Terahertz Graphene Optics
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The magnitude of the optical sheet conductance of single-layer graphene is universal, and equal to e2/4ħ (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 ~e2/h and 100 e2/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.
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Terahertz Graphene Optics
)
Abstract
The magnitude of the optical sheet conductance of single-layer graphene is universal, and equal to e2/4ħ (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 ~e2/h and 100 e2/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.
References(48)
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.
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.
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.
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.
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.
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.
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.
Kuzmenko, A. B.; van Heumen, E.; Carbone, F.; van der Marel, D. Universal optical conductance of graphite. Phys. Rev. Lett. 2008, 100, 117401.
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.
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.
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.
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.
Krupka, J.; Strupinski, W. Measurements of the sheet resistance and conductivity of thin epitaxial graphene and SiC films. Appl. Phys. Lett. 2010, 96, 082101.
Krupka, J.; Strupinski, W.; Kwietniewski, N. Microwave conductivity of very thin graphene and metal films. J. Nanosci. Nanotechnol. 2011, 11, 3358-3362.
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.
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.
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.
Rana, F. Graphene terahertz plasmon oscillators. IEEE T. Nanotechnol. 2008, 7, 91-99.
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.
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.
Kang, S.; Burke, P.; Pfeiffer, L.; West, K. Resonant frequency response of plasma wave detectors. Appl. Phys. Lett. 2006, 89, 213512.
Dragoman, M.; Muller, A.; Dragoman, D.; Coccetti, F.; Plana, R. Terahertz antenna based on graphene. J. Appl. Phys. 2010, 107, 104313.
Burke, P. J.; Li, S. D.; Yu, Z. Quantitative theory of nanowire and nanotube antenna performance. arXiv: cond-mat/0408418v1 2004.
Burke, P. J.; Li, S. D.; Yu, Z. Quantitative theory of nanowire and nanotube antenna performance. IEEE T. Nanotechnol. 2006, 5, 314-334.
Hanson, G. W. Fundamental transmitting properties of carbon nanotube antennas. IEEE T. Antenn. Propag. 2005, 53, 3426-3435.
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.
Russer, P.; Fichtner, N.; Lugli, P.; Porod, W.; Russer, J. A.; Yordanov, H. Nanoelectronics-based integrated antennas. IEEE Microw. Mag. 2010, 11, 58-71.
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.
Falkovsky, L. A. Optical properties of graphene and IV-VI semiconductors. Phys. -Usp. 2008, 51, 887-897.
Gusynin, V.; Sharapov, S.; Carbotte, J. On the universal ac optical background in graphene. New J. Phys. 2009, 11, 095013.
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.
Lenski, D. R.; Fuhrer, M. S. Raman and optical characterization of multilayer turbostratic graphene grown via chemical vapor deposition. J. Appl. Phys. 2011, 110, 013720.
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.
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.
Ceremuga-Mazierska, J. Transmission of microwave signals through superconducting thin films in waveguides. Supercond. Sci. Tech. 1992, 5, 391.
Balanis, C. A. Advanced engineering electromagnetics; Wiley: New York, 1989.
Rugheimer, N.; Lehoczky, A.; Briscoe, C. Microwave transmission-and reflection-coefficient ratios of thin superconducting films. Phys. Rev. 1967, 154, 414-421.
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.
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.
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.
Glover, R. E.; Tinkham, M. Conductivity of superconducting films for photon energies between 0.3 and 40 kTc. Phys. Rev. 1957, 108, 243-256.
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.
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.
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.
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.
Koppens, F. H. L.; Chang, D. E.; Garciía de Abajo, F. J. Graphene plasmonics: A platform for strong light-matter interactions. Nano Lett. 2011, 11, 3370-3377.
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.
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.
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Acknowledgements
This work was funded by the Army Research Office (MURI W911NF-11-1-0024, ARO W911NF-09-1-0319, and DURIP W911NF-11-1-0315) and by Ministerio de Educación y Ciencia (FPU and Consolider CSD2008- 0068).
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