Magneto-optical selection rules in bilayer Bernal graphene

ACS Nano

Volumn 4, Issue 3, 2010, Pages 1465-1472

  Ho, Yen Hung ^a,b   Chiu, Yu Huang ^a   Lin, De Hone ^b   Chang, Chen Peng ^c   Lin, Ming Fa ^a  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^b NATIONAL SUN YAT SEN UNIVERSITY   (Taiwan)

^c TAINAN UNIVERSITY OF TECHNOLOGY   (Taiwan)

Author keywords

Graphene; Landau level; Magnetic field; Optical absorption; Selection rule; Tight binding model

Indexed keywords

LANDAU LEVEL; LANDAU LEVELS; OPTICAL ABSORPTION; SELECTION RULES; TIGHT BINDING MODEL;

ABSORPTION; COMPLEXATION; GRAPHENE; GRAPHITE; LIGHT ABSORPTION; MAGNETIC FIELDS; MAGNETOS; MONOLAYERS; WAVE FUNCTIONS;

OPTICAL PROPERTIES;

EID: 77950157179     PISSN: 19360851     EISSN: 1936086X     Source Type: Journal    
DOI: 10.1021/nn9015339     Document Type: Article

References (46)

1. Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Firsov, A. A. Electric Field Effect in Atomically Thin Carbon Films. Science 2004, 306, 666.
2. 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, 197-200.
3. Berger, C.; Song, Z. M.; Li, T. B.; Li, X. B.; Ogbazghi, A. Y.; Feng, R.; Dai, Z. T.; Marchenkov, A. N.; Conrad, E. H.; First, P. N.; de Heer, W. A. Ultrathin Epitaxial Graphite: 2D Electron Gas Properties and a Route toward Graphene-Based Nanoelectronics. J. Phys. Chem. B 2004, 108, 19912-19916.
4. Rutter, G. M.; Crain, J. N.; Guisinger, N. P.; Li, T.; First, P. N.; Stroscio, J. A. Scattering and Interference in Epitaxial Graphene. Science 2007, 317, 219-222.
5. Wallace, P. R. The Band Theory of Graphite. Phys. Rev. 1947, 71, 622-634.
6. Grüneis, A.; Attaccalite, C.; Wirtz, L.; Shiozawa, H.; Saito, R.; Pichler, T.; Rubio, A. Tight-Binding Description of the Quasiparticle Dispersion of Graphite and Few-Layer Graphene. Phys. Rev. B 2008, 78, 205425.
7. Slonczewski, J. C.; Weiss, P. R. Band Structure of Graphite. Phys. Rev. 1958, 109, 272-279.
8. Charlier, J.-C.; Michenaud, J.-P. First-Principles Study of the Electronic Properties of Simple Hexagonal Graphite. Phys. Rev. B 1992, 46, 4531-4539.
9. Latil, S.; Henrard, L. Charge Carriers in Few-Layer Graphene Films. Phys. Rev. Lett. 2006, 97, 036803.
10. Partoens, B.; Peeters, F. M. From Graphene to Graphite: Electronic Structure around the K Point. Phys. Rev. B 2006, 74, 075404.
11. Lu, C. L.; Chang, C. P.; Huang, Y. C.; Chen, R. B.; Lin, M. F. Influence of an Electric Field on the Optical Properties of Few-Layer Graphene with AB Stacking. Phys. Rev. B 2006, 73, 144427.
12. Lai, Y. H.; Ho, J. H.; Chang, C. P.; Lin, M. F. Magnetoelectronic Properties of Bilayer Bernal Graphene. Phys. Rev. B 2008, 77, 085426.
13. McCann, E.; Fal'ko, V. I. Landau-Level Degeneracy and Quantum Hall Effect in a Graphite Bilayer. Phys. Rev. Lett. 2006, 96, 086805.
14. Abergel, D. S. L.; Fal'ko, V. I. Optical and Magneto-Optical Far-Infrared Properties of Bilayer Graphene. Phys. Rev. B 2007, 75, 155430.
15. Charlier, J.-C.; Gonze, X.; Michenaud, J.-P. First-Principles Study of the Electronic Properties of Graphite. Phys. Rev. B 1991, 43, 4579-4589.
16. Nakao, J. Landau Level Structure and Magnetic Breakthrough in Graphite. J. Phys. Soc. Jpn. 1976, 40, 761-768.
17. Kuzmenko, A. B.; Crassee, I.; van der Marel, D. Determination of the Gate-Tunable Band Gap and Tight-Binding Parameters in Bilayer Graphene Using Infrared Spectroscopy. Phys. Rev. B 2009, 80, 165406.
18. Ohta, T.; Bostwick, A.; Seller, T.; Horn, K.; Rotenberg, E. Controlling the Electronic Structure of Bilayer Graphene. Science 2006, 313, 951-954.
19. Ohta, T.; Bostwick, A.; McChesney, J. L.; Seyller, T.; Horn, K.; Rotenberg, E. Interlayer Interaction and Electronic Screening in Multilayer Graphene Investigated with Angle-Resolved Photoemission Spectroscopy. Phys. Rev. Lett. 2007, 98, 206802.
20. Novoselov, K. S.; McCann, E.; Morozov, S. V.; Fal'ko, V. I.; Katsnelson, M. I.; Zeitler, U.; Jiang, D.; Schedin, F.; Geim, A. K. Unconventional Quantum Hall Effect and Berry's Phase of 2π in Bilayer Graphene. Nat. Phys. 2006, 2, 177-180.
21. 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, 201-204.
22. Miller, D. L.; Kubista, K. D.; Rutter, G. M.; Ruan, M.; de Heer, W. A.; First, P. N.; Stroscio, J. A. Observing the Quantization of Zero Mass Carriers in Graphene. Science 2009, 324, 924-927.
23. Li, G.; Andrei, E. Y. Observation of Landau Levels of Dirac Fermions in Graphite. Nat. Phys. 2007, 3, 623-627.
24. Matsui, T.; Kambara, H.; Niimi, Y.; Tagami, K.; Tsukada, M.; Fukuyama, H. STS Observations of Landau Levels at Graphite Surfaces. Phys. Rev. Lett. 2005, 94, 226403.
25. Deacon, R. S.; Chuang, K.-C.; Nicholas, R. J.; Novoselov, K. S.; Geim, A. K. Cyclotron Resonance Study of the Electron and Hole Velocity in Graphene Monolayers. Phys. Rev. B 2007, 76, 081406.
26. Henriksen, E. A.; Jiang, Z.; Tung, L.-C.; Schwartz, M. E.; Takita, M.; Wang, Y.-J.; Kim, P.; Stormer, H. L. Cyclotron Resonance in Bilayer Graphene. Phys. Rev. Lett. 2008, 100, 087403.
27. McClure, J. W. Diamagnetism of Graphite. Phys. Rev. 1956, 104, 666-671.
28. Zheng, Y.; Ando, T. Hall Conductivity of a Two-Dimensional Graphite System. Phys. Rev. B 2002, 65, 245420.
29. Ho, J. H.; Lai, Y. H.; Chiu, Y. H.; Lin, M. F. Landau Levels in Graphene. Physica E 2008, 40, 1722-1725.
30. Koshino, M.; Ando, T. Magneto-Optical Properties of Multilayer Graphene. Phys. Rev. B 2008, 77, 115313.
31. Sadowski, M. L.; Martinez, G.; Potemski, M.; Berger, C.; de Heer, W. A. Landau Level Spectroscopy of Ultrathin Graphite Layers. Phys. Rev. Lett. 2006, 97, 266405.
32. Plochocka, P.; Faugeras, C.; Orlita, M.; Sadowski, M. L.; Martinez, G.; Potemski, M.; Goerbig, M. O.; Fuchs, J.-N.; Berger, C.; de Heer, W. A. High-Energy Limit of Massless Dirac Fermions in Multilayer Graphene Using Magneto-Optical Transmission Spectroscopy. Phys. Rev. Lett. 2008, 100, 087401.
33. Benfatto, L.; Sharapov, S. G.; Carbotte, J. P. Robustness of the Optical Conductivity Sum Rule in Bilayer Graphene. Phys. Rev. B 2008, 77, 125422.
34. Nicol, E. J.; Carbotte, J. P. Optical Conductivity of Bilayer Graphene with and without an Asymmetry Gap. Phys. Rev. B 2008, 77, 155409.
35. Mucha-Kruczyński, M.; Abergel, D. S. L.; McCann, E.; Fal'ko, V. I. On Spectral Properties of Bilayer Graphene: The Effect of an SiC Substrate and Infrared Magneto-Spectroscopy. J. Phys.: Condens. Matter 2009, 21, 344206.
36. Mucha-Kruczyński, M.; McCann, E.; Fal'ko, V. I. The Influence of Interlayer Asymmetry on The Magnetospectroscopy of Bilayer Graphene. Solid State Commun. 2009, 149, 1111-1116.
37. Chang, C. P.; Lu, C. L.; Shyu, F. L.; Chen, R. B.; Fang, Y. K.; Lin, M. F. Magnetoelectronic Properties of a Graphite Sheet. Carbon 2004, 42, 2975-2980.
38. Chiu, Y. H.; Lai, Y. H.; Ho, J. H.; Chuu, D. S.; Lin, M. F. Electronic Structure of a Two-Dimensional Graphene Monolayer in a Spatially Modulated Magnetic Field: Peierls Tight-Binding Model. Phys. Rev. B 2008, 77, 045407.
39. Ho, J. H.; Lai, Y. H.; Chiu, Y. H.; Lin, M. F. Modulation Effects on Landau Levels in a Monolayer Graphene. Nanotechnology 2008, 19, 035712.
40. Huang, Y. C.; Chang, C. P.; Lin, M. F. Magnetic and Quantum Confinement Effects on Electronic and Optical Properties of Graphene Ribbons. Nanotechnology 2007, 18, 495401.
41. Chiu, Y. H.; Ho, J. H.; Chang, C. P.; Chuu, D. S.; Lin, M. F. Low-Frequency Magneto-Optical Excitations of a Graphene Monolayer: Peierls Tight-Binding Model and Gradient Approximation Calculation. Phys. Rev. B 2008, 78, 245411.
42. Huang, Y. C.; Lin, M. F.; Chang, C. P. Landau Levels and Magneto-Optical Properties of Graphene Ribbons. J. Appl. Phys. 2008, 103, 073709.
43. Lin, M. F.; Shung, K. W.-K. Plasmons and Optical Properties of Carbon Nanotubes. Phys. Rev. B 1994, 50, 17744-17747.
44. Johnson, J. G.; Dresselhaus, G. Optical Properties of Graphite. Phys. Rev. B 1979, 7, 2275-2285.
45. Chuang, K.-C.; Baker, A. M. R.; Nicholas, R. J. Magnetoabsorption Study of Landau Levels in Graphite. Phys. Rev. B 2009, 80, 161410(R).
46. Ho, Y. H.; Chiu, Y. H.; Lin, M. F. Unpublished results.