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Direct mapping of edge states in bilayer zigzag phosphorene nanoribbons into a SSH ladder model and optimizing their thermoelectric performance via edge state engineering

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Abstract

Zigzag Phosphorene nanoribbon supports topological edge states in the gap region near the Ferm level. We consider a bilayer system consisting of two coupled Phosphorene layers with zigzag edges and investigate the thermoelectric properties of the system by engineering its corresponding edge modes. To this end, we first map the edge states of zigzag bilayer phosphorene nanoribbon (ZBPNR) into an effective Su-Schrieffer-Heeger (SSH) ladder model with momentum dependent hopping probabilities which allow us to obtain their corresponding band dispersion and wave functions analytically. Then, by applying the energy filtering method and employing non-equilibrium Green’s function approach, we show that the electric power and thermoelectric efficiency of the ZBPNRs can be improved remarkably in the presence of mid-gap edge states. We also argue how to engineer the edge modes to further optimize thermoelectric power and efficiency of the system by applying periodic point potentials at the boundaries

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References

  1. D.M. Rowe, Thermoelectrics Handbook: Macro to Nano (CRC Press, Boca Raton, 2006)

    Google Scholar 

  2. H.J. Goldsmid, Introduction to Thermoelectricity Springer Series in Materials Science (Springer, Berlin, 2009)

    Google Scholar 

  3. L.D. Hicks, M.S. Dresselhaus, Phys. Rev. B 47, 12727 (1993)

    Article  ADS  Google Scholar 

  4. L.D. Hicks, M.S. Dresselhaus, Phys. Rev. B 47, 16631 (1993)

    Article  ADS  Google Scholar 

  5. A.A. Balandin, O.L. Lazarenkova, Appl. Phys. Lett. 82, 415 (2003)

    Article  ADS  Google Scholar 

  6. P. Murphy, S. Mukerjee, J. Moore, Phys. Rev. B 78, 161406(R) (2008)

    Article  ADS  Google Scholar 

  7. M. Esposito, K. Lindenberg, C. van den Broeck, Eur. Phys. Lett. 85, 60010 (2009)

    Article  ADS  Google Scholar 

  8. M. Leijnse, M.R. Wegewijs, K. Flensberg, Phys. Rev. B 82, 045412 (2010)

    Article  ADS  Google Scholar 

  9. B. Zhou, B. Zhou, X. Chen, W. Liao, G. Zhou, J. Phys.: Condens. Matter 27, 465301 (2015)

    ADS  Google Scholar 

  10. H. Karbaschi, J. Lovén, K. Courteaut, A. Wacker, M. Leijnse, Phys. Rev. B 94, 115414 (2016)

    Article  ADS  Google Scholar 

  11. Y. Zhang, X. Wang, M. Cleary, L. Schoensee, N. Kempf, J. Richardson, Appl. Therm. Eng. 96, 83 (2016)

    Article  Google Scholar 

  12. N.T. Hung, E.H. Hasdeo, A.R.T. Nugraha, M.S. Dresselhaus, R. Saito, Phys. Rev. Lett. 117, 036602 (2016)

    Article  ADS  Google Scholar 

  13. M. Rezaei, H. Karbaschi, M. Amini, M. Soltani, G. Rashedi, Nanotechnology 32, 375704 (2021)

    Article  Google Scholar 

  14. L. Li, Y. Yu, G.J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X.H. Chen, Y. Zhang, Nat. Nanotechnol. 9, 372 (2014)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  16. Y. Takao, A. Morita, Physica B+C 105, 93 (1981)

  17. J. Dai, X.C. Zeng, J. Phys. Chem. Lett. 5, 1289 (2014)

    Article  Google Scholar 

  18. A. Carvalho, M. Wang, X. Zhu, A.S. Rodin, H. Su, A.H. Castro Neto, Nat. Rev. Mater. 1, 16061 (2016)

  19. R.S. Whitney, Phys. Rev. Lett. 112, 130601 (2014)

    Article  ADS  Google Scholar 

  20. R.S. Whitney, Phys. Rev. B 91, 115425 (2015)

    Article  ADS  Google Scholar 

  21. B. Zhou, J. Yuan, X. Zhou, B. Zhou, J. Phys.: Condens. Matter 32, 435502 (2020)

    ADS  Google Scholar 

  22. L.L. Li, D. Moldovan, W. Xu, F.M. Peeters, Phys. Rev. B 96, 155425 (2017)

    Article  ADS  Google Scholar 

  23. A.N. Rudenko, S. Yuan, M.I. Katsnelson, Phys. Rev. B 92, 085419 (2015)

    Article  ADS  Google Scholar 

  24. S. Soleimanikahnoj, I. Knezevic, J. Comput. Electron. 16, 568 (2017)

    Article  Google Scholar 

  25. T. Tan, C. Li, W. Yao, Phys. Rev. B 104, 245419 (2021)

    Article  ADS  Google Scholar 

  26. M. Amini, M. Soltani, J. Phys.: Condens. Matter 31, 215301 (2019)

    ADS  Google Scholar 

  27. M. Amini, M. Soltani, M. Sharbafiun, Phys. Rev. B 99, 085403 (2019)

    Article  ADS  Google Scholar 

  28. D. Wu, X.-H. Cao, P.-Z. Jia, Y.-J. Zeng, Y.-X. Feng, L.-M. Tang, W.-X. Zhou, K.-Q. Chen, Science China Physics. Mech. Astron. 63, 276811 (2020)

    Article  ADS  Google Scholar 

  29. X. Chen, M. Pang, T. Chen, D. Du, K. Chen, A.C.S. Appl, Mater. Interfaces 12, 15517 (2020)

    Article  Google Scholar 

  30. X.-K. Chen, K.-Q. Chen, J. Phys.: Condens. Matter 32, 153002 (2020)

    ADS  Google Scholar 

  31. W. Hu, J. Yang, J. Phys. Chem. C 119, 20474 (2015)

    Article  Google Scholar 

  32. Y. Cai, Q. Ke, G. Zhang, B.I. Yakobson, Y.-W. Zhang, J. Am. Chem. Soc. 138, 10199 (2016)

    Article  Google Scholar 

  33. M. Poljak, T. Suligoj, Nano Res. 9, 1723 (2016)

    Article  Google Scholar 

  34. B. Kiraly, N. Hauptmann, A.N. Rudenko, M.I. Katsnelson, A.A. Khajetoorians, Nano Lett. 17, 3607 (2017)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of Isfahan, Isfahan, 81746-73441, Iran

    Shima Sodagar, Hossein Karbaschi, Morteza Soltani & Mohsen Amini

Authors
  1. Shima Sodagar
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  2. Hossein Karbaschi
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  3. Morteza Soltani
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  4. Mohsen Amini
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Corresponding author

Correspondence to Hossein Karbaschi.

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Sodagar, S., Karbaschi, H., Soltani, M. et al. Direct mapping of edge states in bilayer zigzag phosphorene nanoribbons into a SSH ladder model and optimizing their thermoelectric performance via edge state engineering. Eur. Phys. J. Plus 137, 722 (2022). https://doi.org/10.1140/epjp/s13360-022-02942-x

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