From optical graphene to topological insulator

Transcription

1 From optical graphene to topological insulator Xiangdong Zhang Beijing Institute of Technology (BIT), China Collaborator: Wei Zhong (PhD student, BNU)

2 Outline Background: From solid state physics to Photonic Crystal Photonic monolayer graphene materials Multilayer photonic graphene materials Dirac-cone photonic surface states Probing photonic surface states by STEM Summary

3 1.Background (1) Corresponding between disorder system for electrons and wave in random medium Disorder electron system 1984 Wave in random medium Ballistic Diffusion Weak localization Anderson localization (2) Corresponding between electron and wave system for periodic and quasi-periodic structures Solid state physics (electron system) 1987 Photonic or phononic crystal

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5 Various applications based on photonic crystals Cavity and laser Optical fibers Waveguide Channel drop filter

6 Unusual features of wave in the band regions Negative refraction, self-collimation, ultrarefraction Some devices such as flat lens, splitter can be done

7 X. Zhang, Phys. Rev. B, 70, (2004)

8 Recent progress in Condensed Matter Physics: graphene material Science 306, 666 (2004) carbon atom

9 The physical properties of graphene materials (1) The quasiparticle excitations around the Dirac point obey linear Dirac-like energy dispersion (Rev. Mod. Phys. 80, 1337 (2008)). (2) Chiral tunnelling and Klein paradox, Zitterbewegung Nature physics 2, 621 (2006); Phys. Rev. B 76, (2007)

10 (3) Edge states (Rev. Mod. Phys. 81, 109 (2009)) Nature London 438, 197 (2005); 438, 201 (2005). (4) Unconventional quantum Hall effect, Andreev reflection

11 (5) Optical properties of graphene A graphene-based broadband optical modulator Transformation Optics Using Graphene M. Liu et. al., Nature 4 7 4, 64 (2011) Ashkan Vakil, et al., Science 332, 1291 (2011)

12 The question: Can we construct a nanostructure to control light similar to the graphene to control electrons?

13 2. Photonic monolayer graphene materials (a) 2D systems

14 not around Dirac point not Diffusion behavior similar to the case in random medium

15 for gap for band

16 diffusion behavior X. Zhang, Phys. Lett. A 372, 3512 (2008)

17 Ballistic behavior Near Dirac point Diffusion behavior Corresponding to the gap region X. Zhang, Phys. Rev. Lett. 100, (2008)

18 Why? The phenomenon originates from the crossed linear dispersion around the Dirac point Two linear resolutions of Dirac equation

19 Dirac Equation inside the sample Maxwell equation outside the sample Applying boundary condition of flux conservation Sepkhanov,et.al Phys. Rev A 75, (2007)

20 Some interesting phenomena can be observed Zitterbewegung for photon and acoustic wave X. Zhang, Phys. Rev. Lett. 100, (2008) X.Zhang and Z. Liu, Phys. Rev. Lett. 101, (2008)

21 valley beam splitter or collimator J. L. Garcia-Pomar, Phys. Rev. Lett. 100, (2008)

22 Electromagnetic one-way edge modes analogous to quantum Hall edge states F. D. M. Haldane, Phys. Rev. Lett. 100, (2008) Zheng Wang,et.al., Phys. Rev. Lett. 100, (2008) Zongfu Yu, et. al., Phys. Rev. Lett. 100, (2008)

23 Dirac cones induced by accidental degeneracy and zero-refractive-index materials X. Huang et. al., Nature Materials 10, 582 (2011)

24 (b) Monolayer graphene consisting of metal spheres dipole and quadrupole modes. Dezhuan Han, et. al., Phys. Rev. Lett. 102, (2009)

25 (c) Monolayer acoustic graphene consisting of spheres Steel spheres in air, R=0.28a ρ=7670kg/m3 cl=6010m/s ct=3230m/s Rubber spheres in water with R=0.2a

26 Wei Zhong and X. Zhang, Phys. Lett. A 375, 3533 (2011)

27 Wei Zhong and Xiangdong Zhang, Phys. Lett. A 375, 3533 (2011)

28 3. Multilayer photonic graphene materials (1) Multilayer graphene for electrons The electronic properties strongly depend on the stacking sequence

29 \pi band

30 Transition between metallic state and insulator The problem: can we find the similar phenomena for the photon?

31 (b) Multilayer photonic graphene Three types of stacking: every layer consisting of metallic sphere, which the Drude-type permittivity The radius of the sphere is 10nm; the lattice constant a=60nm

32 Multiple scattering method to calculate energy spectra of three-dimensional photonic crystal slab N l i + E + E ( ) exp( ) ( ) ( ˆ sc r = bjlm ik Rn hl qrnj X lm rnj ) j= 1 l= 1 m= l q Rn + H + + b exp( ) ( ) ( ˆ jlm ik Rn hl qrnj X lm rnj ). Rn l ' i E H E ( ) ( ) ( ˆˆ j sc r = b j lm jl qrnj X lm rnj ) + b j lm jl ( qrnj ) X lm( rnj ), l= 1 m= l q b T b a + N P P PP P 0P jlm = jlm Ω + jlm, j l m j l m + jlm j = 1 P = E, H lm. det δ δ δ δ Ω T = 0, PP P PP jj ll mm jlm, j l m jlm, j l m lmp Wei Zhong and X. Zhang, Phys. Rev. A 84, (2011)

33 AAA stacking N=2 Wei Zhong and Xiangdong Zhang, Phys. Rev. A 84, (2011)

34 ABA stacking (Bernal) N=2 N=3 Parabolic d=1.0a N=4 N=5 Corresponding electron system Wei Zhong and Xiangdong Zhang, Phys. Rev. A 84, (2011)

35 ABC stacking (Rhombohedral) N=3 N=4 d=1.0a N=5 N=6 Corresponding electron system Wei Zhong and Xiangdong Zhang, Phys. Rev. A 84, (2011)

36 Similar energy spectra for the electron in multilayer graphenes have been observed for the photon in the present photonic graphene structures. This means that the transport properties of light similar to the case of electrons in multilayer graphene can be realized by constructing photonic nanostructures. our findings provide a way to control the transport of light similar to the multilayer graphene for electrons.

37 4. Dirac-cone photonic surface states (1) Topological insulator for electrons Dirac-cone surface state

38 topological insulator The number of holes is called genus in topology =

39 (2) Dirac-cone photonic surface states (CAABB ) type I (CCBB.) type II 3D photonic crystal slab in diamond [111] planes with 7 monolayers, every monolayer consisting of metallic spheres coated by dielectric layer. The metallo-dielectric spheres

40 type I surface coating layer is 2% in radius

41 type II surfaces surface state with a single Dirac cone The coating layer is radius 10% in radius Phys. Rev. Lett. 105, Wei Zhong and X. Zhang, Optics. Express 19, (2011)

42 The thickness of the dielectric coating 10%, 20%, 30%, 40%, 50%, 60% and 65% of the sphere radius

43 3D PC High 16 Layers, length (10a) width (11a) NA=0.3 Guide mode Mode gap Dirac point Wei Zhong and Xiangdong Zhang, Optics. Express 19, (2011)

44 5. Probing photonic surface states by STEM STEM (or EELS) and Dielectric Materials STEM:scanning transmission electron microscopy

45 The basic principle of STEM is that we can obtain some information of dielectric material from electron energy loss spectroscopy (EELS). The interaction between a moving charged particle (Ze) with velocity V and dielectric materials

46 STEM and EELS are important tools to probe the structure and the physical properties of the dielectric materials Recent investigations have shown that some unusual properties of linear metamaterials can be explored by STEM or EELS. J. Xu, Y. Dong, and X. Zhang, Phys. Rev. E 78, (2008); Phys. Lett. A, 372(2008); Opt. Express 17, 4758 (2009)

47 sc E = d tv E ( r, t) = ωd ωp( ω). t 0 1 iωt sc P( ω) = d tre{ e v E ( r t, ω)}. πω

48 6. Summary 1. We have developed the multiple scattering method to study energy spectra and surface states of 3D phononic crystal slab. 2. We have demonstrated multilayer photonic graphene and found Dirac-cone photonic surface states, they can be probed by STEM. Electron multilayer graphene Electron topological insulator photonic graphene Dirac-cone photonic surface states

49 Other related works (1) Second harmonic generation and nonlinear Smith-Purcell effect J. Xu and Xiangdong Zhang, Optics Express 20, 1669 (2012) J. Xu and Xiangdong Zhang, Optics Express 19, (2011) Y. liu, J.Xu and Xiangdong Zhang, J. Optics (in press) (2012) (2) Photon entangled states by nonlinear photonic crystal Y. Dong and X. Zhang, Phys. Rev. A. 81, (2010). S. Wei, Y. Dong, H. Wang and X. Zhang, Phys. Rev. A. 81, (2010). Y. Dong and Xiangdong Zhang, Optics Express 16, (2008) Y. Dong and Xiangdong Zhang, J. Optics 13, (2011)

50 (3) Unusual light spin Hall effect Hailei Wang and Xiangdong Zhang, Phys. Rev.A 83, (2011) Hailei Wang and Xiangdong Zhang, J. Opt. Soc. Am. B (2012) (4)The holographic method to fabricate the circular photonic crystals and microlaser T. Zhai, Y. Zhou, S. Chen, Z. Wang, J. Shi, D. Liu and X. D. Zhang, Phys. Rev. A 82, (2010) T. Zhai, Z. Wang, R. Zhao, J. Zhou, D. Liu, and X. Zhang, Appl. Phys. Lett. 93, (2008) Z. Ren, Z. Wang, T. Zhai, H. Gao, D Liu and X. Zhang, Phys. Rev. B. 76, (2007). (5) Correlated optics and ghost image S. Gan, S-H Zhang, J. Xiong, X. Zhang and K. Wang, Appl. Phys. Lett. 98, (2011) S-H Zhang, S. Gan, J. Xiong, X. Zhang and K. Wang, Phys. Rev. A. 82, (R) (2 S-H Zhang, S. Gan, D-Z Cao, J. Xiong, X. Zhang and K. Wang, Phys. Rev. A. 80, (R) (2009)

51 Experimental Observation of Quantum Talbot Effects X-B Song, H-B Wang, J Xiong, K Wang, X. Zhang, Phys. Rev. Lett. 107, (2011) X-B Song, J. Xiong, X. Zhang, and K. Wang, Phys. Rev. A 82, (2010).

52 Thanks for your attention!