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Transport in 2D Complex Plasma Crystals

  • Evdokiya Georgieva Kostadinova
Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

In this chapter, we investigate numerically the transport properties of a 2D complex plasma crystal by examining the propagation of coplanar dust lattice waves. In the limit where the Hamiltonian interactions can be decoupled from the non-Hamiltonian effects, we identify two distinct regimes of wave transport: Anderson-type delocalization and long-distance excitation. We use the spectral approach to evaluate the contribution from the Anderson problem, i.e. to determine whether the initial lattice perturbation delocalized through nearest neighbor (short distance) interaction. The theoretical predictions are then compared against the results from a mulecular dynamics simulation. Any major deviations between the predicted and observed crystal dynamics are contributed to non-Hamiltonian effects. The benefit of our approach is twofold. First, the use of complex plasma system allows for tunability of the initial conditions and investigation of the transport problem at the kinetic level. In addition, the 2D dust crystal exhibit hexagonal symmetry, which makes it an ideal macroscopic analogue for materials, such as graphene. Second, the Hamiltonian part of the transport problem is analyzed using a theoretical approach, which determines delocalization in an infinite disordered system without the use of finite-size scaling or periodic boundary conditions. Thus, the comparison between theoretical and numerical results can be used to evaluate the effect of the actual physical boundaries and system size.

Here we focus on cases, where the wave did not spread far away from the initially perturbed dust particle, yet excitations are observed in remote parts of the lattice. In all simulations examined we established that long-distance excitations involve dust grains located around crystal defects. This makes sense physically since lattice defects consist of particles that are displaced from their position in the unperturbed lattice and are, therefore, in unstable equilibrium. In the decoupled Hamiltonian regime, the observed effects can be contributed to the dust lattice interaction with the plasma environment.

We start with a brief introduction to basic complex plasma physics concepts (Sect. 6.1). The use of the two-dimensional dust lattice as a macroscopic analogue for materials such as graphene is discussed in Sect. 6.2. Next, we provide an overview of transport problems in the classical regime and their application to non-Hamiltonian systems, such as the complex plasma crystals (Sect. 6.3). Section 6.4 presents the results from a series of numerical simulations, where an in-plane dust lattice wave is induced in a disordered 2D dust crystal. In Sect. 6.5 we analyze the dynamics of the crystal using the spectral approach and evaluate the contribution from non-Hamiltonian effects.

Keywords

Complex (dusty) plasma Long-distance interaction Anomalous transport 

Bibliography

  1. 1.
    G. Hebner, M. Riley, D. Johnson, P. Ho, R. Buss, Direct determination of particle-particle interactions in a 2D plasma dust crystal. Phys. Rev. Lett. 87(23), 235001 (2001)ADSCrossRefGoogle Scholar
  2. 2.
    K. Qiao, T.W. Hyde, Dispersion properties of the out-of-plane transverse wave in a two-dimensional Coulomb crystal. Phys. Rev. E 68(4), 046403 (2003)ADSCrossRefGoogle Scholar
  3. 3.
    P. Hartmann et al., Crystallization dynamics of a single layer complex plasma. Phys. Rev. Lett. 105, 115004 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    P. Hartmann, A. Kovács, A. Douglass, J. Reyes, L. Matthews, T. Hyde, Slow plastic creep of 2D dusty plasma solids. Phys. Rev. Lett. 113, 025002 (2014)ADSCrossRefGoogle Scholar
  5. 5.
    C.K. Goertz, Dusty plasmas in the solar system. Rev. Geophys. 27(2), 271–292 (1989)ADSCrossRefGoogle Scholar
  6. 6.
    T.G. Northrop, Dusty plasmas. Phys. Scr. 45(5), 475 (1992)ADSCrossRefGoogle Scholar
  7. 7.
    V.N. Tsytovich, Dust plasma crystals, drops, and clouds. Phys.-Uspekhi 40(1), 53 (1997)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    E.C. Whipple, Potentials of surfaces in space. Rep. Prog. Phys. 44(11), 1197 (1981)ADSCrossRefGoogle Scholar
  9. 9.
    P.A. Robinson, P. Coakley, Spacecraft charging-progress in the study of dielectrics and plasmas. IEEE Trans. Electr. Insul. 27(5), 944–960 (1992)ADSCrossRefGoogle Scholar
  10. 10.
    V.E. Fortov, A.G. Khrapak, S.A. Khrapak, V.I. Molotkov, O.F. Petrov, Dusty plasmas. Phys.-Uspekhi 47(5), 447–492 (2004)ADSCrossRefGoogle Scholar
  11. 11.
    P.K. Shukla, A.A. Mamun, Introduction to dusty plasma physics (CRC Press, 2001)Google Scholar
  12. 12.
    V.E. Fortov, A.V. Ivlev, S.A. Khrapak, A.G. Khrapak, G.E. Morfill, Complex (dusty) plasmas: current status, open issues, perspectives. Phys. Rep. 421(1–2), 1–103 (2005)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    H. Thomas, G.E. Morfill, V. Demmel, J. Goree, B. Feuerbacher, D. Möhlmann, Plasma crystal: coulomb crystallization in a dusty plasma. Phys. Rev. Lett. 73(5), 652–655 (1994)ADSCrossRefGoogle Scholar
  14. 14.
    Y. Hayashi, K. Tachibana, Observation of coulomb-crystal formation from carbon particles grown in a methane plasma. Jpn. J. Appl. Phys. 33(Part 2, 6A), L804–L806 (1994)ADSCrossRefGoogle Scholar
  15. 15.
    A.V. Filinov, M. Bonitz, Y.E. Lozovik, Wigner crystallization in mesoscopic 2D electron systems. Phys. Rev. Lett. 86(17), 3851–3854 (2001)ADSCrossRefGoogle Scholar
  16. 16.
    W.M. Itano, J.J. Bollinger, J.N. Tan, B. Jelenković, X.-P. Huang, D.J. Wineland, Bragg diffraction from crystallized ion plasmas. Science 279(5351), 686–689 (1998)ADSCrossRefGoogle Scholar
  17. 17.
    O. Arp, D. Block, A. Piel, A. Melzer, Dust coulomb balls: three-dimensional plasma crystals. Phys. Rev. Lett. 93(16), 165004 (2004)ADSCrossRefGoogle Scholar
  18. 18.
    M. Bonitz et al., Structural properties of screened coulomb balls. Phys. Rev. Lett. 96(7), 075001 (2006)ADSCrossRefGoogle Scholar
  19. 19.
    S. De Palo, F. Rapisarda, G. Senatore, Excitonic condensation in a symmetric electron-hole bilayer. Phys. Rev. Lett. 88(20), 206401 (2002)ADSCrossRefGoogle Scholar
  20. 20.
    M. Polini, F. Guinea, M. Lewenstein, H.C. Manoharan, V. Pellegrini, Artificial honeycomb lattices for electrons, atoms and photons. Nat. Nanotechnol. 8(9), 625–633 (2013)ADSCrossRefGoogle Scholar
  21. 21.
    P. Soltan-Panahi et al., Multi-component quantum gases in spin-dependent hexagonal lattices. Nat. Phys. 7(5), 434–440 (2011)CrossRefGoogle Scholar
  22. 22.
    K.K. Gomes, W. Mar, W. Ko, F. Guinea, H.C. Manoharan, Designer Dirac fermions and topological phases in molecular graphene. Nature 483(7389), 306–310 (2012)ADSCrossRefGoogle Scholar
  23. 23.
    Y. Plotnik et al., Observation of unconventional edge states in ‘photonic graphene. Nat. Mater. 13(1), 57–62 (2014)ADSCrossRefGoogle Scholar
  24. 24.
    M. Bellec, U. Kuhl, G. Montambaux, F. Mortessagne, Topological transition of Dirac points in a microwave experiment. Phys. Rev. Lett. 110(3), 033902 (2013)ADSCrossRefGoogle Scholar
  25. 25.
    S.P. Scheeler et al., Plasmon coupling in self-assembled gold nanoparticle-based honeycomb islands. J. Phys. Chem. C 117(36), 18634–18641 (2013)CrossRefGoogle Scholar
  26. 26.
    J. González, F. Guinea, M.A.H. Vozmediano, Electron-electron interactions in graphene sheets. Phys. Rev. B 63(13), 134421 (2001)ADSCrossRefGoogle Scholar
  27. 27.
    V.E. Fortov et al., Crystallization of a dusty plasma in the positive column of a glow discharge. J. Exp. Theor. Phys. Lett. 64(2), 92–98 (1996)CrossRefGoogle Scholar
  28. 28.
    R.A. Quinn, J. Goree, Experimental test of two-dimensional melting through disclination unbinding. Phys. Rev. E 64(5), 051404 (2001)ADSCrossRefGoogle Scholar
  29. 29.
    T.E. Sheridan, Monte Carlo study of melting in a finite two-dimensional dusty plasma. Phys. Plasmas 16(8), 083705 (2009)ADSCrossRefGoogle Scholar
  30. 30.
    V. Nosenko, S.K. Zhdanov, Dynamics of dislocations in a 2D plasma crystal. Contrib. Plasma Physics 49(4–5), 191–198 (2009)ADSCrossRefGoogle Scholar
  31. 31.
    V. Nosenko, S. Zhdanov, G. Morfill, Supersonic dislocations observed in a plasma crystal. Phys. Rev. Lett. 99(2), 025002 (2007)ADSCrossRefGoogle Scholar
  32. 32.
    S. Zhdanov et al., Dissipative dark solitons in a dc complex plasma. EPL Europhys. Lett. 89(2), 25001 (2010)ADSCrossRefGoogle Scholar
  33. 33.
    D.S. Wiersma, P. Bartolini, A. Lagendijk, R. Righini, Localization of light in a disordered medium. Nature 390(6661), 671–673 (1997)ADSCrossRefGoogle Scholar
  34. 34.
    R. Dalichaouch, J.P. Armstrong, S. Schultz, P.M. Platzman, S.L. McCall, Microwave localization by two-dimensional random scattering. Nature 354(6348), 53–55 (1991)ADSCrossRefGoogle Scholar
  35. 35.
    A.A. Chabanov, M. Stoytchev, A.Z. Genack, Statistical signatures of photon localization. Nature 404(6780), 850–853 (2000)ADSCrossRefGoogle Scholar
  36. 36.
    A.A. Chabanov, A.Z. Genack, Photon localization in resonant media. Phys. Rev. Lett. 87(15), 153901 (2001)ADSCrossRefGoogle Scholar
  37. 37.
    M. Störzer, P. Gross, C.M. Aegerter, G. Maret, Observation of the critical regime near Anderson localization of light. Phys. Rev. Lett. 96(6), 063904 (2006)ADSCrossRefGoogle Scholar
  38. 38.
    T. Schwartz, G. Bartal, S. Fishman, M. Segev, Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446(7131), 52–55 (2007)ADSCrossRefGoogle Scholar
  39. 39.
    F. Riboli et al., Anderson localization of near-visible light in two dimensions. Opt. Lett. 36(2), 127 (2011)ADSCrossRefGoogle Scholar
  40. 40.
    J. Armijo, R. Allio, Observation of coherent back-scattering and its dynamics in a transverse 2D photonic disorder: from weak to strong localization. Cond. Mat. Physicsphys. (2015)Google Scholar
  41. 41.
    O. Richoux, V. Tournat, T. Le Van Suu, Acoustic wave dispersion in a one-dimensional lattice of nonlinear resonant scatterers. Phys. Rev. E 75(2), 026615 (2007)ADSCrossRefGoogle Scholar
  42. 42.
    O. Richoux, E. Morand, L. Simon, Analytical study of the propagation of acoustic waves in a 1D weakly disordered lattice. Class. Phys. 324, 1983–1995 (2009)ADSzbMATHGoogle Scholar
  43. 43.
    H. Hu, A. Strybulevych, J.H. Page, S.E. Skipetrov, B.A. van Tiggelen, Localization of ultrasound in a three-dimensional elastic network. Nat. Phys. 4(12), 945–948 (2008)CrossRefGoogle Scholar
  44. 44.
    S. Faez, A. Strybulevych, J.H. Page, A. Lagendijk, B.A. van Tiggelen, Observation of multifractality in Anderson localization of ultrasound. Phys. Rev. Lett. 103(15), 155703 (2009)ADSCrossRefGoogle Scholar
  45. 45.
    A.C. Hladky-Hennion, J.O. Vasseur, S. Degraeve, C. Granger, M. de Billy, Acoustic wave localization in one-dimensional Fibonacci phononic structures with mirror symmetry. J. Appl. Phys. 113(15), 154901 (2013)ADSCrossRefGoogle Scholar
  46. 46.
    N. Mott, Metal-insulator transitions. Phys. Today 31(11), 42–45 (1978)CrossRefGoogle Scholar
  47. 47.
    R. Kosloff, Quantum thermodynamics: a dynamical viewpoint. Entropy 15(6), 2100–2128 (2013)ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    L.S. Matthews, T.W. Hyde, Effect of dipole–dipole charge interactions on dust coagulation. New J. Phys. 11(6), 063030 (2009)ADSCrossRefGoogle Scholar
  49. 49.
    L.S. Matthews, T.W. Hyde, Effects of the charge-dipole interaction on the coagulation of fractal aggregates. IEEE Trans. Plasma Sci. 32(2), 586–593 (2004)ADSCrossRefGoogle Scholar
  50. 50.
    L.S. Matthews, T.W. Hyde, Charged grains in Saturn’s F-Ring: interaction with Saturn’s magnetic field. Adv. Space Res. 33(12), 2292–2297 (2004)ADSCrossRefGoogle Scholar
  51. 51.
    L.S. Matthews, T.W. Hyde, Charging and growth of fractal dust grains. IEEE Trans. Plasma Sci. 36(1), 310–314 (2008)ADSCrossRefGoogle Scholar
  52. 52.
    L.S. Matthews, T.W. Hyde, Gravitoelectrodynamics in Saturn’s F ring: encounters with Prometheus and Pandora. J. Phys. Math. Gen. 36(22), 6207 (2003)ADSCrossRefGoogle Scholar
  53. 53.
    M. Sun, L.S. Matthews, T.W. Hyde, Effect of multi-sized dust distribution on local plasma sheath potentials. Adv. Space Res. 38(11), 2575–2580 (2006)ADSCrossRefGoogle Scholar
  54. 54.
    L.S. Matthews, K. Qiao, T.W. Hyde, Dynamics of a dust crystal with two different size dust species. Adv. Space Res. 38(11), 2564–2570 (2006)ADSCrossRefGoogle Scholar
  55. 55.
    K. Qiao, J. Kong, Z. Zhang, L.S. Matthews, T.W. Hyde, Mode couplings and conversions for horizontal dust particle pairs in complex plasmas. IEEE Trans. Plasma Sci. 41(4), 745–753 (2013)ADSCrossRefGoogle Scholar
  56. 56.
    S. Nunomura, J. Goree, S. Hu, X. Wang, A. Bhattacharjee, Dispersion relations of longitudinal and transverse waves in two-dimensional screened Coulomb crystals. Phys. Rev. E 65(6), 066402 (2002)ADSCrossRefGoogle Scholar
  57. 57.
    D.J. Thouless, Electrons in disordered systems and the theory of localization. Phys. Rep. 13(3), 93–142 (1974)ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Evdokiya Georgieva Kostadinova
    • 1
  1. 1.Center for Astrophysics, Space Physics and Engineering ResearchBaylor UniversityWacoUSA

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