Terahertz Dynamics of Quantum-Confined Electrons in Carbon Nanomaterials

  • Lei Ren
  • Qi Zhang
  • Sébastien Nanot
  • Iwao Kawayama
  • Masayoshi Tonouchi
  • Junichiro Kono
Article

Abstract

Low-dimensional carbon nanostructures, such as single-wall carbon nanotubes (SWCNTs) and graphene, offer new opportunities for terahertz science and technology. Being zero-gap systems with a linear, photon-like energy dispersion, metallic SWCNTs and graphene exhibit a variety of extraordinary properties. Their DC and linear electrical properties have been extensively studied in the last decade, but their unusual finite-frequency, nonlinear, and/or non-equilibrium properties are largely unexplored, although they are predicted to be useful for new terahertz device applications. Terahertz dynamic conductivity measurements allow us to probe the dynamics of such photon-like electrons, or massless Dirac fermions. Here, we use terahertz time-domain spectroscopy and Fourier transform infrared spectroscopy to investigate terahertz conductivities of one-dimensional and two-dimensional electrons, respectively, in films of highly aligned SWCNTs and gated large-area graphene. In SWCNTs, we observe extremely anisotropic terahertz conductivities, promising for terahertz polarizer applications. In graphene, we demonstrate that terahertz and infrared properties sensitively change with the Fermi energy, which can be controlled by electrical gating and thermal annealing.

Keywords

Terahertz Nanotube Graphene Anisotropic Polarization 

References

  1. 1.
    H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E. Smalley, Nature 318, 162 (1985)CrossRefGoogle Scholar
  2. 2.
    S. Iijima, Nature 354, 56 (1991)CrossRefGoogle Scholar
  3. 3.
    A. Oberlin, M. Endo, T. Koyama, J. Crystal Growth 32, 335 (1976)CrossRefGoogle Scholar
  4. 4.
    S. Iijima, T. Ichihashi, Nature 363, 603 (1993)CrossRefGoogle Scholar
  5. 5.
    D.S. Bethune, C.H. Klang, M.S. de Vries, G. Gorman, R. Savoy, J. Vazquez, R. Beyers, Nature 363, 605 (1993)CrossRefGoogle Scholar
  6. 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)CrossRefGoogle Scholar
  7. 7.
    M.E. Portnoi, O.V. Kibis, M. Rosenau da Costa, Proc. SPIE 6328, 632805 (2006)CrossRefGoogle Scholar
  8. 8.
    V. Ryzhii, Jpn. J. Appl. Phys. 45, L923 (2006)CrossRefGoogle Scholar
  9. 9.
    O.V. Kibis, M. Rosenau da Costa, M.E. Portnoi, Nano Lett. 7, 3414 (2007)CrossRefGoogle Scholar
  10. 10.
    S.A. Mikhailov, K. Ziegler, J. Phys.: Condens. Matter 20, 384204 (2008)CrossRefGoogle Scholar
  11. 11.
    S.A. Mikhailov, Microelectron. J. 40, 712 (2009)CrossRefGoogle Scholar
  12. 12.
    V.A. Sablikov, B.S. Shchamkhalova, JETP Lett. 66, 41 (1997)CrossRefGoogle Scholar
  13. 13.
    A. Rosch, N. Andrei, Phys. Rev. Lett. 85, 1092 (2000)CrossRefGoogle Scholar
  14. 14.
    T. Ando, J. Phys. Soc. Jpn. 71, 2505 (2002)CrossRefGoogle Scholar
  15. 15.
    P.J. Burke, IEEE Trans. Nanotechnol. 1, 129 (2002)CrossRefGoogle Scholar
  16. 16.
    M. Pustilnik, M. Khodas, A. Kamenev, L.I. Glazman, Phys. Rev. Lett. 96, 196405 (2006)CrossRefGoogle Scholar
  17. 17.
    T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, Oxford, 2004)MATHGoogle Scholar
  18. 18.
    Q. Si, S. Rabello, K. Ingersent, J.L. Smith, Nature 413, 804 (2001)CrossRefGoogle Scholar
  19. 19.
    S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999)Google Scholar
  20. 20.
    F. Bommeli, L. Degiorgi, P. Wachter, W.S. Bacsa, W.A. de Heer, L. Forro, Solid State Commun. 99, 513 (1996)CrossRefGoogle Scholar
  21. 21.
    A. Ugawa, A.G. Rinzler, D.B. Tanner, Phys. Rev. B 60, R11305 (1999)CrossRefGoogle Scholar
  22. 22.
    M.E. Itkis, S. Niyogi, M.E. Meng, M.A. Hamon, H. Hu, R.C. Haddon, Nano Lett. 2, 155 (2002)CrossRefGoogle Scholar
  23. 23.
    T.I. Jeon, K.J. Kim, C. Kang, S.J. Oh, J.H. Son, K.H. An, D.J. Bae, Y.H. Lee, Appl. Phys. Lett. 80, 3403 (2002)CrossRefGoogle Scholar
  24. 24.
    T.I. Jeon, K.J. Kim, C. Kang, I.H. Maeng, J.H. Son, K.H. An, J.Y. Lee, Y.H. Lee, J. Appl. Phys. 95, 5736 (2004)CrossRefGoogle Scholar
  25. 25.
    T.I. Jeon, J.H. Son, K.H. An, Y.H. Lee, Y.S. Lee, J. Appl. Phys. 98, 034316 (2005)CrossRefGoogle Scholar
  26. 26.
    N. Akima, Y. Iwasa, S. Brown, A.M. Barbour, J. Cao, J.L. Musfeldt, H. Matsui, N. Toyota, M. Shiraishi, H. Shimoda, O. Zhou, Adv. Mater. 18, 1166 (2006)CrossRefGoogle Scholar
  27. 27.
    F. Borondics, K. Kamarás, M. Nikolou, D.B. Tanner, Z.H. Chen, A.G. Rinzler, Phys. Rev. B 74, 045431 (2006)CrossRefGoogle Scholar
  28. 28.
    H. Nishimura, N. Minami, R. Shimano, Appl. Phys. Lett. 91, 011108 (2007)CrossRefGoogle Scholar
  29. 29.
    T. Kampfrath, K. von Volkmann, C.M. Aguirre, P. Desjardins, R. Martel, M. Krenz, C. Frischkorn, M. Wolf, L. Perfetti, Phys. Rev. Lett. 101(26), 267403 (2008)CrossRefGoogle Scholar
  30. 30.
    T. Nakanishi, T. Ando, J. Phys. Soc. Jpn. 78, 114708 (2009)CrossRefGoogle Scholar
  31. 31.
    G.Y. Slepyan, M.V. Shuba, S.A. Maksimenko, C. Thomsen, A. Lakhtakia, Phys. Rev. B 81, 205423 (2010)CrossRefGoogle Scholar
  32. 32.
    N.H. Shon, T. Ando, J. Phys. Soc. Jpn. 67, 2421 (1998)CrossRefGoogle Scholar
  33. 33.
    Y. Zheng, T. Ando, Phys. Rev. B 65, 245420 (2002)CrossRefGoogle Scholar
  34. 34.
    T. Ando, Y. Zheng, H. Suzuura, J. Phys. Soc. Jpn. 71, 1318 (2002)CrossRefGoogle Scholar
  35. 35.
    N.M.R. Peres, F. Guinea, A.H. Castro Neto, Phys. Rev. B 73, 125411 (2006)CrossRefGoogle Scholar
  36. 36.
    V.P. Gusynin, S.G. Sharapov, Phys. Rev. B 73, 245411 (2006)CrossRefGoogle Scholar
  37. 37.
    V.P. Gusynin, S.G. Sharapov, J.P. Carbotte, Phys. Rev. Lett. 96, 256802 (2006)CrossRefGoogle Scholar
  38. 38.
    V.P. Gusynin, S.G. Sharapov, J.P. Carbotte, Phys. Rev. Lett. 98, 157402 (2007)CrossRefGoogle Scholar
  39. 39.
    S. Ryu, C. Mudry, A. Furusaki, A.W.W. Ludwig, Phys. Rev. B 75, 205344 (2007)CrossRefGoogle Scholar
  40. 40.
    D.S.L. Abergel, V.I. Fal’ko, Phys. Rev. B 75, 155430 (2007)CrossRefGoogle Scholar
  41. 41.
    E.G. Mishchenko, Phys. Rev. Lett. 98, 216801 (2007)CrossRefGoogle Scholar
  42. 42.
    V.P. Gusynin, S.G. Sharapov, J.P. Carbotte, Phys. Rev. B 75, 165407 (2007)CrossRefGoogle Scholar
  43. 43.
    V. Ryzhii, M. Ryzhii, T. Otsuji, J. Appl. Phys. 101, 083114 (2007)CrossRefGoogle Scholar
  44. 44.
    L.A. Falkovsky, A.A. Varlamov, Eur. Phys. J. B 56, 281 (2007)CrossRefGoogle Scholar
  45. 45.
    S.A. Mikhailov, K. Ziegler, Phys. Rev. Lett. 99, 016803 (2007)CrossRefGoogle Scholar
  46. 46.
    S.A. Mikhailov, Europhys. Lett. 79, 27002 (2007)CrossRefGoogle Scholar
  47. 47.
    L.A. Falkovsky, S.S. Pershoguba, Phys. Rev. B 76, 153410 (2007)CrossRefGoogle Scholar
  48. 48.
    D.E. Sheehy, J. Schmalian, Phys. Rev. Lett. 99, 226803 (2007)CrossRefGoogle Scholar
  49. 49.
    I.F. Herbut, V. Juričić, O. Vafek, Phys. Rev. Lett. 100, 046403 (2008)CrossRefGoogle Scholar
  50. 50.
    M. Koshino, T. Ando, Phys. Rev. B 77, 115313 (2008)CrossRefGoogle Scholar
  51. 51.
    E.G. Mishchenko, Europhys. Lett. 83, 17005 (2008)CrossRefGoogle Scholar
  52. 52.
    M. Lewkowicz, B. Rosenstein, Phys. Rev. Lett. 102, 106802 (2009)CrossRefGoogle Scholar
  53. 53.
    V. Ryzhii, M. Ryzhii, V. Mitin, M.S. Shur, Appl. Phys. Exp. 2, 034503 (2009)CrossRefGoogle Scholar
  54. 54.
    S.A. Mikhailov, Phys. Rev. B 79, 241309(R) (2009)CrossRefGoogle Scholar
  55. 55.
    P. Ingenhoven, J.Z. Bernád, U. Zülicke, R. Egger, Phys. Rev. B 81, 035421 (2010)CrossRefGoogle Scholar
  56. 56.
    V. Juričić, O. Vafek, I.F. Herbut, Phys. Rev. B 82, 235402 (2010)CrossRefGoogle Scholar
  57. 57.
    R.R. Nair, P. Blake, A.N. Grigorenko, K.S. Novoselov, T.J. Booth, T. Stauber, N.M.R. Peres, A.K. Geim, Science 320, 1308 (2008)CrossRefGoogle Scholar
  58. 58.
    K.F. Mak, M.Y. Sfeir, Y. Wu, C.H. Lui, J.A. Misewich, T.F. Heinz, Phys. Rev. Lett. 101, 196405 (2008)CrossRefGoogle Scholar
  59. 59.
    Z.Q. Li, E.A. Henriksen, Z. Jiang, Z. Hao, M.C. Martin, P. Kim, H.L. Stormer, D.N. Basov, Nature Phys. 4, 532 (2008)CrossRefGoogle Scholar
  60. 60.
    H. Choi, F. Borondics, D.A. Siegel, S.Y. Zhou, M.C. Martin, A. Lanzara, R.A. Kaindl, Appl. Phys. Lett. 94, 172102 (2009)CrossRefGoogle Scholar
  61. 61.
    J. Horng, C.F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H.A. Bechtel, M. Martin, A. Zettl, M.F. Crommie, Y.R. Shen, F. Wang, Phys. Rev. B 83, 165113 (2011)CrossRefGoogle Scholar
  62. 62.
    W. Liu, R.V. Aguilar, Y. Hao, R.S. Ruoff, N.P. Armitage, J. Appl. Phys. 110, 083510 (2011)CrossRefGoogle Scholar
  63. 63.
    H. Yan, F. Xia, W. Zhu, M. Freitag, C. Dimitrakopoulos, A.A. Bol, G. Tulevski, P. Avouris, ACS Nano 5, 9854 (2011)CrossRefGoogle Scholar
  64. 64.
    I. Maeng, S. Lim, S.J. Chae, Y.H. Lee, H. Choi, J.H. Son, Nano Lett. 12, 551 (2012)CrossRefGoogle Scholar
  65. 65.
    B. Sensale-Rodriguez, R. Yan, M.M. Kelly, T. Fang, K. Tahy, W.S. Hwang, D. Jena, L. Liu, H.G. Xing, Nat. Commun. 3, 780 (2012)CrossRefGoogle Scholar
  66. 66.
    M.L. Sadowski, G. Martinez, M. Potemski, C. Berger, W.A. de Heer, Phys. Rev. Lett. 97, 266405 (2006)CrossRefGoogle Scholar
  67. 67.
    Z. Jiang, E.A. Henriksen, L.C. Tung, Y.J. Wang, M.E. Schwartz, M.Y. Han, P. Kim, H.L. Stormer, Phys. Rev. Lett. 98, 197403 (2007)CrossRefGoogle Scholar
  68. 68.
    R.S. Deacon, K.C. Chuang, R.J. Nicholas, K.S. Novoselov, A.K. Geim, Phys. Rev. B 76, 081406 (2007)CrossRefGoogle Scholar
  69. 69.
    E.A. Henriksen, Z. Jiang, L.C. Tung, M.E. Schwartz, M. Takita, Y.J. Wang, P. Kim, H.L. Stormer, Phys. Rev. Lett. 100, 087403 (2008)CrossRefGoogle Scholar
  70. 70.
    M. Orlita, C. Faugeras, P. Plochocka, P. Neugebauer, G. Martinez, D.K. Maude, A.L. Barra, M. Sprinkle, C. Berger, W.A. de Heer, M. Potemski, Phys. Rev. Lett. 101, 267601 (2008)CrossRefGoogle Scholar
  71. 71.
    P. Neugebauer, M. Orlita, C. Faugeras, A.L. Barra, M. Potemski, Phys. Rev. Lett. 103, 136403 (2009)CrossRefGoogle Scholar
  72. 72.
    E.A. Henriksen, P. Cadden-Zimansky, Z. Jiang, Z.Q. Li, L.C. Tung, M.E. Schwartz, M. Takita, Y.J. Wang, P. Kim, H.L. Stormer, Phys. Rev. Lett. 104, 067404 (2010)CrossRefGoogle Scholar
  73. 73.
    I. Crassee, J. Levallois, A.L. Walter, M. Ostler, A.B.E. Rotenberg, T. Seyller, D. van der Marel, A.B. Kuzmenko, Nature Phys. 7, 48 (2011)CrossRefGoogle Scholar
  74. 74.
    A.M. Witowski, M. Orlita, R. Stȩpniewski, A. Wysmołek, J.M. Baranowski, W. Strupiński, C. Faugeras, G. Martinez, M. Potemski, Phys. Rev. B 82, 165305 (2010)CrossRefGoogle Scholar
  75. 75.
    M. Orlita, C. Faugeras, R. Grill, A. Wysmolek, W. Strupinski, C. Berger, W.A. de Heer, G. Martinez, M. Potemski, Phys. Rev. Lett. 107, 216603 (2011)CrossRefGoogle Scholar
  76. 76.
    I. Crassee, J. Levallois, D. van der Marel, A.L. Walter, T. Seyller, A.B. Kuzmenko, Phys. Rev. B 84, 035103 (2011)CrossRefGoogle Scholar
  77. 77.
    L.G. Booshehri, C.H. Mielke, D.G. Rickel, S.A. Crooker, Q. Zhang, L. Ren, E.H. Hároz, A. Rustagi, C.J. Stanton, Z. Jin, Z. Sun, Z. Yan, J.M. Tour, J. Kono, Phys. Rev. B 85, 205407 (2012)CrossRefGoogle Scholar
  78. 78.
    M.S. Dresselhaus, G. Dresselhaus, P. Avouris (eds.), Carbon Nanotubes: Synthesis, Structure, Properties, and Applications. No. 18 in Topics in Applied Physics (Springer, Berlin, 2001)Google Scholar
  79. 79.
    M.J. O’Connell (ed.), Carbon Nanotubes: Properties and Applications (CRC Press, Taylor & Francis Group, Boca Raton, 2006)Google Scholar
  80. 80.
    A. Jorio, G. Dresselhaus, M.S. Dresselhaus (eds.), Carbon Nanotubes: Advanced Topics in the Synthesis, Structure, Properties and Applications (Springer, Berlin, 2008)Google Scholar
  81. 81.
    S.J. Tans, M.H. Devoret, H. Dai, A. Thess, R.E. Smalley, L.J. Geerligs, C. Dekker, Nature 386, 474 (1997)CrossRefGoogle Scholar
  82. 82.
    A. Srivastava, H. Htoon, V.I. Klimov, J. Kono, Phys. Rev. Lett. 101, 087402 (2008)CrossRefGoogle Scholar
  83. 83.
    M.F. Islam, D.E. Milkie, C.L. Kane, A.G. Yodh, J.M. Kikkawa, Phys. Rev. Lett. 93, 037404 (2004)CrossRefGoogle Scholar
  84. 84.
    S. Zaric, G.N. Ostojic, J. Kono, J. Shaver, V.C. Moore, M.S. Strano, R.H. Hauge, R.E. Smalley, X. Wei, Science 304, 1129 (2004)CrossRefGoogle Scholar
  85. 85.
    S. Zaric, G.N. Ostojic, J. Kono, J. Shaver, V.C. Moore, R.H. Hauge, R.E. Smalley, X. Wei, Nano Lett. 4, 2219 (2004)CrossRefGoogle Scholar
  86. 86.
    M.F. Islam, D.E. Milkie, O.N. Torrens, A.G. Yodh, J.M. Kikkawa, Phys. Rev. B 71, 201401(R) (2005)CrossRefGoogle Scholar
  87. 87.
    O.N. Torrens, D.E. Milkie, H.Y. Ban, M. Zheng, G.B. Onoa, T.D. Gierke, J.M. Kikkawa, J. Am. Chem. Soc. 129, 252 (2007)CrossRefGoogle Scholar
  88. 88.
    J. Shaver, A.N.G. Parra-Vasquez, S. Hansel, O. Portugall, C.H. Mielke, M. von Ortenberg, R.H. Hauge, M. Pasquali, J. Kono, ACS Nano 3, 131 (2009)CrossRefGoogle Scholar
  89. 89.
    H. Ajiki, T. Ando, J. Phys. Soc. Jpn. 62, 2470 (1993)CrossRefGoogle Scholar
  90. 90.
    J.P. Lu, Phys. Rev. Lett. 74, 1123 (1995)CrossRefGoogle Scholar
  91. 91.
    M.A.L. Marques, M. d’Avezac, F. Mauri, Phys. Rev. B 73, 125433 (2006)CrossRefGoogle Scholar
  92. 92.
    Y. Murakami, E. Einarsson, T. Edamura, S. Maruyama, Phys. Rev. Lett. 94, 087402 (2005)CrossRefGoogle Scholar
  93. 93.
    J.A. Fagan, J.R. Simpson, B.J. Landi, L.J. Richter, I. Mandelbaum, V. Bajpai, D.L. Ho, R. Raffaelle, A.R. Walker, B.J. Bauer, E.K. Hobbie, Phys. Rev. Lett. 98, 147402 (2007)CrossRefGoogle Scholar
  94. 94.
    J. Shaver, S.A. Crooker, J.A. Fagan, E.K. Hobbie, N. Ubrig, O. Portugall, V. Perebeinos, P. Avouris, J. Kono, Phys. Rev. B 78, 081402 (2008)CrossRefGoogle Scholar
  95. 95.
    L. Ren, C.L. Pint, L.G. Booshehri, W.D. Rice, X. Wang, D.J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R.H. Hauge, J. Kono, Nano Lett. 9, 2610 (2009)CrossRefGoogle Scholar
  96. 96.
    L. Ren, C.L. Pint, T. Arikawa, K. Takeya, I. Kawayama, M. Tonouchi, R.H. Hauge, J. Kono, Nano Lett. 12, 787 (2012)CrossRefGoogle Scholar
  97. 97.
    A. Rodger, B. Nordén, Circular Dichroism and Linear Dichroism (Oxford University Press, 1997)Google Scholar
  98. 98.
    J. Kyoung, E.Y. Jang, M.D. Lima, H.R. Park, R.O. Robls, X. Lepro, Y.H. Kim, R.H. Baughman, D.S. Kim, Nano Lett. 11, 4227 (2011)CrossRefGoogle Scholar
  99. 99.
    C.L. Pint, Y.Q. Xu, S. Moghazy, T. Cherukuri, N.T. Alvarez, E.H. Hároz, S. Mahzooni, S.K. Doorn, J. Kono, M. Pasquali, R.H. Hauge, ACS Nano 4, 1131 (2010)CrossRefGoogle Scholar
  100. 100.
    A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183 (2007)CrossRefGoogle Scholar
  101. 101.
    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)CrossRefGoogle Scholar
  102. 102.
    F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, Y.R. Shen, Science 320, 206 (2008)CrossRefGoogle Scholar
  103. 103.
    S. Pisana, M. Lazzeri, C. Casiraghi, K.S. Novoselov, A.K. Geim, A.C. Ferrari, F. Mauri, Nat. Mater. 6, 198 (2007)CrossRefGoogle Scholar
  104. 104.
    J. Yan, Y. Zhang, P. Kim, A. Pinczuk, Phys. Rev. Lett. 98, 166802 (2007)CrossRefGoogle Scholar
  105. 105.
    L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J.M. Tour, J. Kono, Nano Lett. (2012). doi:10.1021/nl301496r
  106. 106.
    Z. Sun, Z. Yan, J. Yao, E. Beitler, Y. Zhu, J.M. Tour, Nature 468, 549 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Lei Ren
    • 1
  • Qi Zhang
    • 1
  • Sébastien Nanot
    • 1
  • Iwao Kawayama
    • 2
  • Masayoshi Tonouchi
    • 2
  • Junichiro Kono
    • 1
  1. 1.Department of Electrical & Computer EngineeringRice UniversityHoustonUSA
  2. 2.Institute of Laser EngineeringOsaka UniversityOsakaJapan

Personalised recommendations