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Electronic transport across a junction between armchair graphene nanotube and zigzag nanoribbon

Transmission in an armchair nanotube without a zigzag half-line of dimers

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Abstract

Based on the well known nearest-neighbor tight-binding approximation for graphene, an exact expression for the electronic conductance across a zigzag nanoribbon/armchair nanotube junction is presented for non-interacting electrons. The junction results from the removal of a half-row of zigzag dimers in armchair nanotube, or equivalently by partial rolling of zigzag nanoribbon and insertion of a half-row of zigzag dimers in between. From the former point of view, a discrete form of Dirichlet condition is imposed on a zigzag half-line of dimers assuming the vanishing of wave function outside the physical structure. A closed form expression is provided for the reflection and transmission moduli for the outgoing wave modes for each given electronic wave mode incident from either side of the junction. It is demonstrated that such a contact junction between the nanotube and nanoribbon exhibits negligible backscattering, and the transmission has been found to be nearly ballistic. In contrast to the previously reported studies for partially unzipped carbon nanotubes (CNTs), using the same tight binding model, it is found that due to the “defect” there is certain amount of mixing between the electronic wave modes with even and odd reflection symmetries. But the junction remains a perfect valley filter for CNTs at certain energy ranges. Applications aside from the electronic case, include wave propagation in quasi-one-dimensional honeycomb structures of graphene-like constitution. The paper includes several numerical calculations, analytical derivations, and graphical results, which complement the provision of succinct closed form expressions.

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References

  1. S. Iijima et al., Nature 354, 56 (1991)

    Article  ADS  Google Scholar 

  2. N. Hamada, S.I. Sawada, A. Oshiyama, Phys. Rev. Lett. 68, 1579 (1992)

    Article  ADS  Google Scholar 

  3. Y. Kobayashi, K. Fukui, T. Enoki, K. Kusakabe, Y. Kaburagi, Phys. Rev. B 71, 193406 (2005)

    Article  ADS  Google Scholar 

  4. 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 

  5. S.J. Tans, A.R. Verschueren, C. Dekker, Nature 393, 49 (1998)

    Article  ADS  Google Scholar 

  6. B. Trauzettel, D.V. Bulaev, D. Loss, G. Burkard, Nat. Phys. 3, 192 (2007)

    Article  Google Scholar 

  7. A.A. Balandin, Nat. Mater. 10, 569 (2011)

    Article  ADS  Google Scholar 

  8. M. Fujita, K. Wakabayashi, K. Nakada, K. Kusakabe, J. Phys. Soc. Jpn. 65, 1920 (1996)

    Article  ADS  Google Scholar 

  9. K. Nakada, M. Fujita, G. Dresselhaus, M.S. Dresselhaus, Phys. Rev. B 54, 17954 (1996)

    Article  ADS  Google Scholar 

  10. J.W. Wilder, L.C. Venema, A.G. Rinzler, R.E. Smalley, C. Dekker, Nature 391, 59 (1998)

    Article  ADS  Google Scholar 

  11. X. Jia et al., Science 323, 1701 (2009)

    Article  ADS  Google Scholar 

  12. M.C. Rechtsman, J.M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, Nature 496, 196 (2013)

    Article  ADS  Google Scholar 

  13. Y. Pennec, J.O. Vasseur, B. Djafari-Rouhani, L. Dobrzynski, P.A. Deymier, Surf. Sci. Rep. 65, 229 (2010)

    Article  ADS  Google Scholar 

  14. M. Polini, F. Guinea, M. Lewenstein, H.C. Manoharan, V. Pellegrini, Nat. Nanotechnol. 8, 625 (2013)

    Article  ADS  Google Scholar 

  15. R. Saito, G. Dresselhaus, M. Dresselhaus, Physical properties of carbon nanotubes (Imperial College Press, London, 1998)

  16. N. Agra"i"t, A.L. Yeyati, J.M. Van Ruitenbeek, Phys. Rep. 377, 81 (2003)

    Article  ADS  Google Scholar 

  17. M. Fuhrer et al., Science 288, 494 (2000)

    Article  ADS  Google Scholar 

  18. A. Bachtold, P. Hadley, T. Nakanishi, C. Dekker, Science 294, 1317 (2001)

    Article  ADS  Google Scholar 

  19. M.F. De Volder, S.H. Tawfick, R.H. Baughman, A.J. Hart, Science 339, 535 (2013)

    Article  ADS  Google Scholar 

  20. D.V. Kosynkin, A.L. Higginbotham, A. Sinitskii, J.R. Lomeda, A. Dimiev, B.K. Price, J.M. Tour, Nature 458, 872 (2009)

    Article  ADS  Google Scholar 

  21. L. Jiao, L. Zhang, X. Wang, G. Diankov, H. Dai, Nature 458, 877 (2009)

    Article  ADS  Google Scholar 

  22. A.L. Elías, A.R. Botello-Méndez, D. Meneses-Rodríguez, V. Jehová González, D. Ramírez-González, L. Ci, E. Muñoz-Sandoval, P.M. Ajayan, H. Terrones, M. Terrones, Nano Lett. 10, 366 (2009)

    Article  ADS  Google Scholar 

  23. A. Cano-Márquez, F. Rodríguez-Macías, J. Campos-Delgado, C. Espinosa-González, F. Tristán-López, D. Ramírez-González, D. Cullen, D. Smith, M. Terrones, Y. Vega-Cantú, Nano Lett. 9, 1527 (2009)

    Article  ADS  Google Scholar 

  24. Y. Yoon, S. Salahuddin, Appl. Phys. Lett. 97, 033102 (2010)

    Article  ADS  Google Scholar 

  25. S. Costamagna, A. Schulz, L. Covaci, F. Peeters, Appl. Phys. Lett. 100, 232104 (2012)

    Article  ADS  Google Scholar 

  26. J.S. Friedman, A. Girdhar, R.M. Gelfand, G. Memik, H. Mohseni, A. Taflove, B.W. Wessels, J.P. Leburton, A.V. Sahakian, Nat. Commun. 8, 15635 (2017)

    Article  ADS  Google Scholar 

  27. H. Santos, L. Chico, L. Brey, Phys. Rev. Lett. 103, 086801 (2009)

    Article  ADS  Google Scholar 

  28. Y.O. Klymenko, Eur. Phys. J. B 77, 433 (2010)

    Article  ADS  Google Scholar 

  29. L. Chico, H. Santos, A. Ayuela, W. Jaskólski, M. Pelc, L. Brey, Acta Phys. Pol. A 118, 433 (2010)

    Article  Google Scholar 

  30. K.L. Ma, X.H. Yan, Y.D. Guo, Y. Xiao, Eur. Phys. J. B 83, 487 (2011)

    Article  ADS  Google Scholar 

  31. B.L. Sharma, Z. Angew. Math. Phys. 69, 16 (2018)

    Article  Google Scholar 

  32. J.B. David, K. Ferry, S.M. Goodnick, Transport in nanostructures, 2nd edn. (Cambridge University Press, Cambridge, UK, 2009)

  33. M. Brandbyge, M.R. Sørensen, K.W. Jacobsen, Phys. Rev. B 56, 14956 (1997)

    Article  ADS  Google Scholar 

  34. M. Brandbyge, J.L. Mozos, P. Ordejón, J. Taylor, K. Stokbro, Phys. Rev. B 65, 165401 (2002)

    Article  ADS  Google Scholar 

  35. P.R. Wallace, Phys. Rev. 71, 622 (1947)

    Article  ADS  Google Scholar 

  36. J. Callaway, Energy band theory, in Pure and applied physics (Academic Press, New York, 1964)

  37. E. Hückel, Z. Phys. 60, 423 (1930)

    Article  ADS  Google Scholar 

  38. R. Mittra, Y.L. Hou, V. Jamnejad, IEEE Trans. Microw. Theory Tech. 28, 36 (1980)

    Article  ADS  Google Scholar 

  39. J.T. Londergan, J.P. Carini, D.P. Murdock, Binding and scattering in two-dimensional systems: applications to quantum wires, waveguides, and photonic crystals, 1st edn. Lecture notes in physics monographs, (Springer, Berlin, Heidelberg, 2000)

  40. S. Datta, in Electronic transport in mesoscopic systems. Cambridge studies in semiconductor physics and microelectronic engineering (Cambridge University Press, Cambridge, UK, 1995), Vol. 3

  41. B. Noble, Methods based on the Wiener–Hopf technique (Pergamon Press, London, 1958)

  42. B.L. Sharma, Z. Angew. Math. Phys. 66, 3591 (2015)

    Article  MathSciNet  Google Scholar 

  43. R. Landauer, IBM J. Res. Dev. 1, 223 (1957)

    Article  Google Scholar 

  44. R. Landauer, Phys. Scripta 1992, 110 (1992)

    Article  Google Scholar 

  45. C. Hamaguchi, Quantum structures (Springer, Berlin, Heidelberg, 2001), p. 307

  46. P.L. Chebyshev, Mém. Acad. Sci. Pétersb. 7, 539 (1854)

    Google Scholar 

  47. J.C. Mason, D.C. Handscomb, Chebyshev polynomials (Chapman & Hall/CRC, Boca Raton, FL, 2003)

  48. N. Cortés, L. Chico, M. Pacheco, L. Rosales, P. Orellana, EPL 108, 46008 (2014)

    Article  ADS  Google Scholar 

  49. P. Orellana, L. Rosales, L. Chico, M. Pacheco, J. Appl. Phys. 113, 213710 (2013)

    Article  ADS  Google Scholar 

  50. B.L. Sharma, Waves Random Complex Media 28, 96 (2018)

    Article  MathSciNet  Google Scholar 

  51. A. Weisshaar, J. Lary, S.M. Goodnick, V.K. Tripathi, J. Appl. Phys. 70, 355 (1991)

    Article  ADS  Google Scholar 

  52. W.D. Sheng, J. Phys. Condens. Matter 9, 8369 (1997)

    Article  ADS  Google Scholar 

  53. B.L. Sharma, Wave Motion 65, 55 (2016)

    Article  MathSciNet  Google Scholar 

  54. B.L. Sharma, Wave Motion 59, 52 (2015)

    Article  MathSciNet  Google Scholar 

  55. B.L. Sharma, Z. Angew. Math. Phys. 66, 2719 (2015)

    Article  MathSciNet  Google Scholar 

  56. K. Yates, Hückel molecular orbital theory (Academic Press, New York, 1978)

  57. E. Economou, Green’s functions in quantum physics (Springer, Heidelberg, 1979)

  58. B.L. Sharma, Int. J. Solids Struct. 80, 465 (2016)

    Article  Google Scholar 

  59. M.J. Ablowitz, A.S. Fokas, Complex variables: introduction and applications (Cambridge University Press, Cambridge, UK, New York, 1997)

  60. A. Weisshaar, J. Lary, S. Goodnick, V. Tripathi, Appl. Phys. Lett. 55, 2114 (1989)

    Article  ADS  Google Scholar 

  61. K. Wakabayashi, Y. Takane, M. Yamamoto, M. Sigrist, Carbon 47, 124 (2009)

    Article  Google Scholar 

  62. B.L. Sharma, SIAM J. Appl. Math. 76, 1355 (2016)

    Article  MathSciNet  Google Scholar 

  63. T. Wehling, A.M. Black-Schaffer, A.V. Balatsky, Adv. Phys. 63, 1 (2014)

    Article  ADS  Google Scholar 

  64. Y. Kobayashi, K. Fukui, T. Enoki, K. Kusakabe, Phys. Rev. B 73, 125415 (2006)

    Article  ADS  Google Scholar 

  65. B. Wang, J. Wang, Phys. Rev. B 81, 045425 (2010)

    Article  ADS  Google Scholar 

  66. Y.W. Son, M.L. Cohen, S.G. Louie, Phys. Rev. Lett. 97, 216803 (2006)

    Article  ADS  Google Scholar 

  67. L. Yang, C.H. Park, Y.W. Son, M.L. Cohen, S.G. Louie, Phys. Rev. Lett. 99, 186801 (2007)

    Article  ADS  Google Scholar 

  68. Y.V. Nazarov, Quantum transport: introduction to nanoscience, 1st edn. (Cambridge University Press, Cambridge, UK, 2009)

  69. F.A. Buot, Phys. Rep. 234, 73 (1993)

    Article  ADS  Google Scholar 

  70. T. Ihn, in Electronic quantum transport in mesoscopic semiconductor structures, 1st edn. Springer tracts in modern physics, (Springer-Verlag, New York, 2004), Vol. 192

  71. D.A. Wharam, T.J. Thornton, R. Newbury, M. Pepper, H. Ahmed, J.E.F. Frost, D.G. Hasko, D.C. Peacock, D.A. Ritchie, G.A.C. Jones, J. Phys. C: Solid State Phys. 21, L209 (1988)

    Article  ADS  Google Scholar 

  72. B.J. van Wees, H. van Houten, C.W.J. Beenakker, J.G. Williamson, L.P. Kouwenhoven, D. van der Marel, C.T. Foxon, Phys. Rev. Lett. 60, 848 (1988)

    Article  ADS  Google Scholar 

  73. J. Park, G. He, R.M. Feenstra, A.P. Li, Nano Lett. 13, 3269 (2013)

    Article  ADS  Google Scholar 

  74. R. Egger, A.O. Gogolin, Phys. Rev. Lett. 79, 5082 (1997)

    Article  ADS  Google Scholar 

  75. C. Kane, L. Balents, M.P.A. Fisher, Phys. Rev. Lett. 79, 5086 (1997)

    Article  ADS  Google Scholar 

  76. A.R. Hernández, C.H. Lewenkopf, Phys. Rev. B 86, 155439 (2012)

    Article  ADS  Google Scholar 

  77. J. Tworzydło, C. Groth, C. Beenakker, Phys. Rev. B 78, 235438 (2008)

    Article  ADS  Google Scholar 

  78. L.I. Slepyan, Models and phenomena in fracture mechanics (Springer, New York, Berlin, Heidelberg, 2002)

  79. B.L. Sharma, SIAM J. Appl. Math. 75, 1171 (2015)

    Article  MathSciNet  Google Scholar 

  80. B.L. Sharma, Sādhanā 42, 901 (2017)

    Google Scholar 

  81. N. Wiener, E. Hopf, Sitzungsber. Preuss. Akad. Wiss. Berl. Phys. Math. 32, 696 (1931)

    Google Scholar 

  82. I. Singer, E. Turkel, J. Comput. Phys. 201, 439 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  83. J.P. Berenger, J. Comput. Phys. 114, 185 (1994)

    Article  ADS  MathSciNet  Google Scholar 

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  1. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, U.P., 208016, India

    Basant Lal Sharma

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Sharma, B.L. Electronic transport across a junction between armchair graphene nanotube and zigzag nanoribbon. Eur. Phys. J. B 91, 84 (2018). https://doi.org/10.1140/epjb/e2018-80647-2

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