Skip to main content
SpringerLink
Log in

Even-odd-dependent optical transitions of zigzag monolayer black phosphorus nanoribbons

  • Article
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

We analytically study the electronic structure and optical properties of zigzag-edged phosphorene nanoribbons (ZPNRs) using the tight-binding Hamiltonian and Kubo formula. By directly solving the discrete Schrodinger equation, we obtain the energy spectra and wavefunctions for N-ZPNR (where TV is the number of transverse zigzag atomic chains) and classify the eigenstates according to the lattice symmetry. Then, we obtain the optical transition selection rule of ZPNRs on the basis of symmetry analysis and analytical expressions of optical transition matrix elements. Under incident light that is linearly polarized along the ribbon, we determine that the optical transition selection rule for N-ZPNR with even- or odd-N is qualitatively different. Specifically, for even-N ZPNRs, the inter- (intra-) band selection rule is An =odd (even) because the parity of the wavefunction corresponding to the n-th subband in the conduction (valence) band is (-1)n[(-1)(n+1)] owing to the presence of C2x symmetry. However, the optical transitions between any subbands are possible owing to the absence of C2x symmetry. Our results provide a further understanding on the electronic states and optical properties of ZPNRs, which are useful for explaining the optical experiment data on ZPNR samples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, Nat. Nanotech. 9, 372 (2014), arXiv: 1401.4117.

    ADS  Google Scholar 

  2. H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tomanek, and P. D. Ye, ACS Nano 8, 4033 (2014).

    Google Scholar 

  3. F. Xia, H. Wang, and Y. Jia, Nat. Commun. 5, 4458 (2014), arXiv: 1402.0270.

    ADS  Google Scholar 

  4. S. P. Koenig, R. A. Doganov, H. Schmidt, A. H. Castro Neto, and B. Ozyilmaz, Appl. Phys. Lett. 104, 103106 (2014), arXiv: 1402.5718.

    ADS  Google Scholar 

  5. J. Qiao, X. Kong, Z. X. Hu, F. Yang, and W. Ji, Nat. Commun. 5, 4475 (2014), arXiv: 1401.5045.

    ADS  Google Scholar 

  6. M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. J. van der Zant, and A. Castellanos-Gomez, Nano Lett. 14, 3347 (2014), arXiv: 1403.0565.

    ADS  Google Scholar 

  7. A. Castellanos-Gomez, L. Vicarelli, E. Prada, J. O. Island, K. L. Narasimha-Acharya, S. I. Blanter, D. J. Groenendijk, M. Buscema, G. A. Steele, J. V. Alvarez, H. W. Zandbergen, J. J. Palacios, and H. S. J. van der Zant, 2D Mater. 1, 025001 (2014), arXiv: 1403.0499.

    Google Scholar 

  8. W. Lu, H. Nan, J. Hong, Y Chen, C. Zhu, Z. Liang, X. Ma, Z. Ni, C. Jin, and Z. Zhang, Nano Res. 7, 853 (2014).

    Google Scholar 

  9. X. Wang, A. M. Jones, K. L. Seyler, V. Iran, Y Jia, H. Zhao, H. Wang, L. Yang, X. Xu, and F. Xia, Nat. Nanotech. 10, 517 (2015), arXiv: 1411.1695.

    ADS  Google Scholar 

  10. X. Ling, H. Wang, S. Huang, F. Xia, and M. S. Dresselhaus, Proc. Natl. Acad. Sci. USA 112, 4523 (2015), arXiv: 1503.08367.

    ADS  Google Scholar 

  11. A. Castellanos-Gomez, J. Phys. Chem. Lett. 6, 4280 (2015).

    Google Scholar 

  12. L. Li, J. Kim, C. Jin, G. J. Ye, D. Y. Qiu, F. H. da Jornada, Z. Shi, L. Chen, Z. Zhang, F. Yang, K. Watanabe, T. Taniguchi, W. Ren, S. G. Louie, X. H. Chen, Y. Zhang, and F. Wang, Nat. Nanotech. 12, 21 (2017), arXiv: 1601.03103.

    ADS  Google Scholar 

  13. S. J. R. Tan, I. Abdelwahab, L. Chu, S. M. Poh, Y. Liu, J. Lu, W. Chen, and K. P. Loh, Adv. Mater. 30, 1704619 (2018).

    Google Scholar 

  14. K. Zhao, Z. M. Wei, and X. W. Jiang, Sci. China-Phys. Mech. Astron. 63, 237331 (2020).

    Google Scholar 

  15. A. S. Rodin, A. Carvalho, and A. H. Castro Neto, Phys. Rev. Lett. 112, 176801 (2014), arXiv: 1401.1801.

    ADS  Google Scholar 

  16. X. Y. Zhou, R. Zhang, J. P. Sun, Y. L. Zou, D. Zhang, W. K. Lou, F. Cheng, G. H. Zhou, F. Zhai, and K. Chang, Sci. Rep. 5, 12295 (2015), arXiv: 1411.4275.

    ADS  Google Scholar 

  17. X. Zhou, W. K. Lou, F. Zhai, and K. Chang, Phys. Rev. B 92, 165405 (2015).

    ADS  Google Scholar 

  18. R. Zhang, X. Y. Zhou, D. Zhang, W. K. Lou, F. Zhai, and K. Chang, 2D Mater. 2, 045012 (2015), arXiv: 1507.03808.

    Google Scholar 

  19. X. Zhou, W. K. Lou, D. Zhang, F. Cheng, G. Zhou, and K. Chang, Phys. Rev. B 95, 045408 (2017).

    ADS  Google Scholar 

  20. T. Low, A. S. Rodin, A. Carvalho, Y. Jiang, H. Wang, F. Xia, and A. H. Castro Neto, Phys. Rev. B 90, 075434 (2014), arXiv: 1404.4030.

    ADS  Google Scholar 

  21. V. Tran, and L. Yang, Phys. Rev. B 89, 245407 (2014), arXiv: 1404.2247.

    ADS  Google Scholar 

  22. L. L. Li, B. Partoens, W. Xu, and F. M. Peeters, 2D Mater. 6, 015032 (2019).

    Google Scholar 

  23. R. Zhang, Z. Wu, X. J. Li, and K. Chang, Phys. Rev. B 95, 125418 (2017), arXiv: 1705.04794.

    ADS  Google Scholar 

  24. A. N. Rudenko, and M. I. Katsnelson, Phys. Rev. B 89, 201408(R) (2014), arXiv: 1404.0618.

    ADS  Google Scholar 

  25. A. N. Rudenko, S. Yuan, and M. I. Katsnelson, Phys. Rev. B 92, 085419 (2015), arXiv: 1506.01954.

    ADS  Google Scholar 

  26. A. Carvalho, A. S. Rodin, and A. H. Castro Neto, EPL 108, 47005 (2014), arXiv: 1404.5115.

    Google Scholar 

  27. X. Han, H. M. Stewart, S. A. Shevlin, C. R. A. Catlow, and Z. X. Guo, Nano Lett. 14, 4607 (2014).

    ADS  Google Scholar 

  28. M. Ezawa, New J. Phys. 16, 115004 (2014).

    ADS  Google Scholar 

  29. E. Taghizadeh Sisakht, M. H. Zare, and F. Fazileh, Phys. Rev. B 91, 085409 (2015), arXiv: 1408.6249.

    ADS  Google Scholar 

  30. Z. Nourbakhsh, and R. Asgari, Phys. Rev. B 94, 035437 (2016), arXiv: 1606.01683.

    ADS  Google Scholar 

  31. P. Liu, X. Zhou, X. Xiao, B. Zhou, and G. Zhou, J. Phys.-Condens. Matter 32, 285301 (2020).

    ADS  Google Scholar 

  32. L. Zhang, and Y. Hao, Sci. Rep. 8, 6089 (2018).

    ADS  Google Scholar 

  33. H. Guo, N. Lu, J. Dai, X. Wu, and X. C. Zeng, J. Phys. Chem. C 118, 14051 (2014).

    Google Scholar 

  34. M. C. Watts, L. Picco, F. S. Russell-Pavier, P. L. Cullen, T. S. Miller, S. P. Bartuś, O. D. Payton, N. T. Skipper, V. Tileli, and C. A. Howard, Nature 568, 216 (2019).

    ADS  Google Scholar 

  35. Z. Zhu, C. Li, W Yu, D. Chang, Q. Sun, and Y. Jia, Appl. Phys. Lett. 105, 113105 (2014).

    ADS  Google Scholar 

  36. G. Yang, S. Xu, W. Zhang, T. Ma, and C. Wu, Phys. Rev. B 94, 075106 (2016), arXiv: 1604.06324.

    ADS  Google Scholar 

  37. Y. Ren, F. Cheng, Z. H. Zhang, and G. Zhou, Sci. Rep. 8, 2932 (2018).

    ADS  Google Scholar 

  38. E. Taghizadeh Sisakht, F. Fazileh, M. H. Zare, M. Zarenia, and F. M. Peeters, Phys. Rev. B 94, 085417 (2016), arXiv: 1608.05387.

    ADS  Google Scholar 

  39. B. Zhou, B. Zhou, X. Zhou, and G. Zhou, J. Phys. D-Appl. Phys. 50, 045106 (2017).

    ADS  Google Scholar 

  40. S. Shekarforoush, F. Khoeini, and D. Shiri, Mat. Express 8, 489 (2018).

    Google Scholar 

  41. R. Ma, H. Geng, W. Y. Deng, M. N. Chen, L. Sheng, and D. Y. Xing, Phys. Rev. B 94, 125410 (2016), arXiv: 1606.01656.

    ADS  Google Scholar 

  42. S. Datta, Quantum Transport-Atom to Transistor (Cambridge University Press, Cambridge, 2005).

    MATH  Google Scholar 

  43. K. Wakabayashi, K. Sasaki, T. Nakanishi, and T. Enoki, Sci. Tech. Adv. Mater. 11, 054504 (2010).

    Google Scholar 

  44. V. A. Saroka, M. V. Shuba, and M. E. Portnoi, Phys. Rev. B 95, 155438 (2017), arXiv: 1705.00757.

    ADS  Google Scholar 

  45. H. Watanabe, H. C. Po, M. P. Zaletel, and A. Vishwanath, Phys. Rev. Lett. 117, 096404 (2016), arXiv: 1603.05646.

    ADS  Google Scholar 

  46. M. Amini, and M. Soltani, J. Phys.-Condens. Matter 31, 215301 (2019), arXiv: 1810.03042.

    ADS  Google Scholar 

  47. M. Moradinasab, H. Nematian, M. Pourfath, M. Fathipour, and H. Kosina, J. Appl. Phys. 111, 074318 (2012).

    ADS  Google Scholar 

  48. T. Ando, and Y. Uemura, J. Phys. Soc. Jpn. 36, 959 (1974).

    ADS  Google Scholar 

  49. M. Koshino, and T. Ando, Phys. Rev. B 77, 115313 (2008), arXiv: 0803.3023.

    ADS  Google Scholar 

  50. P. Y. Yu, and M. Cardona, Fundamentals of Semiconductors Physics and Materials Properties (4th ed.) (Springer, New York, 2010).

    MATH  Google Scholar 

  51. H. Hsu, and L. E. Reichl, Phys. Rev. B 76, 045418 (2007).

    ADS  Google Scholar 

  52. H. C. Chung, M. H. Lee, C. P. Chang, and M. F. Lin, Opt. Express 19, 23350 (2011).

    ADS  Google Scholar 

  53. D. Zhang, W. Lou, M. Mao, S. Zhang, and K. Chang, Phys. Rev. Lett. 111, 156402 (2013), arXiv: 1308.6353.

    ADS  Google Scholar 

  54. Y. L. Zou, J. Song, C. Bai, and K. Chang, Phys. Rev. B 94, 035431 (2016), arXiv: 1603.04579.

    ADS  Google Scholar 

  55. L. L. Li, and F. M. Peeters, Phys. Rev. B 97, 075414 (2018).

    ADS  Google Scholar 

  56. P. Srivastava, K. P. S. S. Hembram, H. Mzuseki, K. R. Lee, S. S. Han, and S. Kim, J. Phys. Chem. C 119, 6530 (2015).

    Google Scholar 

  57. C. Guo, C. Xia, L. Fang, T. Wang, and Y. Liu, Phys. Chem. Chem. Phys. 18, 25869 (2016).

    Google Scholar 

  58. B. Deng, V. Tran, Y Xie, H. Jiang, C. Li, Q. Guo, X. Wang, H. Tian, S. J. Koester, H. Wang, J. J. Cha, Q. Xia, L. Yang, and F. Xia, Nat. Commun. 8, 14474 (2017), arXiv: 1612.04475.

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Key Laboratory for Low-Dimensional Structures and Quantum Manipulation (Ministry of Education), Synergetic Innovation Center for Quantum Effects and Applications of Hunan, Hunan Normal University, Changsha, 410081, China

    Pu Liu, XianZhe Zhu, XiaoYing Zhou & GuangHui Zhou

  2. SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083, China

    Kai Chang

Authors
  1. Pu Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. XianZhe Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. XiaoYing Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. GuangHui Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kai Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to XiaoYing Zhou, GuangHui Zhou or Kai Chang.

Additional information

(Grant Nos. 11804092, 11774085, 61674145, and 69876039), the Project Funded by China Postdoctoral Science Foundation (Grant Nos. BX20180097, and 2019M652777), and the Hunan Provincial Natural Science Foundation of China (Grant No. 2019JJ40187). Supporting Information The supporting information is available online at phys.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, P., Zhu, X., Zhou, X. et al. Even-odd-dependent optical transitions of zigzag monolayer black phosphorus nanoribbons. Sci. China Phys. Mech. Astron. 64, 217811 (2021). https://doi.org/10.1007/s11433-020-1599-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-020-1599-2

Keyword

Search

Navigation