of materials, J. Phys.: Condens. Matter 21(39), 395502 (2009) https://doi.org/10.1088/0953-8984/21/39/395502
J. Deslippe, G. Samsonidze, D. A. Strubbe, M. Jain, M. L. Cohen, and S. G. Louie, BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures, Comput. Phys. Commun. 183(6), 1269 (2012) https://doi.org/10.1016/j.cpc.2011.12.006
G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6(1), 15 (1996) https://doi.org/10.1016/0927-0256(96)00008-0
33
A. N. Rudenko and M. I. Katsnelson, Quasiparticle band structure and tight-binding model for single- and bilayer black phosphorus, Phys. Rev. B 89(20), 201408 (2014) https://doi.org/10.1103/PhysRevB.89.201408
34
H. Asahina and A. Morita, Band structure and optical properties of black phosphorus, J. Phys. C Solid State Phys. 17(11), 1839 (1984) https://doi.org/10.1088/0022-3719/17/11/006
35
E. Gaufrès, F. Fossard, V. Gosselin, L. Sponza, F. Ducastelle, Z. Li, S. G. Louie, R. Martel, M. Côté, and A. Loiseau, Momentum-resolved dielectric response of free-standing mono-, Bi-, and tri-layer black phosphorus, Nano Lett. 19(11), 8303 (2019) https://doi.org/10.1021/acs.nanolett.9b03928
36
D. C. Reynolds, B. Jogai, P. W. Yu, K. R. Evans, and C. E. Stutz, Increased screening of the hydrogenic donor due to modulation doping in quantum wells, Phys. Rev. B 46(23), 15274 (1992) https://doi.org/10.1103/PhysRevB.46.15274
37
T. Low, A. S. Rodin, A. Carvalho, Y. Jiang, H. Wang, F. Xia, and A. H. C. Neto, Tunable optical properties of multilayer black phosphorus thin films, Phys. Rev. B 90(7), 075434 (2014) https://doi.org/10.1103/PhysRevB.90.075434
