Abstract
In this review, we discuss our recent theoretical work on the nonlinear optical response of graphene and its sister structure in terahertz (THz) and near-infrared frequency regime. Due to Dirac-like linear energy-momentum dispersion, the third-order nonlinear current in graphene is much stronger than that in conventional semiconductors. The nonlinear current grows rapidly with increasing temperature and decreasing frequency. The third-order nonlinear current can be as strong as the linear current under moderate electric field strength of 104 V/cm. In bilayer graphene (BLG) with low energy trigonal warping effect, not only the optical response is strongly nonlinear, the optical nonlinearity is well-preserved at elevated temperature. In the presence of a bandgap (such as semihydrogenated graphene (SHG)), there exists two well separated linear response and nonlinear response peaks. This suggests that SHG can have a unique potential as a two-color nonlinear material in the THz frequency regime where the relative intensity of the two colors can be tuned with the electric field. In a graphene superlattice structure of Kronig-Penney type periodic potential, the Dirac cone is elliptically deformed. We found that not only the optical nonlinearity is preserved in such a system, the total optical response is further enhanced by a factor proportional to the band anisotropy. This suggests that graphene superlattice is another potential candidate in THz device application.
Similar content being viewed by others
References
Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A. Two-dimensional gas of massless Dirac fermions in graphene. Nature, 2005, 438(7065): 197–200
Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A. Electric field effect in atomically thin carbon films. Science, 2004, 306(5696): 666–669
Wallace P R. The band theory of graphite. Physical Review, 1947, 71(9): 622–634
Katsnelson M I, Novoselov K S, Geim A K. Chiral tunnelling and the Klein paradox in graphene. Nature Physics, 2006, 2(9): 620–625
Klein O. Die reflexion von elektronen an einem potentialsprung nach der relativistischen dynamik von Dirac. Zeitschrift fur Physik, 1929, 53(3–4): 157–165
Young A F, Kim P. Quantum interference and Klein tunnelling in graphene heterojunctions. Nature Physics, 2009, 5(3): 222–226
Stander N, Huard B, Goldhaber-Gordon D. Evidence for Klein tunneling in graphene p-n junctions. Physical Review Letters, 2009, 102(2): 026807
Wright A R, Cao J C, Zhang C. Enhanced optical conductivity of bilayer graphene nanoribbons in the terahertz regime. Physical Review Letters, 2009, 103(20): 207401
Wang X L, Dou S X, Zhang C. Zero-gap materials for future spintronics, electronics and optics. NPG Asia Materials, 2010, 2(1): 31–38
Liu J, Ma Z, Wright A R, Zhang C. Orbital magnetization of graphene and graphene nanoribbons. Journal of Applied Physics, 2008, 103(10): 103711
Yu D C, Lupton E M, Gao H J, Zhang C, Liu F. A unified geometric rule for designing nanomagnetism in graphene. Nano Research, 2008, 1(6): 497–501
Cai J Z, Lu L, Kong W J, Zhu H W, Zhang C, Wei B Q, Wu D H, Liu F. Pressure-induced transition in magnetoresistance of singlewalled carbon nanotubes. Physical Review Letters, 2006, 97(2): 026402
Bolotin K I, Sikes K J, Jiang Z, Klima M, Fudenberg G, Hone J, Kim P, Stormer H L. Ultrahigh electron mobility in suspended graphene. Solid State Communications, 2008, 146(9–10): 351–355
Chen J H, Jang C, Xiao S, Ishigami M, Fuhrer M S. Intrinsic and extrinsic performance limits of graphene devices on SiO2. Nature Nanotechnology, 2008, 3(4): 206–209
Geim A K, Novoselov K S. The rise of graphene. Nature Materials, 2007, 6(3): 183–191
Xia F, Farmer D B, Lin Y M, Avouris P. Graphene field-effect transistors with high on/off current ratio and large transport band gap at room temperature. Nano Letters, 2010, 10(2): 715–718
Schwierz F. Graphene transistors. Nature Nanotechnology, 2010, 5(7): 487–496
Zhang Y, Tan Y W, Stormer H L, Kim P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature, 2005, 438(7065): 201–204
Gusynin V P, Sharapov S G. Unconventional integer quantum Hall effect in graphene. Physical Review Letters, 2005, 95(14): 146801
Novoselov K S, Jiang Z, Zhang Y, Morozov S V, Stormer H L, Zeitler U, Maan J C, Boebinger G S, Kim P, Geim A K. Roomtemperature quantum Hall effect in graphene. Science, 2007, 315(5817): 1379
Ziegler K. Minimal conductivity of graphene: nonuniversal values from the Kubo formula. Physical Review B: Condensed Matter and Materials Physics, 2007, 75(23): 233407
Herbut I F, Juricic V, Vafek O. Coulomb interaction, ripples, and the minimal conductivity of graphene. Physical Review Letters, 2008, 100(4): 046403
Peres N M R, Guinea F, Castro Neto A H. Electronic properties of disordered two-dimensional carbon. Physical Review B: Condensed Matter and Materials Physics, 2006, 73(12): 125411
Cserti J, Csordás A, Dávid G. Role of the trigonal warping on the minimal conductivity of bilayer graphene. Physical Review Letters, 2007, 99(6): 066802
Martin J, Akerman N, Ulbricht G, Lohmann T, Smet J H, von Klitzing K, Yacoby A. Observation of electron-hole puddles in graphene using a scanning single-electron transistor. Nature Physics, 2008, 4(2): 144–148
Falkovsky L A, Pershoguba S S. Optical far-infrared properties of a graphene monolayer and multilayer. Physical Review B: Condensed Matter and Materials Physics, 2007, 76(15): 153410
Zhang C, Chen L, Ma Z. Orientation dependence of the optical spectra in graphene at high frequencies. Physical Review B, 2008, 77(24): 241402
Gusynin V P, Sharapov S G, Carbotte J P. Unusual microwave response of dirac quasiparticles in graphene. Physical Review Letters, 2006, 96(25): 256802
Nair R R, Blake P, Grigorenko A N, Novoselov K S, Booth T J, Stauber T, Peres NMR, Geim A K. Fine structure constant defines visual transparency of graphene. Science, 2008, 320(5881): 1308
Li Z Q, Henriksen E A, Jiang Z, Hao Z, Martin M C, Kim P, Stormer H L, Basov D N. Dirac charge dynamics in graphene by infrared spectroscopy. Nature Physics, 2008, 4(7): 532–535
Kuzmenko A B, van Heumen E, Carbone F, van der Marel D. Universal optical conductance of graphite. Physical Review Letters, 2008, 100(11): 117401
Rycerz A, TworzydŁo J, Beenakker C W J. Valley filter and valley valve in graphene. Nature Physics, 2007, 3(3): 172–175
Gunlycke D, White C T. Graphene valley filter using a line defect. Physical Review Letters, 2011, 106(13): 136806
Garcia-Pomar J L, Cortijo A, Nieto-Vesperinas M. Fully valleypolarized electron beams in graphene. Physical Review Letters, 2008, 100(23): 236801
Pereira J M Jr, Peeters F M, Costa Filho R N, Farias G A. Valley polarization due to trigonal warping on tunneling electrons in graphene. Journal of Physics Condensed Matter, 2009, 21(4): 045301
Chaves A, Covaci L, Rakhimov K Y, Farias G A, Peeters F M. Wave-packet dynamics and valley filter in strained graphene. Physical Review B: Condensed Matter and Materials Physics, 2010, 82(20): 205430
Moldovan D, Masir M R, Covaci L, Peeters F M. Resonant valley filtering of massive Dirac electrons. Physical Review B: Condensed Matter and Materials Physics, 2012, 86(11): 115431
Zhai F, Chang K. Valley filtering in graphene with a Dirac gap. Physical Review B: Condensed Matter and Materials Physics, 2012, 85(15): 155415
Péterfalvi C G, Oroszlány L, Lambert C J, Cserti J. Intraband electron focusing in bilayer graphene. New Journal of Physics, 2012, 14(6): 063028
Majidi L, Zareyan M. Pseudospin polarized quantum transport in monolayer graphene. Physical Review B: Condensed Matter and Materials Physics, 2011, 83(11): 115422
San-Jose P, Prada E, McCann E, Schomerus H. Pseudospin valve in bilayer graphene: towards graphene-based pseudospintronics. Physical Review Letters, 2009, 102(24): 247204
Trushin M, Schliemann J. Pseudospin in optical and transport properties of graphene. Physical Review Letters, 2011, 107(15): 156801
Min H, Borghi G, Polini M, MacDonald A H. Pseudospin magnetism in graphene. Physical Review B, 2008, 77(4): 041407
Majidi L, Zareyan M. Enhanced Andreev reflection in gapped graphene. Physical Review B: Condensed Matter and Materials Physics, 2012, 86(7): 075443
Brey L, Fertig H A. Electronic states of graphene nanoribbons studied with the Dirac equation. Physical Review B: Condensed Matter and Materials Physics, 2006, 73(23): 235411
Han M Y, Ozyilmaz B, Zhang Y, Kim P. Energy band-gap engineering of graphene nanoribbons. Physical Review Letters, 2007, 98(20): 206805
Ezawa M. Peculiar width dependence of the electronic properties of carbon nanoribbons. Physical Review B: Condensed Matter and Materials Physics, 2006, 73(4): 045432
Park C H, Yang L, Son Y W, Cohen M L, Louie S G. Anisotropic behaviours of massless Dirac fermions in graphene under periodic potentials. Nature Physics, 2008, 4(3): 213–217
Park C H, Yang L, Son Y W, Cohen M L, Louie S G. New generation of massless Dirac fermions in graphene under external periodic potentials. Physical Review Letters, 2008, 101(12): 126804
Park C H, Son Y W, Yang L, Cohen M L, Louie S G. Electron beam supercollimation in graphene superlattices. Nano Letters, 2008, 8(9): 2920–2924
Morozov S V, Novoselov K S, Katsnelson M I, Schedin F, Ponomarenko L A, Jiang D, Geim A K. Strong suppression of weak localization in graphene. Physical Review Letters, 2006, 97(1): 016801
Suzuura H, Ando T. Crossover from symplectic to orthogonal class in a two-dimensional honeycomb lattice. Physical Review Letters, 2002, 89(26): 266603
Khveschenko D V. Electron localization properties in graphene. Physical Review Letters, 2006, 97: 036802
Dragoman D, Dragoman M. Giant thermoelectric effect in graphene. Applied Physics Letters, 2007, 91(20): 203116
Wei P, Bao W, Pu Y, Lau C N, Shi J. Anomalous thermoelectric transport of Dirac particles in graphene. Physical Review Letters, 2009, 102(16): 166808
Balandin A A, Ghosh S, Bao W, Calizo I, Teweldebrhan D, Miao F, Lau C N. Superior thermal conductivity of single-layer graphene. Nano Letters, 2008, 8(3): 902–907
Kane C L, Mele E J. Quantum spin Hall effect in graphene. Physical Review Letters, 2005, 95(22): 226801
Nandkishore R, Levitov L S, Chubukov A V. Chiral superconductivity from repulsive interactions in doped graphene. Nature Physics, 2012, 8(2): 158–163
Sarma S D, Adam S, Hwang E H. Electronic transport in twodimensional graphene. Reviews of Modern Physics, 2011, 83(2): 407–439
Bonaccorso F, Sun Z, Hasan T, Ferrari A C. Graphene photonics and optoelectronics. Nature Photonics, 2010, 4(9): 611–622
Castro Neto A H, Guinea F, Peres N M R, Novoselov K S, Geim A K. The electronic properties of graphene. Reviews of Modern Physics, 2009, 81: 109–162
Beenakker C W J. Colloquium: Andreev reflection and Klein tunneling in graphene. Reviews of Modern Physics, 2008, 80(4): 1337–1354
Hasan M Z, Kane C L. Colloquium: topological insulators. Reviews of Modern Physics, 2010, 82(4): 3045–3067
Fleurence A, Friedlein R, Ozaki T, Kawai H, Wang Y, Yamada-Takamura Y. Experimental evidence for epitaxial silicene on diboride thin films. Physical Review Letters, 2012, 108(24): 245501
Vogt P, De Padova P, Quaresima C, Avila J, Frantzeskakis E, Asensio M C, Resta A, Ealet B, Le Lay G. Silicene: compelling experimental evidence for graphenelike two-dimensional silicon. Physical Review Letters, 2012, 108(15): 155501
Bianco E, Butler S, Jiang S, Restrepo O D, Windl W, Goldberger J E. Stability and exfoliation of germanane: a germanium graphane analogue. ACS Nano, 2013, 7(5): 4414–4421
Xu Y, Yan B, Zhang H J, Wang J, Xu G, Tang P, Duan W, Zhang S C. Large-gap quantum spin Hall insulators in tin films. Physical Review Letters, 2013, 111(13): 136804
Shareef S, Ang Y S, Zhang C. Room-temperature strong terahertz photon mixing in grapheme. Journal of the Optical Society of America. B, Optical Physics, 2012, 29(3): 274–279
Ang Y S, Sultan S, Zhang C. Nonlinear optical spectrum of bilayer graphene in the terahertz regime. Applied Physics Letters, 2010, 97(24): 243110
Ang Y S, Zhang C. Subgap optical conductivity in semihydrogenated graphene. Applied Physics Letters, 2011, 98(4): 042107
Ang Y S, Zhang C. Enhanced optical conductance in graphene superlattice due to anisotropic band dispersion. Journal of Physics. D, Applied Physics, 2012, 45(39): 395303
Siegel P H. Terahertz technology. IEEE Transactions on Microwave Theory and Techniques, 2002, 50(3): 910–928
Hendry E, Hale P J, Moger J, Savchenko A K, Mikhailov S A. Coherent nonlinear optical response of graphene. Physical Review Letters, 2010, 105(9): 097401
Mikhailov S A. Non-linear electromagnetic response of graphene. Europhysics Letters, 2007, 79(2): 27002
Mikhailov S A, Ziegler K. Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects. Journal of Physics Condensed Matter, 2008, 20(38): 384204
Dragoman M, Neculoiu D, Deligeorgis G, Konstantinidis G, Dragoman D, Cismaru A, Muller A A, Plana R. Millimeter-wave generation via frequency multiplication in graphene. Applied Physics Letters, 2010, 97(9): 093101
Wright A R, Xu X G, Cao J C, Zhang C. Strong nonlinear optical response of graphene in the terahertz regime. Applied Physics Letters, 2009, 95(7): 072101
Lim G K, Chen Z L, Clark J, Goh R G S, Ng WH, Tan HW, Friend R H, Ho P K H, Chua L L. Giant broadband nonlinear optical absorption response in dispersed graphene single sheets. Nature Photonics, 2011, 5(9): 554–560
Wang J, Hernandez Y, Lotya M, Coleman J N, Blau W J. Broadband nonlinear optical response of graphene dispersions. Advanced Materials, 2009, 21(23): 2430–2435
Hong S Y, Dadap J I, Petrone N, Yeh P C, Hone J, Osgood R M Jr. Optical third-harmonic generation in graphene. Physical Review X, 2013, 3(2): 021014
Wu S, Mao L, Jones A M, Yao W, Zhang C, Xu X. Quantumenhanced tunable second-order optical nonlinearity in bilayer graphene. Nano Letters, 2012, 12(4): 2032–2036
Ishikawa K L. Nonlinear optical response of graphene in time domain. Physical Review B, 2010, 82(20): 201402
Feynman R P. Forces in molecules. Physical Review, 1939, 56(4): 340–343
Zhang C. Frequency-dependent electrical transport under intense terahertz radiation. Physical Review B: Condensed Matter and Materials Physics, 2002, 66(8): 081105
Ludwig A W W, Fisher M P A, Shankar R, Grinstein G. Integer quantum Hall transition: an alternative approach and exact results. Physical Review B: Condensed Matter and Materials Physics, 1994, 50(11): 7526–7552
Chen C F, Park C H, Boudouris B W, Horng J, Geng B, Girit C, Zettl A, Crommie M F, Segalman R A, Louie S G, Wang F. Controlling inelastic light scattering quantum pathways in graphene. Nature, 2011, 471(7340): 617–620
Gao F, Wang G, Zhang C. Strong photon-mixing of terahertz waves in semiconductor quantum wells induced by Rashba spinorbit coupling. Nanotechnology, 2008, 19(46): 465401
Wolff P A, Pearson G A. Theory of optical mixing by mobile carriers in semiconductors. Physical Review Letters, 1966, 17(19): 1015–1017
Dong H M, Xu W, Tan R B. Temperature relaxation and energy loss of hot carriers in graphene. Solid State Communications, 2010, 150(37–38): 1770–1773
Sun D, Wu Z K, Divin C, Li X, Berger C, de Heer W, First P, Norris T. Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy. Physical Review Letters, 2008, 101(15): 157402
Butscher S, Milde F, Hirtschulz M, Malic E, Knorr A. Hot electron relaxation and phonon dynamics in graphene. Applied Physics Letters, 2007, 91(20): 203103
Bao W S, Liu S Y, Lei X L. Hot-electron transport in graphene driven by intense terahertz fields. Physics Letters. [Part A], 2010, 374(10): 1266–1269
McCann E, Fal’ko V I. Landau-level degeneracy and quantum Hall effect in a graphite bilayer. Physical Review Letters, 2006, 96(8): 086805
Koshino M, Ando T. Transport in bilayer graphene: calculations within a self-consistent Born approximation. Physical Review B: Condensed Matter and Materials Physics, 2006, 73(24): 245403
McCann C, Abergel D S L, Fal’ko V I. Electrons in bilayer graphene. Solid State Communications, 2007, 143(-2): 110–115
Chen L, Ma Z, Zhang C. Vertical absorption edge and temperature dependent resistivity in semihydrogenated graphene. Applied Physics Letters, 2010, 96(2): 023107
Edwards W F. Special relativity in anisotropic space. American Journal of Physics, 1963, 31(7): 482–489
Moon C Y, Han J, Lee H, Choi H J. Low-velocity anisotropic Dirac fermions on the side surface of topological insulators. Physical Review B: Condensed Matter and Materials Physics, 2011, 84(19): 195425
Park J, Lee G, Wolff-Fabris F, Koh Y Y, Eom M J, Kim Y K, Farhan M A, Jo Y J, Kim C, Shim J H, Kim J S. Anisotropic Dirac fermions in a Bi square net of SrMnBi2. Physical Review Letters, 2011, 107(12): 126402
Wang J, Hernandez Y, Lotya M, Coleman J N, Blau W J. Broadband nonlinear optical response of graphene dispersions. Advanced Materials, 2009, 21(23): 2430–2435
Lim G K, Chen Z L, Clark J, Goh R G S, Ng WH, Tan HW, Friend R H, Ho P K H, Chua L L. Giant broadband nonlinear optical absorption response in dispersed graphene single sheets. Nature photonics, 2011, 5(9): 554–560
Hwang E H, Das Sarma S. Acoustic phonon scattering limited carrier mobility in two-dimensional extrinsic graphene. Physical Review B: Condensed Matter and Materials Physics, 2008, 77(11): 115449
Song J C, Reizer M Y, Levitov L S. Disorder-assisted electronphonon scattering and cooling pathways in graphene. Physical Review Letters, 2012, 109(10): 106602
Betz A C, Jhang S H, Pallecchi E, Ferreira R, Feve G, Berroir J M, Placais B. Supercollision cooling in undoped graphene. Nature Physics, 2012, 9(2): 109–112
Graham M W, Shi S F, Ralph D C, Park J, McEuen P L. Photocurrent measurements of supercollision cooling in graphene. Nature Physics, 2012, 9(2): 103–108
Xu X G, Cao J C. Nonlinear response induced strong absorptance of graphene in the terahertz regime. Modern Physics Letters B, 2010, 24(21): 2243–2249
Weiss D, Zhang C, Gerhardts R R, Klitzing K, Weimann G. Density of states in a two-dimensional electron gas in the presence of a one-dimensional superlattice potential. Physical Review B: Condensed Matter and Materials Physics, 1989, 39(17): 13020–13023
Author information
Authors and Affiliations
Corresponding author
Additional information
Yee Sin Ang was born in Johor Bahru, Malaysia in 1987. He graduated from the University of Wollongong, Australia, with a Bachelor degree in medical and radiation physics (honors) in 2010. He is currently a PhD candidate (theoretical condensed matter physics) at the University of Wollongong. His research interests include nonlinear optical response and transport properties of graphene and other low dimensional nanostructures.
Qinjun Chen is a PhD student of School of Physics and ISEM, at the University of Wollongong, Australia. He obtained his Bachelor degree from Jiangsu University in 2008 majoring in inorganic non-metal materials. He became a master student of South China University of Technology working in Professor Qinyuan Zhang’s group, where he carried out experimental research on rare earth ions doped laser glasses, such as Ho3+ and Tm3+ doped glass ceramics. He completed his master’s degree in material science and engineering in 2011. Later in July 2011, he joined in Professor Chao Zhang’s group in the University of Wollongong to pursuit his PhD degree. His PhD research on theoretical modeling of transport properties of topological insulator, particularly HgTe quantum well (QW) which is known as the first 2 dimensional topological insulator. He investigated the nonlinear response and photo-mixing effect in HgTe QW topological insulators.
Chao Zhang received his MPhil and PhD degree from City University of New York in 1985 and 1987. He was a postdoctoral fellow at Max-Planck-Institute for Solid State Research in Stuttgart, Germany from 1987 to 1989. He was a research associate at TRIUMF in Vancouver Canada from 1989 to 1992. Since 1993, he has been a faculty member of the School of Physics, University of Wollongong, Australia. Currently he is a professor of physics and group leader in terahertz research. He is a fellow of Australian Institute of Physics. His research interest includes terahertz optoelectronics, nonlinear optical properties of semiconductors and graphene, electronic properties of low dimensional semiconductors with spin-orbit coupling, and thermionics in nanomaterials and nanosystems.
Rights and permissions
About this article
Cite this article
Ang, Y.S., Chen, Q. & Zhang, C. Nonlinear optical response of graphene in terahertz and near-infrared frequency regime. Front. Optoelectron. 8, 3–26 (2015). https://doi.org/10.1007/s12200-014-0428-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12200-014-0428-0