First-principle study on the optical response of phosphorene

Abstract

The optical response of phosphorene nanostructures was studied using time-dependent density functional theory (TDDFT). Compared with the absorption spectrum of graphene, that of the phosphorene nanostructure exhibits high absorbance in the ultraviolet region, which indicates a high light absorptivity. In a low-energy resonance zone, a spectral band extends to the entire near-infrared regions. When the impulse excitation polarizes in the armchair-edge direction, the low-energy plasmon in a few-layer phosphorene nanostructure shows an apparent long-range charge-transfer excitation but is significantly less pronounced along the zigzag-edge direction. The edge configuration significantly affects the absorption spectrum of monolayer phosphorene nanostructures. The armchair-edge and the zigzag-edge serve different functions in the absorption spectrum. Moreover, the absorption spectrum of the few-layer phosphorene nanostructure changes with the number of layers when the impulse excitation polarizes in the armchair-edge direction. In addition, the change in the low-energy resonance zone is significantly different from that in the high-energy resonance zone.

Graphical abstract

Keywords

phosphorene nanostructures

References

[1] K. S. Novoselov, A. K. Geim, S. Morozov, D. Jiang, M. Katsnelson, I. Grigorieva, S. V. Dubonos, and A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature 438(7065), 197 (2005)

[2] Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, Experimental observation of the quantum Hall effect and Berry’s phase in graphene, Nature 438(7065), 201 (2005)

[3] B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, and A. Kis, Single-layer MoS₂ transistors, Nat. Nanotechnol. 6(3), 147 (2011)

[4] H. Fang, M. Tosun, G. Seol, T. C. Chang, K. Takei, and A. Javey, Degenerate n-doping of few-layer transition metal dichalcogenides by potassium, Nano Lett. 13(5), 1991 (2013)

[5] M. Jablan, H. Buljan, and M. Soljacic, Plasmonics in graphene at infrared frequencies, Phys. Rev. B 80(24), 245435 (2009)

[6] F. H. L. Koppens, D. E. Chang, and F. J. G. de Abajo, Graphene plasmonics: A platform for strong light–matter interactions, Nano Lett. 11(8), 3370 (2011)

[7] H. A. Atwater, The promise of plasmonics, Sci. Am. 296(4), 56 (2007)

[8] E. Ozbay, Plasmonics: Merging photonics and electronics at nanoscale dimensions, Science 311(5758), 189 (2006)

[9] A. Boltasseva and H. A. Atwater, Low-loss plasmonic metamaterials, Science 331(6015), 290 (2011)

[10] L. Liao, Y. C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, High-speed graphene transistors with a self-aligned nanowire gate, Nature 467(7313), 305 (2010)

[11] F. Schwierz, Graphene transistors, Nat. Nanotechnol. 5(7), 487 (2010)

[12] Y. Wu, Y. Lin, A. A. Bol, K. A. Jenkins, F. Xia, D. B. Farmer, Y. Zhu, and P. Avouris, High-frequency, scaled graphene transistors on diamond-like carbon, Nature 472(7341), 74 (2011)

[13] Y. L. Chen, X. B. Feng, and D. D. Hou, Optical absorptions in monolayer and bilayer grapheme, Acta Phys. Sin. 62(18), 187301 (2013)

[14] K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Atomically thin MoS₂: A new direct-gap semiconductor, Phys. Rev. Lett. 105(13), 136805 (2010)

[15] A. Splendiani, L. Sun, Y. B. Zhang, T. S. Li, J. Kim, C. Y. Chim, G. Galli, and F. Wang, Emerging photoluminescence in monolayer MoS₂, Nano Lett. 10(4), 1271 (2010)

[16] H. Liu and P. D. Ye, MoS₂ dual-gate MOSFET with atomiclayer-deposited Al₂O₃ as top-gate dielectric, IEEE Electron Device Lett. 33(4), 546 (2012)

[17] H. Liu, A. T. Neal, and P. D. Ye, Channel length scaling of MoS₂ MOSFETs, ACS Nano 6(10), 8563 (2012)

[18] Y. Yoon, K. Ganapathi, and S. Salahuddin, How good can monolayer MoS₂ transistors be? Nano Lett. 11(9), 3768 (2011)

[19] B. Radisavljevic, M. B. Whitwick, and A. Kis, Integrated circuits and logic operations based on single-layer MoS₂, ACS Nano 5(12), 9934 (2011)

[20] H. Wang, L. Yu, Y. H. Lee, Y. Shi, A. Hsu, M. L. Chin, L. J. Li, M. Dubey, J. Kong, and T. Palacios, Integrated circuits based on bilayer Mo₂ transistors, Nano Lett. 12(9), 4674 (2012)

[21] E. S. Reich, Phosphorene excites materials scientists, Nature 506(7486), 19 (2014)

[22] Y. Xu, B. Yan, H.J. Zhang, J. Wang, G. Xu, P. Tang, W. Duan, and S.C. Zhang, Large-gap quantum spin Hall insulators in tin films, Phys. Rev. Lett. 111(13), 136804 (2013)

[23] L. Li, Y. J. Yu, G. J. Ye, Q. Q. Ge, X. D. Ou, Hua Wu, D. L. Feng, X. H. Chen, and Y. Zhang, Black phosphorus field-effect transistors, Nat. Nanotechnol. 2014, 9(5), 372

[24] H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. F. Xu, D. Tomanek, and P. D. Ye, Phosphorene: An unexplored 2D semiconductor with a high hole mobility, ACS Nano 8(4), 4033 (2014)

[25] E. S. Reich, Phosphorene excites materials scientists, Nature 506(7486), 19 (2014)

[26] J. Dai and X. C. Zeng, Bilayer phosphorene: Effect of stacking order on bandgap and its potential applications in thinfilm solar cells, J. Phys. Chem. Lett. 5(7), 1289 (2014)

[27] M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. J. van der Zant, and A. Castellanos-Gomez, Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors, Nano Lett. 14(6), 3347 (2014)

[28] V. Tran and L. Yang, Scaling laws for the band gap and optical response of phosphorene nanoribbons, Phys. Rev. B 89(24), 245407 (2014)

[29] S. A. Fischer, B. F. Habenicht, A. B. Madrid, W. R. Duncan, and O. V. Prezhdo, Regarding the validity of the time-dependent Kohn–Sham approach for electron-nuclear dynamics via trajectory surface hopping, J. Chem. Phys. 134(2), 024102 (2011)

[30] M. A. L. Marques, A. Castro, G. F. Bertsch, and A. Rubio, Octopus: A first-principles tool for excited electron–ion dynamics, Comput. Phys. Commun. 151(1), 60 (2003)

[31] A. Rubio, J. A. Alonso, J. M. Lopez, and M. J. Stott, Surface plasmon excitations in C₆₀, C₆₀K and C₆₀H clusters, Physica B 183(3), 247 (1993)

[32] A. G. Marinopoulos, L. Reining, V. Olevano, A. Rubio, T. Pichler, X. Liu, M. Knupfer, and J. Fink, Anisotropy and interplane interactions in the dielectric response of graphite, Phys. Rev. Lett. 89(7), 076402 (2002)

[33] A. G. Marinopoulos, L. Reining, A. Rubio, and N. Vast, Optical and loss spectra of carbon nanotubes: Depolarization effects and intertube interactions, Phys. Rev. Lett. 91(4), 046402 (2003)

[34] K. De Blauwe, D. J. Mowbray, Y. Miyata, P. Ayala, H. Shiozawa, A. Rubio, P. Hoffmann, H. Kataura, and T. Pichler, Combined experimental and ab initio study of the electronic structure of narrow-diameter single-wall carbon nanotubes with predominant (6,4),(6,5) chirality, Phys. Rev. B 82(12), 125444 (2010)

[35] K. Yabana and G. F. Bertsch, Time-dependent local-density approximation in real time, Phys. Rev. B 54(7), 4484 (1996)

[36] C. Jamorski, M. E. Casida, and D. R. Salahub, Dynamic polarizabilities and excitation spectra from a molecular implementation of time-dependent density-functional response theory: N₂ as a case study, J. Chem. Phys. 104(13), 5134 (1996)

[37] J. O. Joswig, L. O. Tunturivuori, and R. M. Nieminenc, Photoabsorption in sodium clusters on the basis of time-dependent density-functional theory, J. Chem. Phys. 128(1), 014707 (2008)

[38] C. Hartwigsen, S. Goedecker, and J. Hutter, Relativistic separable dual-space Gaussian pseudopotentials from H to Rn, Phys. Rev. B 58(7), 3641 (1998)

[39] A. Rubio-Ponce, A. Conde-Gallardo, and D. Olguin, Firstprinciples study of anatase and rutile TiO₂ doped with Eu ions: A comparison of GGA and LDA+U calculations, Phys. Rev. B 78(3), 0351071 (2008)

[40] A. Delin, L. Fast, B. Johansson, O. Eriksson, and J. M. Wills, Cohesive properties of the lanthanides: Effect of generalized gradient corrections and crystal structure, Phys. Rev. B 58(8), 4345 (1998)

[41] H. Yin and H. Zhang, Plasmons in graphene nanostructures, J. Appl. Phys. 111(10), 103502 (2012)

[42] J. Guan, Z. Zhu, and D. Tománek, Phase coexistence and metal-insulator transition in few-layer phosphorene: A computational study, Phys. Rev. Lett. 113, 046804 (2014)

[43] L. Yang, C. D. Spataru, S. G. Louie, and M. Y. Chou, Enhanced electron-hole interaction and optical absorption in a silicon nanowire, Phys. Rev. B 75(20), 201304 (2007) (R)

[44] M. Reischle, G. J. Beirne, R. Roach, M. Jetter, and P. Michler, Influence of the dark exciton state on the optical and quantum optical properties of single quantum dots, Phys. Rev. Lett. 101(14), 146402 (2008)

[45] V. Tran, R. Soklaski, Y. Liang, and L. Yang, Tunable band gap and anisotropic optical response in few-layer black phosphorus, arXiv: 1402.4192, 2014

[46] J. Qiao, X. Kong, Z. X. Hu, F. Yang, and W. Ji, Highmobility transport anisotropy and linear dichroism in fewlayer black phosphorus, Nat. Commun. 5, 4475 (2014)

[47] N. Zeng, X.-Y. Jiang, Q. Gao, Y. He, and H. Ma, Linear polarization difference imaging and its potential applications, Appl. Opt. 48(35), 6734 (2009)

[48] E. Knill, R. Laflamme, and G. J. Milburn, A scheme for efficient quantum computation with linear optics, Nature 409(6816), 46 (2001)

[49] N. P. Dasgupta and P. Yang, Semiconductor nanowires for photovoltaic and photoelectrochemical energy conversion, Front. Phys. 9(3), 289 (2014)

[50] Y. L. Zhao, Y. L. Song, W. G. Song, W. Liang, X. Y. Jiang, Z. Y. Tang, H. X. Xu, Z. X. Wei, Y. Q. Liu, M. H. Liu, L. Jiang, X. H. Bao, L. J. Wan, and C. L. Bai, Progress of nanoscience in China, Front. Phys. 9(3), 257 (2014)

[51] N. Liu, W. Li, M. Pasta, and Y. Cui, Nanomaterials for electrochemical energy storage, Front. Phys. 9(3), 323 (2014)

[52] W.-J. Li, D.-X. Yao, and E. W. Carlson, Tunable nano Peltier cooling device from geometric effects using a single graphene nanoribbon, Front. Phys. 9(4), 472 (2014)

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg