Skip to main content
Log in

Terahertz graphene optics

  • Research Article
  • Published:
Nano Research Aims and scope Submit manuscript

Abstract

The magnitude of the optical sheet conductance of single-layer graphene is universal, and equal to e 2/4ħ (where 2πħ = h (the Planck constant)). As the optical frequency decreases, the conductivity decreases. However, at some frequency in the THz range, the conductivity increases again, eventually reaching the DC value, where the magnitude of the DC sheet conductance generally displays a sample- and doping-dependent value between ∼e 2/h and 100 e 2/h. Thus, the THz range is predicted to be a non-trivial region of the spectrum for electron transport in graphene, and may have interesting technological applications. In this paper, we present the first frequency domain measurements of the absolute value of multilayer graphene (MLG) and single-layer graphene (SLG) sheet conductivity and transparency from DC to 1 THz, and establish a firm foundation for future THz applications of graphene.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Nair, R. R.; Blake, P.; Grigorenko, A. N.; Novoselov, K. S.; Booth, T. J.; Stauber, T.; Peres, N. M. R.; Geim, A. K. Fine structure constant defines visual transparency of graphene. Science 2008, 320, 1308.

    Article  CAS  Google Scholar 

  2. Li, Z.; Henriksen, E.; Jiang, Z.; Hao, Z.; Martin, M.; Kim, P.; Stormer, H.; Basov, D. Dirac charge dynamics in graphene by infrared spectroscopy. Nat. Phys. 2008, 4, 532–535.

    Article  CAS  Google Scholar 

  3. Horng, J.; Chen, C. F.; Geng, B.; Girit, C.; Zhang, Y.; Hao, Z.; Bechtel, H. A.; Martin, M.; Zettl, A.; Crommie, M. F. Drude conductivity of Dirac fermions in graphene. Phys. Rev. B 2011, 83, 165113.

    Article  Google Scholar 

  4. Ju, L.; Geng, B.; Horng, J.; Girit, C.; Martin, M.; Hao, Z.; Bechtel, H. A.; Liang, X.; Zettl, A.; Shen, Y. R., et al. Graphene plasmonics for tunable terahertz metamaterials. Nat. Nanotechnol. 2011, 6, 630–634.

    Article  CAS  Google Scholar 

  5. Yan, H.; Xia, F.; Zhu, W.; Freitag, M.; Dimitrakopoulos, C.; Bol, A. A.; Tulevski, G.; Avouris, P. Infrared spectroscopy of wafer-scale graphene. ACS Nano 2011, 5, 9854–9860.

    Article  CAS  Google Scholar 

  6. Tomaino, J. L.; Jameson, A. D.; Kevek, J. W.; Paul, M. J.; van der Zande, A. M.; Barton, R. A.; McEuen, P. L.; Minot, E. D.; Lee, Y. -S. Terahertz imaging and spectroscopy of large-area single-layer graphene. Opt. Express 2011, 19, 141–146.

    Article  CAS  Google Scholar 

  7. Liu, W.; Aguilar, R. V.; Hao, Y. F.; Ruoff, R. S.; Armitage, N. P. Broadband microwave and time-domain terahertz spectroscopy of chemical vapor deposition grown graphene. J. Appl. Phys. 2011, 110, 083510.

    Google Scholar 

  8. Kuzmenko, A. B.; van Heumen, E.; Carbone, F.; van der Marel, D. Universal optical conductance of graphite. Phys. Rev. Lett. 2008, 100, 117401.

    Article  CAS  Google Scholar 

  9. Mak, K. F.; Sfeir, M. Y.; Misewich, J. A.; Heinz, T. F. The evolution of electronic structure in few-layer graphene revealed by optical spectroscopy. P. Natl. Acad. Sci. USA 2010, 107, 14999–15004.

    Article  Google Scholar 

  10. Dawlaty, J. M.; Shivaraman, S.; Strait, J.; George, P.; Chandrashekhar, M.; Rana, F.; Spencer, M. G.; Veksler, D.; Chen, Y. Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible. Appl. Phys. Lett. 2008, 93, 131905.

    Article  Google Scholar 

  11. Choi, H.; Borondics, F.; Siegel, D. A.; Zhou, S. Y.; Martin, M. C.; Lanzara, A.; Kaindl, R. A. Broadband electromagnetic response and ultrafast dynamics of few-layer epitaxial graphene. Appl. Phys. Lett. 2009, 94, 172102.

    Article  Google Scholar 

  12. Kim, J. Y.; Lee, C.; Bae, S.; Kim, K. S.; Hong, B. H.; Choi, E. Far-infrared study of substrate-effect on large scale graphene. Appl. Phys. Lett. 2011, 98, 201907.

    Article  Google Scholar 

  13. Krupka, J.; Strupinski, W. Measurements of the sheet resistance and conductivity of thin epitaxial graphene and SiC films. Appl. Phys. Lett. 2010, 96, 082101.

    Article  Google Scholar 

  14. Krupka, J.; Strupinski, W.; Kwietniewski, N. Microwave conductivity of very thin graphene and metal films. J. Nanosci. Nanotechnol. 2011, 11, 3358–3362.

    Article  CAS  Google Scholar 

  15. Skulason, H.; Nguyen, H.; Guermoune, A.; Sridharan, V.; Siaj, M.; Caloz, C.; Szkopek, T. 110 GHz measurement of large-area graphene integrated in low-loss microwave structures. Appl. Phys. Lett. 2011, 99, 153504.

    Article  Google Scholar 

  16. Kundhikanjana, W.; Lai, K.; Wang, H.; Dai, H.; Kelly, M. A.; Shen, Z. Hierarchy of electronic properties of chemically derived and pristine graphene probed by microwave imaging. Nano Lett. 2009, 9, 3762–3765.

    Article  CAS  Google Scholar 

  17. Talanov, V. V.; Barga, C. D.; Wickey, L.; Kalichava, I.; Gonzales, E.; Shaner, E. A.; Gin, A. V.; Kalugin, N. G. Few-layer graphene characterization by near-field scanning microwave microscopy. ACS Nano 2010, 4, 3831–3838.

    Article  CAS  Google Scholar 

  18. Rana, F. Graphene terahertz plasmon oscillators. IEEE T. Nanotechnol. 2008, 7, 91–99.

    Article  Google Scholar 

  19. Burke, P. J.; Spielman, I. B.; Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W. High frequency conductivity of the high-mobility two-dimensional electron gas. Appl. Phys. Lett. 2000, 76, 745–747.

    Article  CAS  Google Scholar 

  20. Allen, S. J.; Tsui, D. C.; Logan, R. A. Observation of 2-dimensional plasmon in silicon inversion layers. Phys. Rev. Lett. 1977, 38, 980–983.

    Article  CAS  Google Scholar 

  21. Kang, S.; Burke, P.; Pfeiffer, L.; West, K. Resonant frequency response of plasma wave detectors. Appl. Phys. Lett. 2006, 89, 213512.

    Article  Google Scholar 

  22. Dragoman, M.; Muller, A.; Dragoman, D.; Coccetti, F.; Plana, R. Terahertz antenna based on graphene. J. Appl. Phys. 2010, 107, 104313.

    Article  Google Scholar 

  23. Burke, P. J.; Li, S. D.; Yu, Z. Quantitative theory of nanowire and nanotube antenna performance. arXiv: cond- mat/0408418v1 2004.

  24. Burke, P. J.; Li, S. D.; Yu, Z. Quantitative theory of nanowire and nanotube antenna performance. IEEE T. Nanotechnol. 2006, 5, 314–334.

    Article  Google Scholar 

  25. Hanson, G. W. Fundamental transmitting properties of carbon nanotube antennas. IEEE T. Antenn. Propag. 2005, 53, 3426–3435.

    Article  Google Scholar 

  26. Slepyan, G. Y.; Shuba, M. V.; Maksimenko, S. A.; Lakhtakia, A. Theory of optical scattering by achiral carbon nanotubes and their potential as optical nanoantennas. Phys. Rev. B 2006, 73, 195416.

    Article  Google Scholar 

  27. Russer, P.; Fichtner, N.; Lugli, P.; Porod, W.; Russer, J. A.; Yordanov, H. Nanoelectronics-based integrated antennas. IEEE Microw. Mag. 2010, 11, 58–71.

    Article  Google Scholar 

  28. Shuba, M. V.; Paddubskaya, A. G.; Plyushch, A. O.; Kuzhir, P. P.; Slepyan, G. Y.; Maksimenko, S. A.; Ksenevich, V. K.; Buka, P.; Seliuta, D.; Kasalynas, I., et al. Experimental evidence of localized plasmon resonance in composite materials containing single-wall carbon nanotubes. Phys. Rev. B 2012, 85, 165435.

    Article  Google Scholar 

  29. Falkovsky, L. A. Optical properties of graphene and IV–VI semiconductors. Phys.-Usp. 2008, 51, 887–897

    Article  CAS  Google Scholar 

  30. Gusynin, V.; Sharapov, S.; Carbotte, J. On the universal ac optical background in graphene. New J. Phys. 2009, 11, 095013.

    Google Scholar 

  31. Li, X.; Cai, W.; An, J.; Kim, S.; Nah, J.; Yang, D.; Piner, R.; Velamakanni, A.; Jung, I.; Tutuc, E., et al. Large-area synthesis of high-quality and uniform graphene films on copper foils. Science 2009, 324, 1312–1314.

    Article  CAS  Google Scholar 

  32. Lenski, D. R.; Fuhrer, M. S. Raman and optical charac- terization of multilayer turbostratic graphene grown via chemical vapor deposition. J. Appl. Phys. 2011, 110, 013720.

    Google Scholar 

  33. Li, X.; Zhu, Y.; Cai, W.; Borysiak, M.; Han, B.; Chen, D.; Piner, R. D.; Colombo, L.; Ruoff, R. S. Transfer of large-area graphene films for high-performance transparent conductive electrodes. Nano Lett. 2009, 9, 4359–4363.

    Article  CAS  Google Scholar 

  34. Barroso, J. J.; Castro, P. J.; Leite Neto, J. P. Electrical conductivity measurement through the loaded Q factor of a resonant cavity. Int. J. Infrared Milli. 2003, 24, 79–86.

    Article  CAS  Google Scholar 

  35. Ceremuga-Mazierska, J. Transmission of microwave signals through superconducting thin films in waveguides. Supercond. Sci. Tech. 1992, 5, 391.

    Article  CAS  Google Scholar 

  36. Balanis, C. A. Advanced engineering electromagnetics; Wiley: New York, 1989.

    Google Scholar 

  37. Rugheimer, N.; Lehoczky, A.; Briscoe, C. Microwave transmission-and reflection-coefficient ratios of thin superconducting films. Phys. Rev. 1967, 154, 414–421.

    Article  CAS  Google Scholar 

  38. Brown, E. R.; Bjarnason, J.; Chan, T. L. J.; Driscoll, D. C.; Hanson, M.; Gossard, A. C. Room temperature, THz photomixing sweep oscillator and its application to spectroscopic transmission through organic materials. Rev. Sci. Instrum. 2004, 75, 5333–5342.

    Article  CAS  Google Scholar 

  39. Demers, J. R.; Logan, R. T.; Bergeron, N. J.; Brown, E. R. A high signal-to-noise ratio, coherent, frequency-domain THz spectrometer employed to characterize explosive compounds. In 33rd International Conference on Infrared, Millimeter and Terahertz Waves, IRMMW-THz, California, USA, 2008, pp. 1–3.

  40. Brown, E.; Mendoza, E. A.; Xia, D.; Brueck, S. Narrow THz spectral signatures through an RNA solution in nanofluidic channels. IEEE Sens. J. 2010, 10, 755–759.

    Article  CAS  Google Scholar 

  41. Glover, R. E.; Tinkham, M. Conductivity of superconducting films for photon energies between 0.3 and 40 kT c. Phys. Rev. 1957, 108, 243–256.

    Article  CAS  Google Scholar 

  42. Abedinpour, S. H.; Vignale, G.; Principi, A.; Polini, M.; Tse, W. K.; MacDonald, A. Drude weight, plasmon dispersion, and ac conductivity in doped graphene sheets. Phys. Rev. B 2011, 84, 045429.

    Google Scholar 

  43. Tan, Y. W.; Zhang, Y.; Bolotin, K.; Zhao, Y.; Adam, S.; Hwang, E.; Das Sarma, S.; Stormer, H.; Kim, P. Measurement of scattering rate and minimum conductivity in graphene. Phys. Rev. Lett. 2007, 99, 246803.

    Article  Google Scholar 

  44. Chen, J.; Jang, C.; Xiao, S.; Ishigami, M.; Fuhrer, M. Intrinsic and extrinsic performance limits of graphene devices on SiO2. Nat. Nanotechnol. 2008, 3, 206–209.

    Article  CAS  Google Scholar 

  45. Shen, T.; Wu, W.; Yu, Q.; Richter, C. A.; Elmquist, R.; Newell, D.; Chen, Y. P. Quantum Hall effect on centimeter scale chemical vapor deposited graphene films. Appl. Phys. Lett. 2011, 99, 232110.

    Article  Google Scholar 

  46. Koppens, F. H. L.; Chang, D. E.; García de Abajo, F. J. Graphene plasmonics: A platform for strong light-matter interactions. Nano Lett. 2011, 11, 3370–3377.

    Article  CAS  Google Scholar 

  47. Sensale-Rodriguez, B.; Yan, R.; Kelly, M. M.; Fang, T.; Tahy, K.; Hwang, W. S.; Jena, D.; Liu, L.; Xing, H. G. Broadband graphene terahertz modulators enabled by intraband transitions. Nat. Commun. 2012, 3: 780.

    Article  Google Scholar 

  48. Sensale-Rodriguez, B.; Yan, R.; Rafique, S.; Zhu, M.; Li, W.; Liang, X. L.; Gundlach, D.; Protasenko, V.; Kelly, M. M.; Jena, D.; Liu, L.; Xing, H. G. Extraordinary Control of Terahertz Beam Reflectance in Graphene Electro-absorption Modulators. Nano Lett. 2012, 9: 4518–4522

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Peter Burke.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rouhi, N., Capdevila, S., Jain, D. et al. Terahertz graphene optics. Nano Res. 5, 667–678 (2012). https://doi.org/10.1007/s12274-012-0251-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12274-012-0251-0

Keywords

Navigation