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Strain engineering of graphene nanoribbons: pseudomagnetic versus external magnetic fields

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Abstract

Bandgap opening due to strain engineering is a key architect for making graphene’s optoelectronic, straintronic, and spintronic devices. We study the bandgap opening due to strain induced ripple waves and investigate the interplay between pseudomagnetic fields and externally applied magnetic fields on the band structures and spin relaxation in graphene nanoribbons (GNRs). We show that electron-hole bands of GNRs are highly influenced (i.e. level crossing of the bands are possible) by coupling two combined effects: pseudomagnetic fields (PMF) originating from strain tensor and external magnetic fields. In particular, we show that the tuning of the spin-splitting band extends to large externally applied magnetic fields with increasing values of pseudomagnetic fields. Level crossings of the bands in strained GNRs can also be observed due to the interplay between pseudomagnetic fields and externally applied magnetic fields. We also investigate the influence of this interplay on the electromagnetic field mediated spin relaxation mechanism in GNRs. In particular, we show that the spin hot spot can be observed at approximately B = 65 T (the externally applied magnetic field) and B0 = 53 T (the magnitude of induced pseudomagnetic field due to ripple waves) which may not be considered as an ideal location for the design of straintronic devices. Our analysis might be used for tuning the bandgaps in strained GNRs and utilized to design the optoelectronic devices for straintronic applications.

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References

  1. S. Das Sarma, S. Adam, E.H. Hwang, E. Rossi, Rev. Mod. Phys. 83, 407 (2011)

    Article  ADS  Google Scholar 

  2. A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)

    Article  ADS  Google Scholar 

  3. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Nature 438, 197 (2005)

    Article  ADS  Google Scholar 

  4. M. Barbier, P. Vasilopoulos, F.M. Peeters, Phys. Rev. B 81, 075438 (2010)

    Article  ADS  Google Scholar 

  5. K.S. Novoselov, D. Jiang, F. Schedin, T.J. Booth, V.V. Khotkevich, S.V. Morozov, A.K. Geim, Proc. Natl. Acad. Soc. 102, 10451 (2005)

    Article  ADS  Google Scholar 

  6. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666 (2004)

    Article  ADS  Google Scholar 

  7. Y. Zhang, Y.-W. Tan, H.L. Stormer, P. Kim, Nature 438, 7065 (2005)

    Google Scholar 

  8. V.B. Shenoy, C.D. Reddy, A. Ramasubramaniam, Y.W. Zhang, Phys. Rev. Lett. 101, 245501 (2008)

    Article  ADS  Google Scholar 

  9. S.-M. Choi, S.-H. Jhi, Y.-W. Son, Phys. Rev. B 81, 081407 (2010)

    Article  ADS  Google Scholar 

  10. W. Bao, K. Myhro, Z. Zhao, Z. Chen, W. Jang, L. Jing, F. Miao, H. Zhang, C. Dames, C.N. Lau, Nano Lett. 12, 5470 (2012)

    Article  ADS  Google Scholar 

  11. E. Cadelano, P.L. Palla, S. Giordano, L. Colombo, Phys. Rev. Lett. 102, 235502 (2009)

    Article  ADS  Google Scholar 

  12. W. Bao, F. Miao, Z. Chen, H. Zhang, W. Jang, C. Dames, C.N. Lau, Nat. Nano 4, 562 (2009)

    Article  Google Scholar 

  13. J.C. Meyer, A.K. Geim, M.I. Katsnelson, K.S. Novoselov, T.J. Booth, S. Roth, Nature 446, 60 (2007)

    Article  ADS  Google Scholar 

  14. L.L. Bonilla, A. Carpio, Phys. Rev. B 86, 195402 (2012)

    Article  ADS  Google Scholar 

  15. F. Guinea, M.I. Katsnelson, A.K. Geim, Nat. Phys. 6, 30 (2010)

    Article  Google Scholar 

  16. M. Gibertini, A. Tomadin, M. Polini, A. Fasolino, M.I. Katsnelson, Phys. Rev. B 81, 125437 (2010)

    Article  ADS  Google Scholar 

  17. A.L. Kitt, V.M. Pereira, A.K. Swan, B.B. Goldberg, Phys. Rev. B 85, 115432 (2012)

    Article  ADS  Google Scholar 

  18. A. Carpio, L.L. Bonilla, Phys. Rev. B 78, 085406 (2008)

    Article  ADS  Google Scholar 

  19. E. Cadelano, L. Colombo, Phys. Rev. B 85, 245434 (2012)

    Article  ADS  Google Scholar 

  20. S. Prabhakar, R. Melnik, L.L. Bonilla, S. Badu, Phys. Rev. B 90, 205418 (2014)

    Article  ADS  Google Scholar 

  21. L.L. Bonilla, M. Ruiz-Garcia, Phys. Rev. B 93, 115407 (2016)

    Article  ADS  Google Scholar 

  22. L.L. Bonilla, A. Carpio, C. Gong, J.H. Warner, Phys. Rev. B 92, 155417 (2015)

    Article  ADS  Google Scholar 

  23. E. Cerda, L. Mahadevan, Phys. Rev. Lett. 90, 074302 (2003)

    Article  ADS  Google Scholar 

  24. A. Fasolino, J.H. Los, M.I. Katsnelson, Nat. Mater. 6, 858 (2007)

    Article  ADS  Google Scholar 

  25. D.V. Tuan, F. Ortmann, D. Soriano, S.O. Valenzuela, S. Roche, Nat. Phys. 10, 857 (2014)

    Article  Google Scholar 

  26. M. Droth, G. Burkard, Phys. Rev. B 84, 155404 (2011)

    Article  ADS  Google Scholar 

  27. M. Droth, G. Burkard, Phys. Rev. B 87, 205432 (2013)

    Article  ADS  Google Scholar 

  28. L.D. Landau, E.M. Lifshitz, Theory of Elasticity (Pergamon Press Ltd., 1970)

  29. F. de Juan, J.L. Mañes, M.A.H. Vozmediano, Phys. Rev. B 87, 165131 (2013)

    Article  ADS  Google Scholar 

  30. L. Meng, W.-Y. He, H. Zheng, M. Liu, H. Yan, W. Yan, Z.-D. Chu, K. Bai, R.-F. Dou, Y. Zhang, Z. Liu, J.-C. Nie, L. He, Phys. Rev. B 87, 205405 (2013)

    Article  ADS  Google Scholar 

  31. F. Guinea, M.I. Katsnelson, M.A.H. Vozmediano, Phys. Rev. B 77, 075422 (2008)

    Article  ADS  Google Scholar 

  32. V. Krueckl, K. Richter, Phys. Rev. B 85, 115433 (2012)

    Article  ADS  Google Scholar 

  33. S. Prabhakar, R. Melnik, L. Bonilla, Phys. Rev. B 93, 115417 (2016)

    Article  ADS  Google Scholar 

  34. N. Levy, S.A. Burke, K.L. Meaker, M. Panlasigui, A. Zettl, F. Guinea, A.H.C. Neto, M.F. Crommie, Science 329, 544 (2010)

    Article  ADS  Google Scholar 

  35. F. Guinea, B. Horovitz, P. Le Doussal, Phys. Rev. B 77, 205421 (2008)

    Article  ADS  Google Scholar 

  36. L. Brey, H.A. Fertig, Phys. Rev. B 73, 235411 (2006)

    Article  ADS  Google Scholar 

  37. J. Klinovaja, D. Loss, Phys. Rev. X 3, 011008 (2013)

    Google Scholar 

  38. A.H. Castro Neto, F. Guinea, N.M.R. Peres, Phys. Rev. B 73, 205408 (2006)

    Article  ADS  Google Scholar 

  39. R. Carrillo-Bastos, C. León, D. Faria, A. Latgé, E.Y. Andrei, N. Sandler, Phys. Rev. B 94, 125422 (2016)

    Article  ADS  Google Scholar 

  40. D.A. Gradinar, M. Mucha-Kruczyński, H. Schomerus, V.I. Fal’ko, Phys. Rev. Lett. 110, 266801 (2013)

    Article  ADS  Google Scholar 

  41. Z. Qi, D.A. Bahamon, V.M. Pereira, H.S. Park, D.K. Campbell, A.H.C. Neto, Nano Lett. 13, 2692 (2013)

    Article  ADS  Google Scholar 

  42. W.-Y. He, Y. Su, M. Yang, L. He, Phys. Rev. B 89, 125418 (2014)

    Article  ADS  Google Scholar 

  43. D.A. Bahamon, Z. Qi, H.S. Park, V.M. Pereira, D.K. Campbell, Nanoscale 7, 15300 (2015)

    Article  ADS  Google Scholar 

  44. E. Merzbacher, Quantum Mechanics (John Wiley & Sons, Inc., New York, 2004)

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Correspondence to Sanjay Prabhakar.

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Prabhakar, S., Melnik, R. & Bonilla, L. Strain engineering of graphene nanoribbons: pseudomagnetic versus external magnetic fields. Eur. Phys. J. B 90, 92 (2017). https://doi.org/10.1140/epjb/e2017-80038-3

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