Abstract
In this paper, hyperbolic plasmonic responses of phosphorene under uniaxial strains have been explored within density functional theory. In the hyperbolic regime, plasmonic slab waveguide modes are found only along armchair direction. Then, uniaxial strains up to 10% have been applied along zigzag and armchair directions, which can significantly modify its plasmonic responses. Under appropriate strain, the signs of permittivities along two in-plane directions can be even reversed, causing switching of the propagating direction of the plasmonic modes into zigzag direction. Our investigations may give a general idea about how to control the hyperbolic plasmonic modes in phosphorene via strain.
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The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
Carvalho A, Wang M, Zhu X, Rodin AS, Su H, Castro Neto AH (2016) Phosphorene: from theory to applications. Nat Rev Mater 1:16061. https://doi.org/10.1038/natrevmats.2016.61
Akinwande D, Huyghebaert C, Wang CH, Serna MI, Goossens S, Li LJ, Philip Wong HS, Koppens FHL (2019) Graphene and two-dimensional materials for silicon technology. Nature 573:507–518. https://doi.org/10.1038/s41586-019-1573-9
Yu H, Peng Y, Yang Y, Li ZY (2019) Plasmon-enhanced light–matter interactions and applications. npj Computational Materials 5, 45. https://doi.org/10.1038/s41524-019-0184-1
TakaoY, Morita A (1981) Electronic structure of black phosphorus: tight binding approach. Physica B+C (Amsterdam) 105, 93. https://doi.org/10.1016/0378-4363(81)90222-9
Rodin AS, Carvalho A, Castro Neto AH (2014) Strain-induced gap modification in black phosphorus. Phys Rev Lett 112:176801. https://doi.org/10.1103/PhysRevLett.112.176801
Yuan H, Liu X, Afshinmanesh F, Li W, Xu G, Sun J, Lian B, Curto AG, Ye G, Hikita Y, Shen Z, Zhang SC, Chen X, Brongersma M, Hwang HY, Cui Y (2015) Polarization-sensitive broadband photodetector using a black phosphorus vertical p–n junction. Nat Nanotechnol 10:707–713. https://doi.org/10.1038/nnano.2015.112
Low T, Roldán R, Wang H, Xia F, Avouris P, Martín Moreno L, Guinea F (2014) Plasmons and screening in monolayer and multilayer black phosphorus. Phys Rev Lett 113:106802. https://doi.org/10.1103/PhysRevLett.113.106802
Jin F, Roldán R, Katsnelson MI, Yuan S (2015) Screening and plasmons in pure and disordered single- and bilayer black phosphorus. Phys Rev B 92:115440. https://doi.org/10.1103/PhysRevB.92.115440
Liu Z, Aydin K (2016) Localized surface plasmons in nanostructured monolayer black phosphorus. Nano Lett 16(6):3457–3462. https://doi.org/10.1021/acs.nanolett.5b05166
Ghosh B, Kumar P, Thakur A, Chauhan YS, Bhowmick S, Agarwal A (2017) Anisotropic plasmons, excitons, and electron energy loss spectroscopy of phosphorene. Phys Rev B 96:035422. https://doi.org/10.1103/PhysRevB.96.035422
Petersen R, Pedersen TG, García de Abajo FJ (2017) Nonlocal plasmonic response of doped and optically pumped graphene, MoS2, and black phosphorus. Phys Rev B 96:205430. https://doi.org/10.1103/PhysRevB.96.205430
Lu H, Gong Y, Mao D, Gan X, Zhao J (2017) Strong plasmonic confinement and optical force in phosphorene pairs. Opt Express 25(5):5255–5263. https://doi.org/10.1364/OE.25.005255
Wang J, Jiang Y (2017) Infrared absorber based on sandwiched two-dimensional black phosphorus metamaterials. Opt Express 25(5):5206–5216. https://doi.org/10.1364/OE.25.005206
Ni X, Wang L, Zhu J, Chen X, Lu W (2017) Surface plasmons in a nanostructured black phosphorus flake. Opt Lett 42(13):2659–2662. https://doi.org/10.1364/OL.42.002659
Wang J, Lu C, Hu ZD, Chen C, Pan L, Ding W (2018) Strong optical force and its confinement applications based on heterogeneous phosphorene pairs. Opt Express 26(18):23221–23232. https://doi.org/10.1364/OE.26.023221
Nong J, Wei W, Wang W, Lan G, Shang Z, Yi J, Tang L (2018) Strong coherent coupling between graphene surface plasmons and anisotropic black phosphorus localized surface plasmons. Opt Express 26(2):1633–1644. https://doi.org/10.1364/OE.26.001633
Wang X, Ma Q, Wu L, Guo J, Lu S, Dai X, Xiang Y (2018) Tunable terahertz/infrared coherent perfect absorption in a monolayer black phosphorus. Opt Express 26(5):5488–5496. https://doi.org/10.1364/OE.26.005488
Fang C, Liu Y, Han G, Shao Y, Zhang J, Hao Y (2018) Localized plasmon resonances for black phosphorus bowtie nanoantennas at terahertz frequencies. Opt Express 26(21):27683–27693. https://doi.org/10.1364/OE.26.027683
Qing YM, Ma HF, Cui TJ (2018a) Strong coupling between magnetic plasmons and surface plasmons in a black phosphorus-spacer-metallic grating hybrid system. Opt Lett 43(20):4985–4988. https://doi.org/10.1364/OL.43.004985
Qing YM, Ma HF, Cui TJ (2018b) Tailoring anisotropic perfect absorption in monolayer black phosphorus by critical coupling at terahertz frequencies. Opt Express 26(25):32442–32450. https://doi.org/10.1364/OE.26.032442
Tong J, Suo F, Ma J, Tobing LYM, Qian L, Zhang DH (2019) Surface plasmon enhanced infrared photodetection. Opto-Electronic Advances 2(1), 180026. https://doi.org/10.29026/oea.2019.180026
Gaufrès E, Fossard F, Gosselin V, Sponza L, Ducastelle F, Li Z, Louie SG, Martel R, Côté M, Loiseau A (2019) Momentum-resolved dielectric response of free-standing mono-, bi-, and trilayer black phosphorus. Nano Lett 19(11):8303–8310. https://doi.org/10.1021/acs.nanolett.9b03928
Veen EV, Nemilentsau A, Kumar A, Roldán R, Katsnelson MI, Low T, Yuan S (2019) Tuning two-dimensional hyperbolic plasmons in black phosphorus. Phys Rev Applied 12:014011. https://doi.org/10.1103/PhysRevApplied.12.014011
Han L, Wang L, Xing H, Chen X (2019) Anisotropic plasmon induced transparency in black phosphorus nanostrip trimer. Opt Mater Express 9(2):352–361. https://doi.org/10.1364/OME.9.000352
Huang Y, Liu X, Liu Y, Shao Y, Zhang S, Fang C, Han G, Zhang J, Hao Y (2019) Nanostructured multiple-layer black phosphorus photodetector based on localized surface plasmon resonance. Opt Mater Express 9(2):739–750. https://doi.org/10.1364/OME.9.000739
Cai Y, Xu KD, Feng N, Guo R, Lin H, Zhu J (2019) Anisotropic infrared plasmonic broadband absorber based on graphene-black phosphorus multilayers. Opt Express 27(3):3101–3112. https://doi.org/10.1364/OE.27.003101
Deng G, Dereshgi SA, Song X, Aydin K (2019) Polarization dependent, plasmon-enhanced infrared transmission through gold nanoslits on monolayer black phosphorus. J Opt Soc Am B 36(8):F109–F116. https://doi.org/10.1364/JOSAB.36.00F109
Liu Z, Yang C, Wan P, Ding L, Xu W (2019) Dielectric-loaded black phosphorus surface plasmon polariton waveguides. Opt Express 27(13):18005–18015. https://doi.org/10.1364/OE.27.018005
Liu C, Li H, Xu H, Zhao M, Xiong C, Zhang B, Wu K (2019) Tunable plasmon-induced transparency absorbers based on few-layer black phosphorus ribbon metamaterials. J Opt Soc Am B 36(11):3060–3065. https://doi.org/10.1364/JOSAB.36.003060
Huang Y, Liu Y, Fang C, Shao Y, Han G, Zhang J, Hao Y (2020) Active tuning of the hybridization effects of mid-infrared surface plasmon resonance in a black phosphorus sheet array and a metal grating slit. Opt Mater Express 10(1):14–28. https://doi.org/10.1364/OME.10.000014
Xia SX, Zhai X, Wang LL, Wen SC (2020a) Polarization-independent plasmonic absorption in stacked anisotropic 2D material nanostructures. Opt Lett 45(1):93–96. https://doi.org/10.1364/OL.45.000093
Xia S, Zhai X, Wang L, Wen S (2020b) Plasmonically induced transparency in in-plane isotropic and anisotropic 2D materials. Opt Express 28(6):7980–8002. https://doi.org/10.1364/OE.389573
Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti GL, Cococcioni M, Dabo I, Corso AD, de Gironcoli S, Fabris S, Fratesi G, Gebauer R, Gerstmann U, Gougoussis C, Kokalj A, Lazzeri M, Martin-Samos L, Marzari N, Mauri F, Mazzarello R, Paolini S, Pasquarello A, Paulatto L, Sbraccia C, Scandolo S, Sclauzero G, Seitsonen AP, Smogunov A, Umari P, Wentzcovitch RM (2009) QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J Phys Condens Matter 21:395502. https://doi.org/10.1088/0953-8984/21/39/395502
Hamann DR (2013) Optimized norm-conserving Vanderbilt pseudopotentials. Phys Rev B 88:085117. https://doi.org/10.1103/PhysRevB.88.085117
Acknowledgments
We thank Dr. C. Q. Shao for the use of their computer cluster.
Funding
This study was funded by National Natural Science Foundation of China (Grant No. 61805062).
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All authors contributed to the study conception and design. DFT and COMSOL calculations were performed by Yu Zhou. COMSOL environment was set up by Zhuohang Zhong. Data collection and analysis were performed by Mingyue Dai. Dr. Chunqiang Shao provided the DELL workstations and technical assistance during the DFT calculations. The first draft of the manuscript was written by Yu Zhou.
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Zhou, Y., Zhong, Z., Dai, M. et al. Reversed Hyperbolic Plasmonic Responses in Phosphorene Under Uniaxial Strain. Plasmonics 16, 1119–1126 (2021). https://doi.org/10.1007/s11468-020-01368-4
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DOI: https://doi.org/10.1007/s11468-020-01368-4