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PLASMA

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PLASMA

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  1. PLASMA Artificial classical atoms and molecules: from electrons to colloids and to superconducting vortices François Peeters V. Bedanov, V. Schweigert, M. Kong, B. Partoens G. Piacente, J. Betouras S. Apolinario

  2. NbSe2 measured by STM Wigner crystal Ground state of the electron gas in metals E. Wigner, Physical Review 46, 1002(1934) „If the electrons had no kinetic energy, they would settle in configurations which correspond to the absolute minima of the potential energy. These are close-packed lattice configurations, with energies very near to that of the body-centered lattice....“ • 2D electrons on liquid helium • C.C. Grimes and G. Adams, PRL 42, 795 (1979) • Colloidal particles on surfaces or interfaces • Dusty plasmas • Charged metallic balls, …. • Superconductors  Abrikosov lattice (1957) • Nobel prize in 2003

  3. Theoretical research on colloids in India • Bangalore (Indian Institute of Science): • A.K. Sood • H.R. Krishnamurthy • J. Chakrabarti • Kolkata (S.N. Bose National Research Centre for Basic Sciences): • S. Sengupta

  4. Confinement • Geometrical constrainted motion • 1D: microchannels • 0D: artificial atoms • Self-organization in reduced dimensions • Reduced phase space • Diffusion (e.g. anisotropic diffusion) • Non-linear dynamics

  5. Hamiltonian (2D) Coupling constant Hamiltonian: artificial atom Energy unit Length unit Kinetic energy Confinement Interaction For vertical quantum dot:

  6. Confinement potential • Typical energy scale • The considered artificial atoms are two-dimensional • The number of electrons, the size and the geometry of artificial atoms can be changed arbitrarily Differences with real atoms Parabolic potential Coulomb potential Real atom Artificial atom • Vertical quantum dot:= 3 meV • Real atom: Ry = 13.6 eV

  7. Potential energy • Ground state  Energy minimalization Classical artificial atoms () New units:

  8. Dusty plasma Electrons on He surface (1,7) (1,7.12) Superfluid helium Bose-Einstein condensate Condensate density Superconducting vortices in a disk W. T. Juan, et al, Phys. Rev. E 58, 6947 (1998) Leiderer et al., Surf. Sci.113, 405 (1982) MIT, Ketterle group, 2001 I.V. Grigorieva et al, Phys. Rev. Lett. 96, 077005 (2006) Vortices in helium, imaged by injecting electrons that become trapped at the vortex core. (R.E. Packard) Ground state configurations Classical configurations (1,7,12) (1,7) • N Configuration • 1 • 2 • 3 • 4 • 5 • 1, 5 • 1, 6 • 1, 7 • 2, 7 • 2, 8 • 3, 8 • 3, 9 • 4, 9 • 4, 10 • 5, 10 • 1, 5, 10 Classical atoms (J.J. Thomson (1904)) V.M. Bedanov and F.M. Peeters, Phys. Rev. B 49, 2667 (1994)

  9. Superparamagnetic colloidal spheres I.V. Grigorieva et al, Phys. Rev. Lett. 96, 077005 (2006) M. Saint Jean et al, Europhys. Lett. 55, 45 (2001) vortex 10 mm Decoration exp. Nb:d = 150 nm; D  1µm; T  3.5 K 1kV~ Metallic balls Generic model (2D)for different systems, energy and length scales

  10. (1,5) (6) Saddle point N=6 M. S. Jean et al ( Europhys. Lett. 55, 45 2001)) Saddle point

  11. 6 2 Normal modesEigenfrequencies and eigenvectors Exp. on dusty plasma: A. Melzer, Phys. Rev. E 67, 016411 (2003) V.A. Schweigert and F. Peeters, Phys. Rev. B 51, 7700 (1995)

  12. Magic numbers exp.

  13. Magic number clusters N=19 (1,6,12) N=20 (1,7,12) V.A. Schweigert and F.M. Peeters, Phys. Rev. B 51, 7700 (1995) A. Melzer, A. Piel (Kiel University) => dusty plasma (Phys. Rev. Lett. 87, 115002 (2001))

  14. Radial fluctuations Relative angular intershell fluctuations Melting: small clusters  1/ = kBT/<V>  Anisotropic melting  Two-step melting process Experiments on paramagnetic colloids: R. Bubeck et al, Phys. Rev. B 82, 3364 (1999). V.M. Bedanov and F.M. Peeters, Phys. Rev. B 49, 2667 (1994)

  15. Artificial molecules d Competition between electron correlations in the single dots and correlations between electrons in the different dots.

  16. Competition between particle correlations in the single atoms and correlations between particles in the different atoms. Classical artificial molecules N=10 B. Partoens and F.M. Peeters, Phys. Rev. Lett. 79, 3990 (1997)

  17. 2x(3 particles) 2x(5 particles) 2x(5 particles) Molecule

  18. One dimensional:Microchannels

  19. =r0/ r0=(2q/m02)2/3 E0=(m 02q4/22)1/3 Phase diagram zig-zag transition Continuous transition  2nd order. Q1D  channels G. Piacente, B. Betouras and F.M. Peeters., PRB 69, 045324 (2004)

  20. Complex plasma y x (B. Liu and J. Goree, Phys. Rev. Lett. 71, 046410 (2005) Ion chains Crystalline ion structures in a Paul trap Institut für Physik, Universität Mainz, M Block, A Drakoudis, H Leuthner, P Seibert and G Werth A. Melzer, Phys. Rev. E 73, 056404 (2006) Experimental evidence for the “zig-zag” transition

  21. shift over a/4 2  4 transition zig-zag Discontinuous transition  1st order

  22. Lorentian shaped constriction Driving force V0’ 1/ Pinning and de-pinning of a Q1D system G. Piacente and F.M. Peeters, PRB 72, 205208 (2005)

  23. Phys. Rev. Lett, 97, 208302 (2006) W=60m L=2mm =4.55 m 2.5 Lane reduction at the constriction 7 lanes 6 lanes Increase of the density (no driving force) Non-linear physics G. Piacente and F.M. Peeters, PRB 72, 205208 (2005)

  24. Elastic Depinning(small values of V0’) Quasi-elastic Depinning(large values of V0’)   f < fc f > fc Pinning Depinning

  25. v  ( f – fc ) β Quasi-elastic depinning Elastic depinning =2/3 as for Infinite 2D Systems

  26. Tuning of the critical exponent Crossover from the elastic to quasi-elastic flow

  27. Conclusions • 0D systems  artificial atoms • Ground state: ring structures  Thomson model • Lowest normal mode: intershell rotation (small N) vortex / antivortex rotation • Melting: anisotropic (radial / angular) • Artificial molecules • ‘Structural’ phase transitions • 1D systems  microchannels • Chains: 1  2: zig-zag transition (continuous) 2  4: first-order transition • Constriction:tuning of the critical exponent: from elastic to quasi-elastic (no plastic depinning)

  28. The end

  29. 14Mhz Dusty Plasma (Complex Plasma) Scheme of the experimental setup. Pictures are taken from the website of Lin I and A. Piel’s group

  30. position of the particle after n iteration steps =x,y i=1,…,N Force: Dynamic matrix: The potential energy in the vicinity of this configuration can be expanded in a Taylor series: Newton optimization technique Eigenfrequencies  normal modes

  31. M. Saint Jean et al, Europhys. Lett. 55, 45 (2001) 10 mm 1kV~ Metallic balls

  32. 5 nm 18 nm InAs/GaAs Real atoms versus artificial atoms