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Deterministic interface states in photonic crystal with graphene-allotrope-like complex unit cells

Jia Zi-Yuan Yang Yu-Ting Ji Li-Yu Hang Zhi-Hong

Deterministic interface states in photonic crystal with graphene-allotrope-like complex unit cells

Jia Zi-Yuan, Yang Yu-Ting, Ji Li-Yu, Hang Zhi-Hong
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  • Topological insulators have aroused much research interest in condensed matter physics in recent years. Topological protected edge states can propagate unidirectionally and backscattering free along the boundaries of the topological insulators' which will be important for future electronic devices for its immunity to defects. Topology is dependent only on the symmetry of lattice of the system rather than its specific wave form. Thus, based on the analogy between electronics and photons, photonic topological insulator has also been demonstrated both theoretically and experimentally. Graphene, composed of a monolayer of carbon atoms in honeycomb lattice, exhibits unusual properties due to its intriguing band diagram. Many types of graphene allotropes have been proposed theoretically. However, due to fabrication difficulties, most of graphene allotropes are unavailable. Here, we propose to study two dimensional (2D) photonic crystal (PC) with complex lattices, similar to that of graphene allotrope. The complex PC structure provides more degrees of freedom in manipulating its symmetry.Interface states can also exist in the interface region between two PCs, if they have different topological properties. Without any surface decoration, deterministic interface states can be created when bulk photonic band inversion can be induced and are demonstrated theoretically and experimentally in 2D PCs with square lattice. By controlling the parameters of PCs, their bulk photonic band properties are engineered and topological phase transition occurs. By inverting the bulk photonic band properties, interface states exist in the common band gaps for two PC systems in the gapped region. Similarly, we proceed to complex honeycomb lattice of PCs. By lowering its original C6v symmetry to C3v, C3, C2v and even C2 symmetry, the degeneracies of valley Dirac dispersion at the corners of Brillouin zone are lifted. Photonic band inversion occurs in all four symmetries and the deterministic interface states are numerically realized in the interface region between two PCs. Unidirectional propagation of interface state immune to backscattering along the interface channels is demonstrated if a source with proper optical vortex index is utilized. Due to its easy fabrication, PC is a perfect platform to explore the topological properties of complex lattice and these acquired topological optical states can be of benefit to the control the propagation of light in the photonic waveguide.
      Corresponding author: Hang Zhi-Hong, zhhang@suda.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11574226), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20170058), and the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions, China.
    [1]

    Klitzing K V, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494

    [2]

    Thouless D J, Kohmoto M, Nightingale M P, den Nijs M 1982 Phys. Rev. Lett. 49 405

    [3]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802

    [4]

    Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666

    [5]

    Yablonovitch E 1987 Phys. Rev. Lett. 58 2059

    [6]

    John S 1987 Phys. Rev. Lett. 58 2486

    [7]

    Sakoda K 2004 Optical Properties of Photonic Crystals (2nd Ed.) (Berlin: Springer)

    [8]

    Joannopoulos J D, Johnson S G, Winn J N, Meade R D 2008 Photonic Crystals: Molding the Flow of Light (2nd Ed.) (New Jersey: Princeton University Press)

    [9]

    Mekis A, Chen J C, Kurland I, Fan S, Villeneuve P R, Joannopoulos J D 1996 Phys. Rev. Lett. 77 3787

    [10]

    Lin S Y, Chow E, Hietala V, Villeneuve P R, Joannopoulos J D 1998 Science 282 274

    [11]

    Robertson W M, Arjavalingam G, Meade R D, Brommer K D, Rappe A M, Joannopoulos J D 1993 Opt. Lett. 18 528

    [12]

    Istrate E, Sargent E H 2006 Rev. Mod. Phys. 78 455

    [13]

    Guo J, Sun Y, Zhang Y, Li H, Jiang H, Chen H 2008 Phys. Rev. E 78 026607

    [14]

    Meade R D, Brommer K D, Rappe A M, Joannopoulos J D 1991 Phys. Rev. B 44 10961

    [15]

    Ramos-Mendieta F, Halevi P 1999 Phys. Rev. B 59 15112

    [16]

    Choi H G, Oh S S, Lee S G, Kim M W, Kim J E, Park H Y, Kee C S 2006 J. Appl. Phys. 100 123105

    [17]

    Xiao M, Zhang Z Q, Chan C T 2014 Phys. Rev. X 4 021017

    [18]

    Huang X Q, Xiao M, Zhang Z Q, Chan C T 2014 Phys.Rev. B 90 075423

    [19]

    Yang Y T, Huang X Q, Hang Z H 2016 Phys. Rev. Appl. 5 034009

    [20]

    Huang X Q, Yang Y T, Hang Z H, Zhang Z Q, Chan C T 2016 Phys. Rev. B 93 085415

    [21]

    Yang Y T, Xu T, Xu X F, Hang Z H 2017 Opt. Lett. 42 3085

    [22]

    Rycerz A, Jakub T J, Beenakker C W J 2007 Nature Phys. 3 172

    [23]

    Xu X D, Yao W, Xiao D, Heinz T F 2014 Nature Phys. 10 343

    [24]

    Garcia-Pomar J L, Cortijo A, Nieto-Vesperinas M 2008 Phys. Rev. Lett. 100 236801

    [25]

    Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett. 99 236809

    [26]

    Mak K F, McGill K L, Park J, McEuen P L 2014 Science 344 1489

    [27]

    Enyashin A N, Ivanovskii A L 2011 Phys. Status Solidi 248 1879

    [28]

    Huang X Q, Lai Y, Hang Z H, Zheng H H, Chan C T 2011 Nature Mater. 10 582

    [29]

    Yang Y T, Xu Y F, Xu T, Wang H X, Jiang J H, Hu X, Hang Z H 2016 arXiv:1610.07780v1

  • [1]

    Klitzing K V, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494

    [2]

    Thouless D J, Kohmoto M, Nightingale M P, den Nijs M 1982 Phys. Rev. Lett. 49 405

    [3]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802

    [4]

    Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666

    [5]

    Yablonovitch E 1987 Phys. Rev. Lett. 58 2059

    [6]

    John S 1987 Phys. Rev. Lett. 58 2486

    [7]

    Sakoda K 2004 Optical Properties of Photonic Crystals (2nd Ed.) (Berlin: Springer)

    [8]

    Joannopoulos J D, Johnson S G, Winn J N, Meade R D 2008 Photonic Crystals: Molding the Flow of Light (2nd Ed.) (New Jersey: Princeton University Press)

    [9]

    Mekis A, Chen J C, Kurland I, Fan S, Villeneuve P R, Joannopoulos J D 1996 Phys. Rev. Lett. 77 3787

    [10]

    Lin S Y, Chow E, Hietala V, Villeneuve P R, Joannopoulos J D 1998 Science 282 274

    [11]

    Robertson W M, Arjavalingam G, Meade R D, Brommer K D, Rappe A M, Joannopoulos J D 1993 Opt. Lett. 18 528

    [12]

    Istrate E, Sargent E H 2006 Rev. Mod. Phys. 78 455

    [13]

    Guo J, Sun Y, Zhang Y, Li H, Jiang H, Chen H 2008 Phys. Rev. E 78 026607

    [14]

    Meade R D, Brommer K D, Rappe A M, Joannopoulos J D 1991 Phys. Rev. B 44 10961

    [15]

    Ramos-Mendieta F, Halevi P 1999 Phys. Rev. B 59 15112

    [16]

    Choi H G, Oh S S, Lee S G, Kim M W, Kim J E, Park H Y, Kee C S 2006 J. Appl. Phys. 100 123105

    [17]

    Xiao M, Zhang Z Q, Chan C T 2014 Phys. Rev. X 4 021017

    [18]

    Huang X Q, Xiao M, Zhang Z Q, Chan C T 2014 Phys.Rev. B 90 075423

    [19]

    Yang Y T, Huang X Q, Hang Z H 2016 Phys. Rev. Appl. 5 034009

    [20]

    Huang X Q, Yang Y T, Hang Z H, Zhang Z Q, Chan C T 2016 Phys. Rev. B 93 085415

    [21]

    Yang Y T, Xu T, Xu X F, Hang Z H 2017 Opt. Lett. 42 3085

    [22]

    Rycerz A, Jakub T J, Beenakker C W J 2007 Nature Phys. 3 172

    [23]

    Xu X D, Yao W, Xiao D, Heinz T F 2014 Nature Phys. 10 343

    [24]

    Garcia-Pomar J L, Cortijo A, Nieto-Vesperinas M 2008 Phys. Rev. Lett. 100 236801

    [25]

    Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett. 99 236809

    [26]

    Mak K F, McGill K L, Park J, McEuen P L 2014 Science 344 1489

    [27]

    Enyashin A N, Ivanovskii A L 2011 Phys. Status Solidi 248 1879

    [28]

    Huang X Q, Lai Y, Hang Z H, Zheng H H, Chan C T 2011 Nature Mater. 10 582

    [29]

    Yang Y T, Xu Y F, Xu T, Wang H X, Jiang J H, Hu X, Hang Z H 2016 arXiv:1610.07780v1

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  • Received Date:  24 July 2017
  • Accepted Date:  13 August 2017
  • Published Online:  20 November 2017

Deterministic interface states in photonic crystal with graphene-allotrope-like complex unit cells

    Corresponding author: Hang Zhi-Hong, zhhang@suda.edu.cn
  • 1. College of Physics, Optoelectronics and Energy and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11574226), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20170058), and the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions, China.

Abstract: Topological insulators have aroused much research interest in condensed matter physics in recent years. Topological protected edge states can propagate unidirectionally and backscattering free along the boundaries of the topological insulators' which will be important for future electronic devices for its immunity to defects. Topology is dependent only on the symmetry of lattice of the system rather than its specific wave form. Thus, based on the analogy between electronics and photons, photonic topological insulator has also been demonstrated both theoretically and experimentally. Graphene, composed of a monolayer of carbon atoms in honeycomb lattice, exhibits unusual properties due to its intriguing band diagram. Many types of graphene allotropes have been proposed theoretically. However, due to fabrication difficulties, most of graphene allotropes are unavailable. Here, we propose to study two dimensional (2D) photonic crystal (PC) with complex lattices, similar to that of graphene allotrope. The complex PC structure provides more degrees of freedom in manipulating its symmetry.Interface states can also exist in the interface region between two PCs, if they have different topological properties. Without any surface decoration, deterministic interface states can be created when bulk photonic band inversion can be induced and are demonstrated theoretically and experimentally in 2D PCs with square lattice. By controlling the parameters of PCs, their bulk photonic band properties are engineered and topological phase transition occurs. By inverting the bulk photonic band properties, interface states exist in the common band gaps for two PC systems in the gapped region. Similarly, we proceed to complex honeycomb lattice of PCs. By lowering its original C6v symmetry to C3v, C3, C2v and even C2 symmetry, the degeneracies of valley Dirac dispersion at the corners of Brillouin zone are lifted. Photonic band inversion occurs in all four symmetries and the deterministic interface states are numerically realized in the interface region between two PCs. Unidirectional propagation of interface state immune to backscattering along the interface channels is demonstrated if a source with proper optical vortex index is utilized. Due to its easy fabrication, PC is a perfect platform to explore the topological properties of complex lattice and these acquired topological optical states can be of benefit to the control the propagation of light in the photonic waveguide.

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