• Frontiers of Optoelectronics
  • Vol. 8, Issue 1, 1 (2015)
Yee Sin ANG1, Qinjun CHEN1、2, and Chao ZHANG1、2、*
Author Affiliations
  • 1School of Physics, University of Wollongong, New South Wales 2522, Australia
  • 2Institute of Superconducting and Electronic Materials, University of Wollongong, New South Wales 2522, Australia
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    DOI: 10.1007/s12200-014-0428-0 Cite this Article
    Yee Sin ANG, Qinjun CHEN, Chao ZHANG. Nonlinear optical response of graphene in terahertz and near-infrared frequency regime[J]. Frontiers of Optoelectronics, 2015, 8(1): 1 Copy Citation Text show less
    References

    [1] 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

    [2] 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

    [3] Wallace P R. The band theory of graphite. Physical Review, 1947, 71(9): 622–634

    [4] Katsnelson M I, Novoselov K S, Geim A K. Chiral tunnelling and the Klein paradox in graphene. Nature Physics, 2006, 2(9): 620–625

    [5] Klein O. Die reflexion von elektronen an einem potentialsprung nach der relativistischen dynamik von Dirac. Zeitschrift fur Physik, 1929, 53(3–4): 157–165

    [6] Young A F, Kim P. Quantum interference and Klein tunnelling in graphene heterojunctions. Nature Physics, 2009, 5(3): 222–226

    [7] Stander N, Huard B, Goldhaber-Gordon D. Evidence for Klein tunneling in graphene p-n junctions. Physical Review Letters, 2009, 102(2): 026807

    [8] 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

    [9] 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

    [10] Liu J, Ma Z, Wright A R, Zhang C. Orbital magnetization of graphene and graphene nanoribbons. Journal of Applied Physics, 2008, 103(10): 103711

    [11] 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

    [12] 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

    [13] 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

    [14] 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

    [15] Geim A K, Novoselov K S. The rise of graphene. Nature Materials, 2007, 6(3): 183–191

    [16] 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

    [17] Schwierz F. Graphene transistors. Nature Nanotechnology, 2010, 5(7): 487–496

    [18] 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

    [19] Gusynin V P, Sharapov S G. Unconventional integer quantum Hall effect in graphene. Physical Review Letters, 2005, 95(14): 146801

    [20] 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

    [21] Ziegler K. Minimal conductivity of graphene: nonuniversal values from the Kubo formula. Physical Review B: Condensed Matter and Materials Physics, 2007, 75(23): 233407

    [22] Herbut I F, Juricic V, Vafek O. Coulomb interaction, ripples, and the minimal conductivity of graphene. Physical Review Letters, 2008, 100(4): 046403

    [23] 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

    [24] 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

    [25] 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

    [26] 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

    [27] Zhang C, Chen L, Ma Z. Orientation dependence of the optical spectra in graphene at high frequencies. Physical Review B, 2008, 77(24): 241402

    [28] Gusynin V P, Sharapov S G, Carbotte J P. Unusual microwave response of dirac quasiparticles in graphene. Physical Review Letters, 2006, 96(25): 256802

    [29] 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

    [30] 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

    [31] Kuzmenko A B, van Heumen E, Carbone F, van der Marel D. Universal optical conductance of graphite. Physical Review Letters, 2008, 100(11): 117401

    [32] Rycerz A, Tworzydlo J, Beenakker C W J. Valley filter and valley valve in graphene. Nature Physics, 2007, 3(3): 172–175

    [33] Gunlycke D, White C T. Graphene valley filter using a line defect. Physical Review Letters, 2011, 106(13): 136806

    [34] Garcia-Pomar J L, Cortijo A, Nieto-Vesperinas M. Fully valleypolarized electron beams in graphene. Physical Review Letters, 2008, 100(23): 236801

    [35] 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

    [36] 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

    [37] 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

    [38] Zhai F, Chang K. Valley filtering in graphene with a Dirac gap. Physical Review B: Condensed Matter and Materials Physics, 2012, 85(15): 155415

    [39] Péterfalvi C G, Oroszlány L, Lambert C J, Cserti J. Intraband electron focusing in bilayer graphene. New Journal of Physics, 2012, 14(6): 063028

    [40] Majidi L, Zareyan M. Pseudospin polarized quantum transport in monolayer graphene. Physical Review B: Condensed Matter and Materials Physics, 2011, 83(11): 115422

    [41] 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

    [42] Trushin M, Schliemann J. Pseudospin in optical and transport properties of graphene. Physical Review Letters, 2011, 107(15): 156801

    [43] Min H, Borghi G, Polini M, MacDonald A H. Pseudospin magnetism in graphene. Physical Review B, 2008, 77(4): 041407

    [44] Majidi L, Zareyan M. Enhanced Andreev reflection in gapped graphene. Physical Review B: Condensed Matter and Materials Physics, 2012, 86(7): 075443

    [45] 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

    [46] Han M Y, Ozyilmaz B, Zhang Y, Kim P. Energy band-gap engineering of graphene nanoribbons. Physical Review Letters, 2007, 98(20): 206805

    [47] Ezawa M. Peculiar width dependence of the electronic properties of carbon nanoribbons. Physical Review B: Condensed Matter and Materials Physics, 2006, 73(4): 045432

    [48] 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

    [49] 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

    [50] 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

    [51] 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

    [52] Suzuura H, Ando T. Crossover from symplectic to orthogonal class in a two-dimensional honeycomb lattice. Physical Review Letters, 2002, 89(26): 266603

    [53] Khveschenko D V. Electron localization properties in graphene. Physical Review Letters, 2006, 97: 036802

    [54] Dragoman D, Dragoman M. Giant thermoelectric effect in graphene. Applied Physics Letters, 2007, 91(20): 203116

    [55] 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

    [56] 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

    [57] Kane C L, Mele E J. Quantum spin Hall effect in graphene. Physical Review Letters, 2005, 95(22): 226801

    [58] Nandkishore R, Levitov L S, Chubukov A V. Chiral superconductivity from repulsive interactions in doped graphene. Nature Physics, 2012, 8(2): 158–163

    [59] Sarma S D, Adam S, Hwang E H. Electronic transport in twodimensional graphene. Reviews of Modern Physics, 2011, 83(2): 407–439

    [60] Bonaccorso F, Sun Z, Hasan T, Ferrari A C. Graphene photonics and optoelectronics. Nature Photonics, 2010, 4(9): 611–622

    [61] 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

    [62] Beenakker C W J. Colloquium: Andreev reflection and Klein tunneling in graphene. Reviews of Modern Physics, 2008, 80(4): 1337–1354

    [63] Hasan M Z, Kane C L. Colloquium: topological insulators. Reviews of Modern Physics, 2010, 82(4): 3045–3067

    [64] 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

    [65] 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

    [66] 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

    [67] 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

    [68] Shareef S, Ang Y S, Zhang C. Room-temperature strong terahertz photon mixing in graphene. Journal of the Optical Society of America. B, Optical Physics, 2012, 29(3): 274–279

    [69] Ang Y S, Sultan S, Zhang C. Nonlinear optical spectrum of bilayer graphene in the terahertz regime. Applied Physics Letters, 2010, 97(24): 243110

    [70] Ang Y S, Zhang C. Subgap optical conductivity in semihydrogenated graphene. Applied Physics Letters, 2011, 98(4): 042107

    [71] 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

    [72] Siegel P H. Terahertz technology. IEEE Transactions on Microwave Theory and Techniques, 2002, 50(3): 910–928

    [73] 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

    [74] Mikhailov S A. Non-linear electromagnetic response of graphene. Europhysics Letters, 2007, 79(2): 27002

    [75] 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

    [76] 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

    [77] 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

    [78] Lim G K, Chen Z L, Clark J, Goh R G S, NgWH, 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

    [79] 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

    [80] 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

    [81] 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

    [82] Ishikawa K L. Nonlinear optical response of graphene in time domain. Physical Review B, 2010, 82(20): 201402

    [83] Feynman R P. Forces in molecules. Physical Review, 1939, 56(4): 340–343

    [84] Zhang C. Frequency-dependent electrical transport under intense terahertz radiation. Physical Review B: Condensed Matter and Materials Physics, 2002, 66(8): 081105

    [85] 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

    [86] 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

    [87] 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

    [88] Wolff P A, Pearson G A. Theory of optical mixing by mobile carriers in semiconductors. Physical Review Letters, 1966, 17(19): 1015–1017

    [89] 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

    [90] 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

    [91] 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

    [92] 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

    [93] McCann E, Fal’ko V I. Landau-level degeneracy and quantum Hall effect in a graphite bilayer. Physical Review Letters, 2006, 96(8): 086805

    [94] 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

    [95] McCann C, Abergel D S L, Fal’ko V I. Electrons in bilayer graphene. Solid State Communications, 2007, 143(–2): 110–115

    [96] Chen L, Ma Z, Zhang C. Vertical absorption edge and temperature dependent resistivity in semihydrogenated graphene. Applied Physics Letters, 2010, 96(2): 023107

    [97] Edwards W F. Special relativity in anisotropic space. American Journal of Physics, 1963, 31(7): 482–489

    [98] 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

    [99] 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

    [100] 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

    [101] Lim G K, Chen Z L, Clark J, Goh R G S, NgWH, 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

    [102] 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

    [103] 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

    [104] 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

    [105] 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

    [106] 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

    [107] 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

    Yee Sin ANG, Qinjun CHEN, Chao ZHANG. Nonlinear optical response of graphene in terahertz and near-infrared frequency regime[J]. Frontiers of Optoelectronics, 2015, 8(1): 1
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