Temperature-dependent of Nonlinear Optical Conductance of Graphene-based Systems in High-intensity Terahertz Field
Corresponding Author: Hui Yan
Nano-Micro Letters,
Vol. 6 No. 2 (2014), Article Number: 153-162
Abstract
For multi-photon processed with the linear dispersion in the high-intensity terahertz (THz) field, we have systematically investigated the temperature-dependent nonlinear optical response of graphene-based systems, including single layer graphene, graphene superlattice and gapped graphene. In the intrinsic single layer graphene system, it demonstrates that, at low temperature, nonlinear optical conductivities of the thirdand fifth-order are respectively five and ten orders of magnitude larger than the universal conductivity with high-intensity and low frequency THz wave.In the graphene superlattice and gapped graphene systems, the optical responses enhanced because of the anisotropic massless and massive Dirac fermions.
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- K. Geim, and K. S. Novoselov, “The rise of graphene”, Nat. Mater. 6, 183–191 (2007). http://dx.doi.org/10.1038/nmat1849
- M. I. Katsnelson, “Graphene: carbon in two dimensions”, Mater. Today 10(1–2), 20–27 (2007). http://dx.doi.org/10.1016/S1369-7021(06)71788-6
- K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene”, Nature 438, 197–200 (2005). http://dx.doi.org/10.1038/nature04233
- Y. Zhang, Y. W. Tan, H. L. Stormer and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene”, Nature 438, 201–204 (2005). http://dx.doi.org/10.1038/nature04235
- C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Konrad, P. N. First and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene”, Science 312(5777), 1191–1196 (2006). http://dx.doi.org/10.1126/science.1125925
- H. Suzuura and T. Ando, “Crossover from symplectic to orthogonal class in a two-dimensional honeycomb lattice”, Phys. Rev. Lett. 89(26), 266603 (2002). http://dx.doi.org/10.1103/PhysRevLett.89.266603
- S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, L. A. Ponomarenko, D. Jiang, and A. K. Geim, “Strong suppression of weak localization in graphene”, Phys. Rev. Lett. 97(01), 016801 (2006). http://dx.doi.org/10.1103/PhysRevLett.97.016801
- D. V. Khveshchenko, “Electron localization properties in graphene”, Phys. Rev. Lett. 97(03), 036802 (2006). http://dx.doi.org/10.1103/PhysRevLett. 97.036802
- R. S. Deacon, K.-C. Chuang, R. J. Nicholas, K. S. Novoselov and A. K. Geim, “Cyclotron resonance study of the electron and hole velocity in graphene monolayers”, Phys. Rev. B 76(08), 081406(R) (2007). http://dx.doi.org/10.1103/PhysRevB.76.081406
- Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim and H. L. Stormer, “Infrared spectroscopy of landau levels of graphene”, Phys. Rev. Lett. 98(19), 197403 (2007). http://dx.doi.org/10.1103/PhysRevLett.98.197403
- R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres and A. K. Geim, “Fine structure constant defines visual transparency of graphene”, Science 320(5881), 1308–1308 (2008). http://dx.doi.org/10.1126/science.1156965
- E. A. Henriksen, Z. Jiang, L. C. Tung, M. E. Schwartz, M. Takita, Y.-J. Wang, P. Kim and H. L. Stormer, “Cyclotron resonance in bilayer graphene”, Phys. Rev. Lett. 100(08), 087403 (2008). http://dx.doi.org/10.1103/PhysRevLett.100.087403
- Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy”, Nature Physics 4, 532–535 (2008). http://dx.doi.org/10.1038/nphys989
- K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich and T. F. Heinz, “Measurement of the optical conductivity of graphene”, Phys. Rev. Lett. 101(19), 196405 (2008). http://dx.doi.org/10.1103/PhysRevLett.101.196405
- E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko and S. A. Mikhailov, “Coherent nonlinear optical response of graphene”, Phys. Rev. Lett. 105, 097401 (2010). http://dx.doi.org/10.1103/PhysRevLett.105.097401
- S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider and M. Helm, “Carrier relaxation in epitaxial graphene photoexcited near the dirac point”, Phys. Rev. Lett. 107(23), 237401 (2011). http://dx.doi.org/10.1103/PhysRevLett.107.237401
- Michael Woerner, Wilhelm Kuehn, Pamela Bowlan, Klaus Reimann and Thomas Elsaesser, “Ultrafast two-dimensional terahertz spectroscopy of elementary excitations in solids”, New J. Phys. 15, 025039 (2013). http://dx.doi.org/10.1088/1367-2630/15/2/025039
- V. P. Gusynin and G. Shand Srapov, “Transport of Dirac quasiparticles in graphene: Hall and optical conductivities”, Phys. Rev. B 73(24), 245411 (2006). http://dx.doi.org/10.1103/PhysRevB.73.245411
- V. P. Gusynin, S. G. Sharapov and J. P. Carbotte, “Magneto-optical conductivity in graphene”, J. Phys. Condens. Matter 19, 026222 (2007). http://dx.doi.org/10.1088/0953-8984/19/2/026222
- L. A. Falkovsky and S. S. Pershoguba, “Optical farinfrared properties of a graphene monolayer and multilayer”, Phys. Rev. B 76(15), 153410 (2007). http://dx.doi.org/10.1103/PhysRevB.76.153410
- S. A. Mikhailov, “Non-linear electromagnetic response of graphene”, Europhys Lett. 79(02), 27002 (2007). http://dx.doi.org/10.1209/0295-5075/79/27002
- S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: Frequency multiplication and the self-consistent-field effects”, J. Phys.: Condens. Matter 20, 384204 (2008). http://dx.doi.org/10.1088/0953-8984/20/38/384204
- A. R. Wright, X. G. Xu, J. C. Cao and C. Zhang,“Strong nonlinear optical response of graphene in the terahertz regime”, Appl. Phys. Lett. 95(07), 072101 (2009). http://dx.doi.org/10.1063/1.3205115
- X. G. Xu and J. C. Cao, “Nonlinear response induced strong absorptance of graphene in the terahertz regime”, Mod. Phys. Lett. B 24(21), 2243–2249 (2010). http://dx.doi.org/10.1142/S0217984910024626
- Y. Zhou and M. W. Wu, “optical response of graphene under intense terahertz fields”, Phys. Rev. B 83(24), 245436 (2011). http://dx.doi.org/10.1103/PhysRevB.83.245436
- Yee Sin Ang, Shareef Sultan and C. Zhang, “Nonlinear optical spectrum of bilayer graphene in the terahertz regime”, Appl. Phys. Lett. 97(24), 243110 (2010). http://dx.doi.org/10.1063/1.3527934
- X. G. Xu, S. Sultan, C. Zhang and J. C. Cao, “Nonlinear optical conductance in a graphene pn junction in the terahertz regime”, Appl. Phys. Lett. 97(01), 011907 (2010). http://dx.doi.org/10.1063/1.3462972
- A. R. Wright, J. C. Cao and C. Zhang, “Enhanced optical conductivity of bilayer graphene nanoribbons in the terahertz regime”, Phys. Rev. Lett. 103(20), 207401 (2009). http://dx.doi.org/10.1103/PhysRevLett.103.20740
- Yee Sin Ang and C. Zhang, “Subgap optical conductivity in semihydrogenated graphene”, Appl. Phys. Lett. 98(04), 042107 (2011). http://dx.doi.org/10.1063/1.3549201
- Yee Sin Ang and C. Zhang, “Enhanced optical conductance in graphene superlattice due to anisotropic band dispersion”, J. Phys. D: Appl. Phys. 45(39), 395303 (2012). http://dx.doi.org/10.1088/0022-3727/45/39/395303
- N. M. R. Peres, “The electronic properties of graphene and its bilayer”, Vacuum 83(10), 1248–1252 (2009). http://dx.doi.org/10.1016/j.vacuum.2009.03.018
References
K. Geim, and K. S. Novoselov, “The rise of graphene”, Nat. Mater. 6, 183–191 (2007). http://dx.doi.org/10.1038/nmat1849
M. I. Katsnelson, “Graphene: carbon in two dimensions”, Mater. Today 10(1–2), 20–27 (2007). http://dx.doi.org/10.1016/S1369-7021(06)71788-6
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene”, Nature 438, 197–200 (2005). http://dx.doi.org/10.1038/nature04233
Y. Zhang, Y. W. Tan, H. L. Stormer and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene”, Nature 438, 201–204 (2005). http://dx.doi.org/10.1038/nature04235
C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Konrad, P. N. First and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene”, Science 312(5777), 1191–1196 (2006). http://dx.doi.org/10.1126/science.1125925
H. Suzuura and T. Ando, “Crossover from symplectic to orthogonal class in a two-dimensional honeycomb lattice”, Phys. Rev. Lett. 89(26), 266603 (2002). http://dx.doi.org/10.1103/PhysRevLett.89.266603
S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, L. A. Ponomarenko, D. Jiang, and A. K. Geim, “Strong suppression of weak localization in graphene”, Phys. Rev. Lett. 97(01), 016801 (2006). http://dx.doi.org/10.1103/PhysRevLett.97.016801
D. V. Khveshchenko, “Electron localization properties in graphene”, Phys. Rev. Lett. 97(03), 036802 (2006). http://dx.doi.org/10.1103/PhysRevLett. 97.036802
R. S. Deacon, K.-C. Chuang, R. J. Nicholas, K. S. Novoselov and A. K. Geim, “Cyclotron resonance study of the electron and hole velocity in graphene monolayers”, Phys. Rev. B 76(08), 081406(R) (2007). http://dx.doi.org/10.1103/PhysRevB.76.081406
Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim and H. L. Stormer, “Infrared spectroscopy of landau levels of graphene”, Phys. Rev. Lett. 98(19), 197403 (2007). http://dx.doi.org/10.1103/PhysRevLett.98.197403
R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres and A. K. Geim, “Fine structure constant defines visual transparency of graphene”, Science 320(5881), 1308–1308 (2008). http://dx.doi.org/10.1126/science.1156965
E. A. Henriksen, Z. Jiang, L. C. Tung, M. E. Schwartz, M. Takita, Y.-J. Wang, P. Kim and H. L. Stormer, “Cyclotron resonance in bilayer graphene”, Phys. Rev. Lett. 100(08), 087403 (2008). http://dx.doi.org/10.1103/PhysRevLett.100.087403
Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy”, Nature Physics 4, 532–535 (2008). http://dx.doi.org/10.1038/nphys989
K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich and T. F. Heinz, “Measurement of the optical conductivity of graphene”, Phys. Rev. Lett. 101(19), 196405 (2008). http://dx.doi.org/10.1103/PhysRevLett.101.196405
E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko and S. A. Mikhailov, “Coherent nonlinear optical response of graphene”, Phys. Rev. Lett. 105, 097401 (2010). http://dx.doi.org/10.1103/PhysRevLett.105.097401
S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider and M. Helm, “Carrier relaxation in epitaxial graphene photoexcited near the dirac point”, Phys. Rev. Lett. 107(23), 237401 (2011). http://dx.doi.org/10.1103/PhysRevLett.107.237401
Michael Woerner, Wilhelm Kuehn, Pamela Bowlan, Klaus Reimann and Thomas Elsaesser, “Ultrafast two-dimensional terahertz spectroscopy of elementary excitations in solids”, New J. Phys. 15, 025039 (2013). http://dx.doi.org/10.1088/1367-2630/15/2/025039
V. P. Gusynin and G. Shand Srapov, “Transport of Dirac quasiparticles in graphene: Hall and optical conductivities”, Phys. Rev. B 73(24), 245411 (2006). http://dx.doi.org/10.1103/PhysRevB.73.245411
V. P. Gusynin, S. G. Sharapov and J. P. Carbotte, “Magneto-optical conductivity in graphene”, J. Phys. Condens. Matter 19, 026222 (2007). http://dx.doi.org/10.1088/0953-8984/19/2/026222
L. A. Falkovsky and S. S. Pershoguba, “Optical farinfrared properties of a graphene monolayer and multilayer”, Phys. Rev. B 76(15), 153410 (2007). http://dx.doi.org/10.1103/PhysRevB.76.153410
S. A. Mikhailov, “Non-linear electromagnetic response of graphene”, Europhys Lett. 79(02), 27002 (2007). http://dx.doi.org/10.1209/0295-5075/79/27002
S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: Frequency multiplication and the self-consistent-field effects”, J. Phys.: Condens. Matter 20, 384204 (2008). http://dx.doi.org/10.1088/0953-8984/20/38/384204
A. R. Wright, X. G. Xu, J. C. Cao and C. Zhang,“Strong nonlinear optical response of graphene in the terahertz regime”, Appl. Phys. Lett. 95(07), 072101 (2009). http://dx.doi.org/10.1063/1.3205115
X. G. Xu and J. C. Cao, “Nonlinear response induced strong absorptance of graphene in the terahertz regime”, Mod. Phys. Lett. B 24(21), 2243–2249 (2010). http://dx.doi.org/10.1142/S0217984910024626
Y. Zhou and M. W. Wu, “optical response of graphene under intense terahertz fields”, Phys. Rev. B 83(24), 245436 (2011). http://dx.doi.org/10.1103/PhysRevB.83.245436
Yee Sin Ang, Shareef Sultan and C. Zhang, “Nonlinear optical spectrum of bilayer graphene in the terahertz regime”, Appl. Phys. Lett. 97(24), 243110 (2010). http://dx.doi.org/10.1063/1.3527934
X. G. Xu, S. Sultan, C. Zhang and J. C. Cao, “Nonlinear optical conductance in a graphene pn junction in the terahertz regime”, Appl. Phys. Lett. 97(01), 011907 (2010). http://dx.doi.org/10.1063/1.3462972
A. R. Wright, J. C. Cao and C. Zhang, “Enhanced optical conductivity of bilayer graphene nanoribbons in the terahertz regime”, Phys. Rev. Lett. 103(20), 207401 (2009). http://dx.doi.org/10.1103/PhysRevLett.103.20740
Yee Sin Ang and C. Zhang, “Subgap optical conductivity in semihydrogenated graphene”, Appl. Phys. Lett. 98(04), 042107 (2011). http://dx.doi.org/10.1063/1.3549201
Yee Sin Ang and C. Zhang, “Enhanced optical conductance in graphene superlattice due to anisotropic band dispersion”, J. Phys. D: Appl. Phys. 45(39), 395303 (2012). http://dx.doi.org/10.1088/0022-3727/45/39/395303
N. M. R. Peres, “The electronic properties of graphene and its bilayer”, Vacuum 83(10), 1248–1252 (2009). http://dx.doi.org/10.1016/j.vacuum.2009.03.018