Reversed Hyperbolic Plasmonic Responses in Phosphorene Under Uniaxial Strain


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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    Carvalho A, Wang M, Zhu X, Rodin AS, Su H, Castro Neto AH (2016) Phosphorene: from theory to applications. Nat Rev Mater 1:16061.

    CAS  Article  Google Scholar 

  2. 2.

    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.

    CAS  Article  PubMed  Google Scholar 

  3. 3.

    Yu H, Peng Y, Yang Y, Li ZY (2019) Plasmon-enhanced light–matter interactions and applications. npj Computational Materials 5, 45.

  4. 4.

    TakaoY, Morita A (1981) Electronic structure of black phosphorus: tight binding approach. Physica B+C (Amsterdam) 105, 93.

  5. 5.

    Rodin AS, Carvalho A, Castro Neto AH (2014) Strain-induced gap modification in black phosphorus. Phys Rev Lett 112:176801.

    CAS  Article  PubMed  Google Scholar 

  6. 6.

    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.

    CAS  Article  PubMed  Google Scholar 

  7. 7.

    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.

    CAS  Article  PubMed  Google Scholar 

  8. 8.

    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.

    CAS  Article  Google Scholar 

  9. 9.

    Liu Z, Aydin K (2016) Localized surface plasmons in nanostructured monolayer black phosphorus. Nano Lett 16(6):3457–3462.

    CAS  Article  PubMed  Google Scholar 

  10. 10.

    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.

    Article  Google Scholar 

  11. 11.

    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.

    Article  Google Scholar 

  12. 12.

    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.

    CAS  Article  PubMed  Google Scholar 

  13. 13.

    Wang J, Jiang Y (2017) Infrared absorber based on sandwiched two-dimensional black phosphorus metamaterials. Opt Express 25(5):5206–5216.

    Article  PubMed  Google Scholar 

  14. 14.

    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.

    CAS  Article  PubMed  Google Scholar 

  15. 15.

    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.

    CAS  Article  PubMed  Google Scholar 

  16. 16.

    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.

    CAS  Article  PubMed  Google Scholar 

  17. 17.

    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.

    CAS  Article  PubMed  Google Scholar 

  18. 18.

    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.

    CAS  Article  PubMed  Google Scholar 

  19. 19.

    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.

    CAS  Article  PubMed  Google Scholar 

  20. 20.

    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.

    CAS  Article  PubMed  Google Scholar 

  21. 21.

    Tong J, Suo F, Ma J, Tobing LYM, Qian L, Zhang DH (2019) Surface plasmon enhanced infrared photodetection. Opto-Electronic Advances 2(1), 180026.

  22. 22.

    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.

    CAS  Article  PubMed  Google Scholar 

  23. 23.

    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.

    Article  Google Scholar 

  24. 24.

    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.

    CAS  Article  Google Scholar 

  25. 25.

    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.

    CAS  Article  Google Scholar 

  26. 26.

    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.

    CAS  Article  PubMed  Google Scholar 

  27. 27.

    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.

    CAS  Article  Google Scholar 

  28. 28.

    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.

    CAS  Article  PubMed  Google Scholar 

  29. 29.

    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.

    CAS  Article  Google Scholar 

  30. 30.

    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.

    CAS  Article  Google Scholar 

  31. 31.

    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.

    CAS  Article  Google Scholar 

  32. 32.

    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.

    Article  PubMed  Google Scholar 

  33. 33.

    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.

    Article  PubMed  Google Scholar 

  34. 34.

    Hamann DR (2013) Optimized norm-conserving Vanderbilt pseudopotentials. Phys Rev B 88:085117.

    CAS  Article  Google Scholar 

Download references


We thank Dr. C. Q. Shao for the use of their computer cluster.


This study was funded by National Natural Science Foundation of China (Grant No. 61805062).

Author information




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.

Corresponding author

Correspondence to Yu Zhou.

Ethics declarations

Competing Interests

The authors declare that they have no competing interests.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhou, Y., Zhong, Z., Dai, M. et al. Reversed Hyperbolic Plasmonic Responses in Phosphorene Under Uniaxial Strain. Plasmonics (2021).

Download citation


  • Phosphorene
  • Plasmonics
  • Hyperbolic
  • Strain