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Dirac-cone photonic surface states in three-dimensional photonic crystal slabWei Zhong and Xiangdong Zhang »View Author Affiliations
Wei Zhong
and Xiangdong Zhang*
Department of Physics, Beijing Normal University, Beijing 100875, China, *Corresponding author: zhangxd@bnu.edu.cn |
Optics Express, Vol. 19, Issue 15, pp. 13738-13749 (2011)
http://dx.doi.org/10.1364/OE.19.013738
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Abstract
We present a multiple-scattering method in conjunction with supercell calculations to study the electromagnetic surface states in three-dimensional photonic crystal slab. Using our technique, we obtain the first prediction of Dirac-cone photonic surface state in some three-dimensional photonic crystal slabs. Such a state can be used to investigate some extremal transmission phenomena of electromagnetic waves near the Dirac point on the surface of the crystal, which is similar to the case of electron on the surface of topological insulators.
© 2011 OSA
OCIS Codes
(240.0240) Optics at surfaces : Optics at surfaces
(160.5298) Materials : Photonic crystals
ToC Category:
Photonic Crystals
History
Original Manuscript: April 26, 2011
Revised Manuscript: June 10, 2011
Manuscript Accepted: June 19, 2011
Published: July 1, 2011
Citation
Wei Zhong and Xiangdong Zhang, "Dirac-cone photonic surface states in three-dimensional photonic crystal slab," Opt. Express 19, 13738-13749 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-13738
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- T. Zhang, P. Cheng, X. Chen, J.-F. Jia, X. Ma, K. He, L. Wang, H. Zhang, X. Dai, Z. Fang, X. Xie, and Q.-K. Xue, “Experimental demonstration of topological surface states protected by time-reversal symmetry,” Phys. Rev. Lett. 103(26), 266803 (2009). [CrossRef] [PubMed]
- H. J. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys. 5(6), 438–442 (2009). [CrossRef]
- D. Hsieh, Y. Xia, D. Qian, L. Wray, F. Meier, J. H. Dil, J. Osterwalder, L. Patthey, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of time-reversal-protected single-dirac-cone topological-insulator states in Bi2Te3 and Sb2Te3,” Phys. Rev. Lett. 103(14), 146401 (2009). [CrossRef] [PubMed]
- D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, J. Osterwalder, L. Patthey, J. G. Checkelsky, N. P. Ong, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A tunable topological insulator in the spin helical Dirac transport regime,” Nature 460(7259), 1101–1105 (2009). [CrossRef] [PubMed]
- Y. L. Chen, J. G. Analytis, J. H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z. X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3,” Science 325(5937), 178–181 (2009). [CrossRef] [PubMed]
- H. Lin, R. S. Markiewicz, L. A. Wray, L. Fu, M. Z. Hasan, and A. Bansil, “Single-Dirac-cone topological surface states in the TlBiSe(2) class of topological semiconductors,” Phys. Rev. Lett. 105(3), 036404 (2010). [CrossRef] [PubMed]
- D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, J. Osterwalder, L. Patthey, J. G. Checkelsky, N. P. Ong, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A tunable topological insulator in the spin helical Dirac transport regime,” Nature 460(7259), 1101–1105 (2009). [CrossRef] [PubMed]
- D. Hsieh, Y. Xia, D. Qian, L. Wray, F. Meier, J. H. Dil, J. Osterwalder, L. Patthey, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of time-reversal-protected single-dirac-cone topological-insulator states in Bi2Te3 and Sb2Te3,” Phys. Rev. Lett. 103(14), 146401 (2009). [CrossRef] [PubMed]
- Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5(6), 398–402 (2009). [CrossRef]
- S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008). [CrossRef]
- F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008). [CrossRef] [PubMed]
- F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59(23), 15112–15120 (1999). [CrossRef]
- F. S. Ham and B. Segall, “Energy bands in periodic lattices: Green’s function method,” Phys. Rev. 124(6), 1786–1796 (1961). [CrossRef]
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- D. Hsieh, Y. Xia, D. Qian, L. Wray, F. Meier, J. H. Dil, J. Osterwalder, L. Patthey, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of time-reversal-protected single-dirac-cone topological-insulator states in Bi2Te3 and Sb2Te3,” Phys. Rev. Lett. 103(14), 146401 (2009). [CrossRef] [PubMed]
- D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G. Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of unconventional quantum spin textures in topological insulators,” Science 323(5916), 919–922 (2009). [CrossRef] [PubMed]
- Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5(6), 398–402 (2009). [CrossRef]
- D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A topological Dirac insulator in a quantum spin Hall phase,” Nature 452(7190), 970–974 (2008). [CrossRef] [PubMed]
- H. Lin, R. S. Markiewicz, L. A. Wray, L. Fu, M. Z. Hasan, and A. Bansil, “Single-Dirac-cone topological surface states in the TlBiSe(2) class of topological semiconductors,” Phys. Rev. Lett. 105(3), 036404 (2010). [CrossRef] [PubMed]
- D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G. Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of unconventional quantum spin textures in topological insulators,” Science 323(5916), 919–922 (2009). [CrossRef] [PubMed]
- Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5(6), 398–402 (2009). [CrossRef]
- D. Hsieh, Y. Xia, D. Qian, L. Wray, F. Meier, J. H. Dil, J. Osterwalder, L. Patthey, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of time-reversal-protected single-dirac-cone topological-insulator states in Bi2Te3 and Sb2Te3,” Phys. Rev. Lett. 103(14), 146401 (2009). [CrossRef] [PubMed]
- D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, J. Osterwalder, L. Patthey, J. G. Checkelsky, N. P. Ong, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A tunable topological insulator in the spin helical Dirac transport regime,” Nature 460(7259), 1101–1105 (2009). [CrossRef] [PubMed]
- D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A topological Dirac insulator in a quantum spin Hall phase,” Nature 452(7190), 970–974 (2008). [CrossRef] [PubMed]
- T. Zhang, P. Cheng, X. Chen, J.-F. Jia, X. Ma, K. He, L. Wang, H. Zhang, X. Dai, Z. Fang, X. Xie, and Q.-K. Xue, “Experimental demonstration of topological surface states protected by time-reversal symmetry,” Phys. Rev. Lett. 103(26), 266803 (2009). [CrossRef] [PubMed]
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- E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987). [CrossRef] [PubMed]
- N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113(1), 49–77 (1998). [CrossRef]
- S. R. Zandbergen and M. J. A. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104(4), 043903 (2010). [CrossRef] [PubMed]
- T. Zhang, P. Cheng, X. Chen, J.-F. Jia, X. Ma, K. He, L. Wang, H. Zhang, X. Dai, Z. Fang, X. Xie, and Q.-K. Xue, “Experimental demonstration of topological surface states protected by time-reversal symmetry,” Phys. Rev. Lett. 103(26), 266803 (2009). [CrossRef] [PubMed]
- H. J. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys. 5(6), 438–442 (2009). [CrossRef]
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- H. J. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys. 5(6), 438–442 (2009). [CrossRef]
- T. Zhang, P. Cheng, X. Chen, J.-F. Jia, X. Ma, K. He, L. Wang, H. Zhang, X. Dai, Z. Fang, X. Xie, and Q.-K. Xue, “Experimental demonstration of topological surface states protected by time-reversal symmetry,” Phys. Rev. Lett. 103(26), 266803 (2009). [CrossRef] [PubMed]
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Appl. Phys. Lett.
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Comput. Phys. Commun.
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Nat. Phys.
- H. J. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys. 5(6), 438–442 (2009). [CrossRef]
- Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5(6), 398–402 (2009). [CrossRef]
Nature
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Opt. Express
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Phys. Rev. A
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Phys. Rev. B
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- X. Zhang, L.-M. Li, Z.-Q. Zhang, and C. Chan, “Surface states in two-dimensional metallodielectric photonic crystals studied by a multiple-scattering method,” Phys. Rev. B 63(12), 125114 (2001). [CrossRef]
- S. Enoch, E. Popov, and N. Bonod, “Analysis of the physical origin of surface modes on finite-size photonic crystals,” Phys. Rev. B 72(15), 155101 (2005). [CrossRef]
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Phys. Rev. B Condens. Matter
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Phys. Rev. Lett.
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- D. Hsieh, Y. Xia, D. Qian, L. Wray, F. Meier, J. H. Dil, J. Osterwalder, L. Patthey, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of time-reversal-protected single-dirac-cone topological-insulator states in Bi2Te3 and Sb2Te3,” Phys. Rev. Lett. 103(14), 146401 (2009). [CrossRef] [PubMed]
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Phys. Today
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Physica A
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Science
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Other
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2010, Moore, Nature
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- X.-L. Qi and S.-C. Zhang, “The quantum spin Hall effect and topological insulators,” Phys. Today 63(1), 33 (2010). [CrossRef]
- H. Lin, R. S. Markiewicz, L. A. Wray, L. Fu, M. Z. Hasan, and A. Bansil, “Single-Dirac-cone topological surface states in the TlBiSe(2) class of topological semiconductors,” Phys. Rev. Lett. 105(3), 036404 (2010). [CrossRef] [PubMed]
- S. R. Zandbergen and M. J. A. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104(4), 043903 (2010). [CrossRef] [PubMed]
- K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009). [CrossRef] [PubMed]
- D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G. Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of unconventional quantum spin textures in topological insulators,” Science 323(5916), 919–922 (2009). [CrossRef] [PubMed]
- Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5(6), 398–402 (2009). [CrossRef]
- Y. L. Chen, J. G. Analytis, J. H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z. X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3,” Science 325(5937), 178–181 (2009). [CrossRef] [PubMed]
- D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, J. Osterwalder, L. Patthey, J. G. Checkelsky, N. P. Ong, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A tunable topological insulator in the spin helical Dirac transport regime,” Nature 460(7259), 1101–1105 (2009). [CrossRef] [PubMed]
- D. Hsieh, Y. Xia, D. Qian, L. Wray, F. Meier, J. H. Dil, J. Osterwalder, L. Patthey, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of time-reversal-protected single-dirac-cone topological-insulator states in Bi2Te3 and Sb2Te3,” Phys. Rev. Lett. 103(14), 146401 (2009). [CrossRef] [PubMed]
- H. J. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys. 5(6), 438–442 (2009). [CrossRef]
- T. Zhang, P. Cheng, X. Chen, J.-F. Jia, X. Ma, K. He, L. Wang, H. Zhang, X. Dai, Z. Fang, X. Xie, and Q.-K. Xue, “Experimental demonstration of topological surface states protected by time-reversal symmetry,” Phys. Rev. Lett. 103(26), 266803 (2009). [CrossRef] [PubMed]
- X. D. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100(11), 113903 (2008). [CrossRef] [PubMed]
- X. D. Zhang and Z. Y. Liu, “Extremal transmission and beating effect of acoustic waves in two-dimensional sonic crystals,” Phys. Rev. Lett. 101(26), 264303 (2008). [CrossRef] [PubMed]
- F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008). [CrossRef] [PubMed]
- S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008). [CrossRef]
- D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A topological Dirac insulator in a quantum spin Hall phase,” Nature 452(7190), 970–974 (2008). [CrossRef] [PubMed]
- R. A. Sepkhanov, Ya. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75(6), 063813 (2007). [CrossRef]
- B. A. Bernevig and S. C. Zhang, “Quantum spin Hall effect,” Phys. Rev. Lett. 96(10), 106802 (2006). [CrossRef] [PubMed]
- C. L. Kane and E. J. Mele, “Z2 topological order and the quantum spin Hall effect,” Phys. Rev. Lett. 95(14), 146802 (2005). [CrossRef] [PubMed]
- S. Enoch, E. Popov, and N. Bonod, “Analysis of the physical origin of surface modes on finite-size photonic crystals,” Phys. Rev. B 72(15), 155101 (2005). [CrossRef]
- X. Zhang, L.-M. Li, Z.-Q. Zhang, and C. Chan, “Surface states in two-dimensional metallodielectric photonic crystals studied by a multiple-scattering method,” Phys. Rev. B 63(12), 125114 (2001). [CrossRef]
- W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, “Robust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84(13), 2853–2856 (2000). [CrossRef] [PubMed]
- A. Moroz, “Three-dimensional complete photonic-band-gap structures in the visible,” Phys. Rev. Lett. 83(25), 5274–5277 (1999). [CrossRef]
- F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59(23), 15112–15120 (1999). [CrossRef]
- W. M. Robertson and M. S. May, “Surface electromagnetic wave excitation on one-dimensional photonic band-gap arrays,” Appl. Phys. Lett. 74(13), 1800–1803 (1999). [CrossRef]
- N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113(1), 49–77 (1998). [CrossRef]
- P. Etchegoin and R. T. Phillips, “Photon focusing, internal diffraction, and surface states in periodic dielectric structures,” Phys. Rev. B Condens. Matter 53(19), 12674–12683 (1996). [CrossRef] [PubMed]
- J. Elson and P. Tran, “Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal,” Phys. Rev. B 54(3), 1711–1715 (1996). [CrossRef]
- R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44(19), R10961 (1991). [CrossRef]
- E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987). [CrossRef] [PubMed]
- S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987). [CrossRef] [PubMed]
- A. Modinos, “Scattering of electromagnetic waves by a plane of spheres-formalism,” Physica A 141(2-3), 575–588 (1987). [CrossRef]
- F. S. Ham and B. Segall, “Energy bands in periodic lattices: Green’s function method,” Phys. Rev. 124(6), 1786–1796 (1961). [CrossRef]
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