Abstract

The generalized tight-binding model with exact diagonalization method is developed to calculate the optical properties of monolayer graphene in the presence of composite magnetic fields. The ratio of the uniform magnetic field and the modulated one accounts for a strong influence on the structure, number, intensity and frequency of absorption peaks, and thus the extra selection rules that are subsequently induced can be explained. When the modulated field increases, each symmetric peak, under a uniform magnetic field, splits into a pair of asymmetric peaks with lower intensities. The threshold absorption frequency exhibits an obvious evolution in terms of a redshift. These absorption peaks obey the same selection rule that is followed by Landau level transitions. Moreover, at a sufficiently strong modulation strength, the extra peaks in the absorption spectrum might arise from different selection rules.

© 2014 Optical Society of America

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2013

Y. C. Ou, Y. H. Chiu, J. M. Lu, W. P. Su, M. F. Lin, “Electric modulation effect on magneto-optical spectrum of monolayer graphene,” Comput. Phys. Commun. 184, 1821–1826 (2013).
[CrossRef]

Y. C. Chuang, J. Y. Wu, M. F. Lin, “Electric Field Dependence of Excitation Spectra in AB-Stacked Bilayer Graphene,” Sci. Rep. 3, 1368 (2013).
[CrossRef] [PubMed]

2012

C. W. Chiu, Y. C. Huang, F. L. Shyu, M. F. Lin, “Optical absorption spectra in ABC-stacked graphene superlattice,” Synth. Met. 162, 800–804 (2012).
[CrossRef]

R. B. Chen, Y. H. Chiu, M. F. Lin, “A theoretical evaluation of the magneto-optical properties of AA-stacked graphite,” Carbon 54, 268–276 (2012).
[CrossRef]

D. A. Stone, C. A. Downing, M. E. Portnoi, “Searching for confined modes in graphene channels: The variable phase method,” Phys. Rev. B 86, 075464 (2012).
[CrossRef]

S. Yuan, R. Roldán, M. I. Katsnelson, “Polarization of graphene in a strong magnetic field beyond the Dirac cone approximation,” Solid State Commun. 152, 1446–1455 (2012).
[CrossRef]

2011

H. C. Kao, M. Lewkowicz, Y. Korniyenko, B. Rosenstein, “Dynamical approach to ballistic transport in graphene,” Comput. Phys. Commun. 182, 112–114 (2011).
[CrossRef]

Y. C. Ou, J. K. Sheu, Y. H. Chiu, R. B. Chen, M. F. Lin, “Influence of modulated fields on the Landau level properties of graphene,” Phys. Rev. B 83, 195405 (2011).
[CrossRef]

S. K. Firoz Islam, N. K. Singh, T. K. Ghosh, “Thermodynamic properties of a magnetically modulated graphene monolayer,” J. Phys.: Condens. Matter 23, 445502 (2011).

M. Tahir, K. Sabeeh, A. MacKinnon, “Temperature effects on the magnetoplasmon spectrum of a weakly modulated graphene monolayer,” J. Phys.: Condens. Matter 23, 425304 (2011).

S. Yuan, R. Roldán, M. I. Katsnelson, “Landau level spectrum of ABA- and ABC-stacked trilayer graphene,” Phys. Rev. B 84, 125455 (2011).
[CrossRef]

J. Y. Wu, S. C. Chen, Oleksiy Roslyak, Godfrey Gumbs, M. F. Lin, “Plasma Excitations in Graphene: Their Spectral Intensity and Temperature Dependence in Magnetic Field,” ACS Nano 5, 1026–1032 (2011).
[CrossRef] [PubMed]

2010

R. Roldán, J. N. Fuchs, M. O. Goerbig, “Spin-flip excitations, spin waves, and magnetoexcitons in graphene Landau levels at integer filling factors,” Phys. Rev. B 82, 205418 (2010).
[CrossRef]

Y. H. Ho, Y. H. Chiu, D. H. Lin, C. P. Chang, M. F. Lin, “Magneto-optical Selection Rules in Bilayer Bernal Graphene,” ACS Nano 4, 1465–1472 (2010).
[CrossRef] [PubMed]

Y. H. Ho, J. Y. Wu, R. B. Chen, Y. H. Chiu, M. F. Lin, “Optical transitions between Landau levels: AA-stacked bilayer graphene,” Appl. Phys. Lett. 97, 101905 (2010).
[CrossRef]

D. P. Arovas, L. Brey, H. A. Fertig, E.-A. Kim, K. Ziegler, “Dirac spectrum in piecewise constant one-dimensional (1D) potentials,” New J. Phys. 12, 123020 (2010).
[CrossRef]

M. Barbier, P. Vasilopoulos, F. M. Peeters, “Extra Dirac points in the energy spectrum for superlattices on single-layer graphene,” Phys. Rev. B 81, 075438 (2010).
[CrossRef]

L.-G. Wang, S.-Y. Zhu, “Electronic band gaps and transport properties in graphene superlattices with one-dimensional periodic potentials of square barriers,” Phys. Rev. B 81, 205444 (2010).
[CrossRef]

R. R. Hartmann, N. J. Robinson, M. E. Portnoi, “Smooth electron waveguides in graphene,” Phys. Rev. B 81, 245431 (2010).
[CrossRef]

2009

K. I. Bolotin, F. Ghahari, M. D. Shulman, H. L. Stormer, P. Kim, “Observation of the fractional quantum Hall effect in graphene,” Nature 462, 196–199 (2009).
[CrossRef] [PubMed]

N. W. Nicholas, L. M. Connors, F. Ding, B. I. Yakobson, H. K. Schmidt, R. H. Hauge, “Templated growth of graphenic materials,” Nanotechnology 20, 245607 (2009).
[CrossRef] [PubMed]

J. Campos-Delgado, Y. A. Kim, T. Hayashi, A. Morelos-Gómez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R. D. Shull, M. S. Dresselhaus, M. Terrones, “Thermal stability studies of CVD-grown graphene nanoribbons: Defect annealing and loop formation,” Chem. Phys. Lett. 469, 177–182 (2009).
[CrossRef]

L. Brey, H. A. Fertig, “Emerging Zero Modes for Graphene in a Periodic Potential,” Phys. Rev. Lett. 103, 046809 (2009).
[CrossRef] [PubMed]

M. Ramezani Masir, P. Vasilopoulos, F. M. Peeters, “Magnetic Kronig–Penney model for Dirac electrons in single-layer graphene,” New J. Phys. 11, 095009 (2009).
[CrossRef]

J. H. Ho, Y. H. Chiu, S. J. Tsai, M. F. Lin, “Semimetallic graphene in a modulated electric potential,” Phys. Rev. B 79, 115427 (2009).
[CrossRef]

2008

J. H. Ho, Y. H. Lai, Y. H. Chiu, M. F. Lin, “Modulation effects on Landau levels in a monolayer graphene,” Nanotechnology 19, 035712 (2008).
[CrossRef] [PubMed]

P. Plochocka, C. Faugeras, M. Orlita, M. L. Sadowski, G. Martinez, M. Potemski, M. O. Goerbig, J.-N. Fuchs, C. Berger, W. A. de Heer, “High-Energy Limit of Massless Dirac Fermions in Multilayer Graphene using Magneto-Optical Transmission Spectroscopy,” Phys. Rev. Lett. 100, 087401 (2008).
[CrossRef] [PubMed]

Y. H. Chiu, J. H. Ho, C. P. Chang, D. S. Chuu, M. F. Lin, “Low-frequency magneto-optical excitations of a graphene monolayer: Peierls tight-binding model and gradient approximation calculation,” Phys. Rev. B 78, 245411 (2008).
[CrossRef]

Y. H. Chiu, Y. H. Lai, J. H. Ho, D. S. Chuu, M. F. Lin, “Electronic structure of a two-dimensional graphene monolayer in a spatially modulated magnetic field: Peierls tight-binding model,” Phys. Rev. B 77, 045407 (2008).
[CrossRef]

Y. H. Lai, J. H. Ho, C. P. Chang, M. F. Lin, “Magnetoelectronic properties of bilayer Bernal graphene,” Phys. Rev. B 77, 085426 (2008).
[CrossRef]

M. Barbier, F. M. Peeters, P. Vasilopoulos, J. M. Pereira, “Dirac and Klein-Gordon particles in one-dimensional periodic potentials,” Phys. Rev. B 77, 115446 (2008).
[CrossRef]

J. Campos-Delgado, J. M. Romo-Herrera, X. Jia, D. A. Cullen, H. Muramatsu, Y. A. Kim, T. Hayashi, Z. Ren, D. J. Smith, Y. Okuno, T. Ohba, H. Kanoh, K. Kaneko, M. Endo, H. Terrones, M. S. Dresselhaus, M. Terrones, “Bulk Production of a New Form of sp2 Carbon: Crystalline Graphene Nanoribbons,” Nano Lett. 8, 2773–2778 (2008).
[CrossRef] [PubMed]

J. H. Ho, Y. H. Lai, Y. H. Chiu, M. F. Lin, “Landau levels in graphene,” Physica E 40, 1722–1725 (2008).
[CrossRef]

J. Coraux, A. T. N’Diaye, C. Busse, T. Michely, “Structural Coherency of Graphene on Ir(111),” Nano Lett. 8, 565–570 (2008).
[CrossRef] [PubMed]

2007

Z. Jiang, E. A. Henriksen, L. C. Tung, Y. J. Wang, M. E. Schwartz, M. Y. Hun, P. Kim, H. L. Stormer, “Infrared Spectroscopy of Landau Levels of Graphene,” Phys. Rev. Lett. 98, 197403 (2007).
[CrossRef] [PubMed]

K. S. Novoselov, Z. Jiang, Y. Zhang, S. V. Morozov, H. L. Stormer, U. Zeitler, J. C. Maan, G. S. Boebinger, P. Kim, A. K. Geim, “Room-Temperature Quantum Hall Effect in Graphene,” Science 315, 1379 (2007).
[CrossRef] [PubMed]

R. S. Deacon, K. C. Chuang, R. J. Nicholas, K. S. Novoselov, A. K. Geim, “Cyclotron resonance study of the electron and hole velocity in graphene monolayers,” Phys. Rev. B 76, 081406 (2007).
[CrossRef]

C. Bai, X. Zhang, “Klein paradox and resonant tunneling in a graphene superlattice,” Phys. Rev. B 76, 075430 (2007).
[CrossRef]

M. Tahir, K. Sabeeh, A. MacKinnon, “Weiss oscillations in the electronic structure of modulated graphene,” J. Phys.: Condens. Matter 19, 406226 (2007).

M. Tahir, K. Sabeeh, “Theory of Weiss oscillations in the magnetoplasmon spectrum of Dirac electrons in graphene,” Phys. Rev. B 76, 195416 (2007).
[CrossRef]

A. Matulis, F. M. Peeters, ”Appearance of enhanced Weiss oscillations in graphene: Theory,” Phys. Rev. B 75, 125429 (2007).
[CrossRef]

N. Nemec, G. Cuniberti, “Hofstadter butterflies of bilayer graphene,” Phys. Rev. B 75, 201404 (2007).
[CrossRef]

A. Iyengar, Jianhui Wang, H. A. Fertig, L. Brey, “Excitations from filled Landau levels in graphene,” Phys. Rev. B 75, 125430 (2007).
[CrossRef]

X.-F. Wang, T. Chakraborty, “Coulomb screening and collective excitations in a graphene bilayer,” Phys. Rev. B 75, 041404 (2007).
[CrossRef]

X.-F. Wang, T. Chakraborty, “Collective excitations of Dirac electrons in a graphene layer with spin-orbit interactions,” Phys. Rev. B 75, 033408 (2007).
[CrossRef]

2006

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

V. P. Gusynin, V. A. Miransky, S. G. Sharapov, I. A. Shovkovy, “Excitonic gap, phase transition, and quantum Hall effect in graphene,” Phys. Rev. B 74, 195429 (2006).
[CrossRef]

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[CrossRef]

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[CrossRef] [PubMed]

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, W. A. de Heer, “Electronic Confinement and Coherence in Patterned Epitaxial Graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

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Solid State Commun.

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Figures (8)

Fig. 1
Fig. 1

The primitive cell of a monolayer graphene in a uniform magnetic field and a spatially modulated magnetic field along the armchair direction.

Fig. 2
Fig. 2

The low ky-dependent energy bands for BMB0 case under (a) the uniform magnetic field B0 = 4 T (red curves) and the composite field B0 = 4 T in conjunction with RM = 500 and BM = 0.5 T (black curves), and (b) B0 = 4 T in conjunction with RM = 500 and BM = 4 T. The triangular and circular symbols correspond to the band-edge states k b e α and k b e β, respectively.

Fig. 3
Fig. 3

The low ky-dependent energy bands for the BM > B0 case at (a) the composite field B0 = 4 T in conjunction with RM = 500 and BM = 32 T, and (b) the pure modulated magnetic field RM = 500, BM =36, 32 and 28 T (red, black and blue curves, respectively). The triangular and circular symbols represent the same meanings as in Fig. 2.

Fig. 4
Fig. 4

The low-frequency density of states at (a) the uniform magnetic field B0 = 4 T (red curves) and the composite field B0 = 4 T in conjunction with RM = 500 and BM = 0.5 T (black curves), (b) B0 = 4 T in conjunction with RM = 500 and BM = 4 T, and (c) B0 = 4 T in conjunction with RM = 500 and BM = 32 T (blue curves), and the pure modulated magnetic field RM = 500 and BM =32 T (black curves).

Fig. 5
Fig. 5

The wave functions with nc,v = 0 and nc = 1 at k b e α for (a)–(d) the uniform magnetic field B0 = 4 T (red curves) and the composite field B0 = 4 T together with RM = 500 and BM = 0.5 T (black curves), (e)–(h) B0 = 4 T combined with RM = 500 and BM = 4 T, and (i)–(l) B0 = 4 T combined with RM = 500 and BM = 32 T. The wave functions with nc = 1 at k1 (solid curves) and k b e e ± (dashed curves) in the pure modulated field RM = 500 and BM = 32 T, are shown in (m)–(p).

Fig. 6
Fig. 6

The low-frequency optical absorption spectra for the BMB0 case corresponding to (a) the uniform magnetic field B0 = 4 T (red curve) and the composite field B0 = 4 T together with RM = 500 and BM = 0.5 T (black curve) and (b) the composite field B0 = 4 T combined with RM = 500 and BM = 4 T.

Fig. 7
Fig. 7

The low-frequency optical absorption spectra for the BM > B0 case corresponding to the composite field B0 = 4 T combined with RM = 500 and BM = 32 T (dashed blue curve) and the pure modulated magnetic field RM = 500 and BM = 32 T (black curve).

Fig. 8
Fig. 8

The dependence of absorption frequencies ω α n n and ω β n n with |Δn| = |nn′| = 1 on the modulated strength BM at B0 = 4 T and RM = 500.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

| Ψ k = m = 1 2 R 1 ( A o c , v | a m k + B o c , v | b m k ) + m = 2 2 R ( A e c , v | a m k + B e c , v | b m k ) ,
b m k | H | a m k = [ t 1 k ( m ) + t 2 k ( m ) ] δ m , m + t 3 k ( m ) δ m , m 1 ,
A ( ω ) c , v , n ˜ , n ˜ 1 s t B Z d k ( 2 π ) 2 | Ψ c ( k , n ) | E ^ P m e | Ψ v ( k , n ) | 2 × Im [ f ( E c ( k , n ) ) f ( E v ( k , n ) ) E c ( k , n ) E v ( k , n ) ω i Γ ] ,
m , m = 1 2 R C [ ( A o c + A e c ) * × ( B o v + B e v ) ] k a m k | H | b m k + h . c . .

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