Abstract

Graphene possesses a unique Landau level system that is non-equidistantly spaced in energy, as thus a large amount of optical transitions may become possible. Here, by utilizing this unique feature, we propose a novel dual field method which combines both external magnetic field and gate electric field together to control the optical response of the graphene-based devices. The key principle of this method is to selectively allow different optical transitions in graphene among Landau levels via an electric gate tuning of the Fermi level. By applying this method to a graphene based amplitude modulator and through an implementation based on transfer matrix method, we numerically demonstrated the well characteristics of switchable modulation on four individual channels, a huge modulation depth up to 80 dB and an extremely low required energy of tuning Fermi level down to 10 meV. Such excellent frequency tunability and gate controlling ability of this dual field method may open up the potential for applications in active optoelectronics, spin optics, ultrafast optics and etc.

© 2016 Optical Society of America

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    [Crossref] [PubMed]
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  38. J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83(16), 165113 (2011).
    [Crossref]

2015 (5)

W.-M. Wang, P. Gibbon, Z.-M. Sheng, and Y.-T. Li, “Tunable Circularly Polarized Terahertz Radiation from Magnetized Gas Plasma,” Phys. Rev. Lett. 114(25), 253901 (2015).
[Crossref] [PubMed]

Q. Li, Z. Tian, X. Zhang, R. Singh, L. Du, J. Gu, J. Han, and W. Zhang, “Active graphene-silicon hybrid diode for terahertz waves,” Nat. Commun. 6, 7082 (2015).
[Crossref] [PubMed]

J. S. Gomez-Diaz, C. Moldovan, S. Capdevila, J. Romeu, L. S. Bernard, A. Magrez, A. M. Ionescu, and J. Perruisseau-Carrier, “Self-biased reconfigurable graphene stacks for terahertz plasmonics,” Nat. Commun. 6, 6334 (2015).
[Crossref] [PubMed]

J. Q. Liu, Y. X. Zhou, L. Li, P. Wang, and A. V. Zayats, “Controlling plasmon-induced transparency of graphene metamolecules with external magnetic field,” Opt. Express 23(10), 12524–12532 (2015).
[Crossref] [PubMed]

S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
[Crossref]

2014 (5)

Y. Zhang, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “Graphene based tunable metamaterial absorber and polarization modulation in terahertz frequency,” Opt. Express 22(19), 22743–22752 (2014).
[Crossref] [PubMed]

M. Wang, Y. Wang, M. Pu, C. Hu, X. Wu, Z. Zhao, and X. Luo, “Circular dichroism of graphene-based absorber in static magnetic field,” J. Appl. Phys. 115(15), 154312 (2014).
[Crossref]

J. M. Woo, M. S. Kim, H. W. Kim, and J. Jang, “Graphene based salisbury screen for terahertz absorber,” Appl. Phys. Lett. 104(8), 081106 (2014).
[Crossref]

M. Mittendorff, F. Wendler, E. Malic, A. Knorr, M. Orlita, M. Potemski, C. Berger, W. A. de Heer, H. Schneider, M. Helm, and S. Winnerl, “Carrier dynamics in Landau-quantized graphene featuring strong Auger scattering,” Nat. Phys. 11(1), 75–81 (2014).
[Crossref]

Y. C. Ou, Y. H. Chiu, P. H. Yang, and M. F. Lin, “The selection rule of graphene in a composite magnetic field,” Opt. Express 22(7), 7473–7491 (2014).
[Crossref] [PubMed]

2013 (6)

S. Fujioka, Z. Zhang, K. Ishihara, K. Shigemori, Y. Hironaka, T. Johzaki, A. Sunahara, N. Yamamoto, H. Nakashima, T. Watanabe, H. Shiraga, H. Nishimura, and H. Azechi, “Kilotesla magnetic field due to a capacitor-coil target driven by high power laser,” Sci. Rep. 3, 1170 (2013).
[Crossref] [PubMed]

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express 21(6), 7614–7632 (2013).
[Crossref] [PubMed]

B. Z. Xu, C. Q. Gu, Z. Li, and Z. Y. Niu, “A novel structure for tunable terahertz absorber based on graphene,” Opt. Express 21(20), 23803–23811 (2013).
[Crossref] [PubMed]

M. Amin, M. Farhat, and H. Bağcı, “An ultra-broadband multilayered graphene absorber,” Opt. Express 21(24), 29938–29948 (2013).
[Crossref] [PubMed]

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

N. Papasimakis, S. Thongrattanasiri, N. I. Zheludev, and F. J. García de Abajo, “The magnetic response of graphene split-ring metamaterials,” Light Sci. Appl. 2(7), e78 (2013).
[Crossref]

2012 (5)

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

I. Maeng, S. Lim, S. J. Chae, Y. H. Lee, H. Choi, and J. H. Son, “Gate-controlled nonlinear conductivity of Dirac fermion in graphene field-effect transistors measured by terahertz time-domain spectroscopy,” Nano Lett. 12(2), 551–555 (2012).
[Crossref] [PubMed]

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref] [PubMed]

R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express 20(27), 28017–28024 (2012).
[Crossref] [PubMed]

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
[Crossref] [PubMed]

2011 (3)

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. C. Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84(23), 235410 (2011).
[Crossref]

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83(16), 165113 (2011).
[Crossref]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

2010 (1)

P. Avouris, “Graphene: electronic and photonic properties and devices,” Nano Lett. 10(11), 4285–4294 (2010).
[Crossref] [PubMed]

2009 (1)

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

2008 (3)

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha, U. V. Waghmare, K. S. Novoselov, H. R. Krishnamurthy, A. K. Geim, A. C. Ferrari, and A. K. Sood, “Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor,” Nat. Nanotechnol. 3(4), 210–215 (2008).
[Crossref] [PubMed]

J. M. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Measurement of ultrafast carrier dynamics in epitaxial graphene,” Appl. Phys. Lett. 92(4), 042116 (2008).
[Crossref]

2007 (2)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and Hall conductivity in graphene,” Phys. Rev. B 75(16), 165407 (2007).
[Crossref]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

2006 (3)

V. P. Gusynin and S. G. Sharapov, “Transport of Dirac quasiparticles in graphene: Hall and optical conductivities,” Phys. Rev. B 73(24), 245411 (2006).
[Crossref]

S. Y. Zhou, G.-H. Gweon, J. Graf, A. V. Fedorov, C. D. Spataru, R. D. Diehl, Y. Kopelevich, D.-H. Lee, S. G. Louie, and A. Lanzara, “First direct observation of Dirac fermions in graphite,” Nat. Phys. 2(9), 595–599 (2006).
[Crossref]

M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. de Heer, “Landau level spectroscopy of ultrathin graphite layers,” Phys. Rev. Lett. 97(26), 266405 (2006).
[Crossref] [PubMed]

2002 (1)

Y. H. Matsuda, F. Herlach, S. Ikeda, and N. Miura, “Generation of 600 T by electromagnetic flux compression with improved implosion symmetry,” Rev. Sci. Instrum. 73(12), 4288–4294 (2002).
[Crossref]

1988 (1)

R. L. Fante and M. T. Mccormack, “Reflection properties of the Salisbury screen,” IEEE Trans. Antenn. Propag. 36(10), 1443–1454 (1988).
[Crossref]

1984 (1)

Alaee, R.

Amin, M.

Avouris, P.

P. Avouris, “Graphene: electronic and photonic properties and devices,” Nano Lett. 10(11), 4285–4294 (2010).
[Crossref] [PubMed]

Azechi, H.

S. Fujioka, Z. Zhang, K. Ishihara, K. Shigemori, Y. Hironaka, T. Johzaki, A. Sunahara, N. Yamamoto, H. Nakashima, T. Watanabe, H. Shiraga, H. Nishimura, and H. Azechi, “Kilotesla magnetic field due to a capacitor-coil target driven by high power laser,” Sci. Rep. 3, 1170 (2013).
[Crossref] [PubMed]

Bagci, H.

Baldacci, L.

S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
[Crossref]

Bao, Q.

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
[Crossref] [PubMed]

Bechtel, H. A.

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83(16), 165113 (2011).
[Crossref]

Berger, C.

M. Mittendorff, F. Wendler, E. Malic, A. Knorr, M. Orlita, M. Potemski, C. Berger, W. A. de Heer, H. Schneider, M. Helm, and S. Winnerl, “Carrier dynamics in Landau-quantized graphene featuring strong Auger scattering,” Nat. Phys. 11(1), 75–81 (2014).
[Crossref]

M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. de Heer, “Landau level spectroscopy of ultrathin graphite layers,” Phys. Rev. Lett. 97(26), 266405 (2006).
[Crossref] [PubMed]

Bernard, L. S.

J. S. Gomez-Diaz, C. Moldovan, S. Capdevila, J. Romeu, L. S. Bernard, A. Magrez, A. M. Ionescu, and J. Perruisseau-Carrier, “Self-biased reconfigurable graphene stacks for terahertz plasmonics,” Nat. Commun. 6, 6334 (2015).
[Crossref] [PubMed]

Bludov, Y. V.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. C. Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84(23), 235410 (2011).
[Crossref]

Capdevila, S.

J. S. Gomez-Diaz, C. Moldovan, S. Capdevila, J. Romeu, L. S. Bernard, A. Magrez, A. M. Ionescu, and J. Perruisseau-Carrier, “Self-biased reconfigurable graphene stacks for terahertz plasmonics,” Nat. Commun. 6, 6334 (2015).
[Crossref] [PubMed]

Capolino, F.

Carbotte, J. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and Hall conductivity in graphene,” Phys. Rev. B 75(16), 165407 (2007).
[Crossref]

Chae, S. J.

I. Maeng, S. Lim, S. J. Chae, Y. H. Lee, H. Choi, and J. H. Son, “Gate-controlled nonlinear conductivity of Dirac fermion in graphene field-effect transistors measured by terahertz time-domain spectroscopy,” Nano Lett. 12(2), 551–555 (2012).
[Crossref] [PubMed]

Chakraborty, B.

A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha, U. V. Waghmare, K. S. Novoselov, H. R. Krishnamurthy, A. K. Geim, A. C. Ferrari, and A. K. Sood, “Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor,” Nat. Nanotechnol. 3(4), 210–215 (2008).
[Crossref] [PubMed]

Chandrashekhar, M.

J. M. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Measurement of ultrafast carrier dynamics in epitaxial graphene,” Appl. Phys. Lett. 92(4), 042116 (2008).
[Crossref]

Chen, C.

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83(16), 165113 (2011).
[Crossref]

Chilwell, J.

Chiu, Y. H.

Choi, C. G.

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

Choi, H.

I. Maeng, S. Lim, S. J. Chae, Y. H. Lee, H. Choi, and J. H. Son, “Gate-controlled nonlinear conductivity of Dirac fermion in graphene field-effect transistors measured by terahertz time-domain spectroscopy,” Nano Lett. 12(2), 551–555 (2012).
[Crossref] [PubMed]

Choi, H. K.

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Li, Q.

Q. Li, Z. Tian, X. Zhang, R. Singh, L. Du, J. Gu, J. Han, and W. Zhang, “Active graphene-silicon hybrid diode for terahertz waves,” Nat. Commun. 6, 7082 (2015).
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W.-M. Wang, P. Gibbon, Z.-M. Sheng, and Y.-T. Li, “Tunable Circularly Polarized Terahertz Radiation from Magnetized Gas Plasma,” Phys. Rev. Lett. 114(25), 253901 (2015).
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Lim, S.

I. Maeng, S. Lim, S. J. Chae, Y. H. Lee, H. Choi, and J. H. Son, “Gate-controlled nonlinear conductivity of Dirac fermion in graphene field-effect transistors measured by terahertz time-domain spectroscopy,” Nano Lett. 12(2), 551–555 (2012).
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Liu, J. Q.

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S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
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M. Wang, Y. Wang, M. Pu, C. Hu, X. Wu, Z. Zhao, and X. Luo, “Circular dichroism of graphene-based absorber in static magnetic field,” J. Appl. Phys. 115(15), 154312 (2014).
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S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
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M. Mittendorff, F. Wendler, E. Malic, A. Knorr, M. Orlita, M. Potemski, C. Berger, W. A. de Heer, H. Schneider, M. Helm, and S. Winnerl, “Carrier dynamics in Landau-quantized graphene featuring strong Auger scattering,” Nat. Phys. 11(1), 75–81 (2014).
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J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83(16), 165113 (2011).
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Figures (6)

Fig. 1
Fig. 1 Sketch of our concept on allowing different optical transitions in LLs system via tuning the Fermi level. Blue rings stand for LLs of holes and red ones stand for LLs of electrons. The two-color mixed sphere at the Dirac point indicates the degenerate state of holes and electrons. Solid green arrows and shadowed gray ones indicate the allowed transitions and forbidden transitions respectively. When Fermi level is between L0 and L1, transition L0->L1 is allowed and transition L1->L2 is forbidden; when Fermi level is shifted between L1 and L2, transition L0->L1 is turned off due to the occupation of both L0 and L1, while transition L1->L2 becomes active. Light blue arrows show some interband-like transitions that are free from Fermi level tuning.
Fig. 2
Fig. 2 (a) Schematic illustration of the graphene amplitude modulator (GAM) under study. Magnetic field B is applied perpendicular to the graphene surface. (b) Relationship between the gate voltage and the Fermi level in GAM, by assuming graphene to be pristine. Inset shows a cross-section illustration of GAM.
Fig. 3
Fig. 3 (a, c) plot the real and imaginary parts of the diagonal optical conductivity of graphene versus the square root of magnetic field B at 4 THz (blue solid) and 9 THz (red solid) respectively. Fermi level is set to zero here. (b, d) plot the real and imaginary parts of the diagonal optical conductivity versus the Fermi level at 4 THz (blue solid) and 9 THz (red solid) respectively. Magnetic field is set to 1 Tesla here. Dashed lines in (b) and (d) plot the conductivity under zero magnetic field, as a comparison.
Fig. 4
Fig. 4 (a, b, c) map the absorption of GAM versus both the magnetic field and the Fermi level at the photon energy of 5 meV, 15 meV and 25 meV respectively. (d, e, f) plot the cut-line view along the three pairs of the dashed white orthogonal lines in (a, b, c) respectively. Note that each pair of the dashed white lines is focused on a local maximum in absorption. (d, e, f) are dual x-axis plots, where the blue solid lines correspond to the down x-axis (a vertical cut) and the red ones correspond to the up x-axis (a horizontal cut). Normal incidence and linearly polarized wave is assumed here as well as in the following figures.
Fig. 5
Fig. 5 (a) maps the reflection spectrum of GAM versus magnetic field B at a Fermi level of 60 meV. Five dashed lines indicate transitions (from up to bottom): L0->L1, L1->L2, L2->L3, L3->L4, and L4->L5. Small local minimums on the up left corner correspond to a series of interband-like transitions, which are much weaker than the intraband-like ones indicated by dashed lines. (b) plots the reflection spectrum of designed four-channel modulation of GAM. The four channels are represented by the four deep valleys which correspond to magnetic fields (from left to right): 0.5 T, 1.4 T, 3.2 T, and 4.5 T. (d) plots the corresponding relative modulation depths of the four channels. (c) plots the relationship between the square root of magnetic field and the reflection of GAM at frequency 16.2 THz (red solid) and 27.9 THz (blue solid) respectively.
Fig. 6
Fig. 6 (a) maps the reflection spectrum of GAM versus Fermi level at B = 1 Tesla. Four dashed lines indicate transitions (from up to bottom): L0->L1, L1->L2, L2->L3, and L7->L8. Note that there exist small deviations between the transitions and the minimums in three of them, except for the transition L1->L2. (b) plots the reflection spectrum of designed four-channel modulation of GAM. The four channels are represented by the four deep valleys which correspond to Fermi levels (from left to right): 78 meV, 58 meV, 48 meV and 28 meV. (d) plots the corresponding relative modulation depths of the four channels. (c) plots an optimized dual channel modulation of GAM. Solid lines correspond to the modulation depths (left axis) and dashed ones correspond to the reflection spectrum (right axis). The two channels of GAM are at frequencies of 2.88 THz (red solid and red dashed) and 4.06 THz (blue solid and blue dashed) respectively.

Equations (5)

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E n =sgn(n) 2 v F 2 eB| n |
C gc e ( V G V 0 )= n c = 2sgn( E F ) π 2 v F 2 0 ε[ f d (ε E F ) f d (ε+ E F )] ε
σ g =[ σ xx σ xy σ yx σ yy ]
σ xx (Ω)= σ yy (Ω)= e 2 v F 2 |eB|(Ω+iΓ) πci × n=0 { [ n F ( E n ) n F ( E n+1 )]+[ n F ( E n+1 ) n F ( E n )] [ ( E n+1 E n ) 2 (Ω+2iΓ) 2 ]( E n+1 E n ) + [ n F ( E n ) n F ( E n+1 )]+[ n F ( E n+1 ) n F ( E n )] [ ( E n+1 + E n ) 2 (Ω+2iΓ) 2 ]( E n+1 + E n ) }
σ xy (Ω)= σ yx (Ω)= e 2 v F 2 eB πc × n=0 { [ n F ( E n ) n F ( E n+1 )][ n F ( E n+1 ) n F ( E n )] ( E n+1 E n ) 2 (Ω+2iΓ) 2 + [ n F ( E n ) n F ( E n+1 )][ n F ( E n+1 ) n F ( E n )] ( E n+1 + E n ) 2 (Ω+2iΓ) 2 }

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