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Nucleation of Vortices in Superconductors in Confined Geometries

Nucleation of Vortices in Superconductors in Confined Geometries. W.M. Wu, M.B. Sobnack and F.V. Kusmartsev Department of Physics Loughborough University, U.K. July 2007. Nucleation of vortices and anti-vortices Characteristics of system Nucleation of vortices

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Nucleation of Vortices in Superconductors in Confined Geometries

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  1. Nucleation of Vortices in Superconductors in Confined Geometries W.M. Wu, M.B. Sobnack and F.V. Kusmartsev Department of Physics Loughborough University, U.K. July 2007

  2. Nucleation of vortices and anti-vortices • Characteristics of system • Nucleation of vortices • Physical boundary conditions • Characteristics of vortex interaction

  3. Geim: paramagnetic Meissner effect • Chibotaru and Mel’nikov: anti-vortices, multi-quanta-vortices • Schweigert: multi-vortex state  giant vortex • Okayasu: no giant vortex A.K. Geim et al., Nature (London)408,784 (2000). L.F. Chibotaru et al., Nature (London)408,833 (2000). A.S. Mel’nikov et al., Phys. Rev. B65, 140501 (2002). V.A. Schweigert et al., Phys. Rev. Lett.81, 2783 (1998). S. Okayasu et al., IEEE 15 (2), 696 (2005).

  4. Grigorieva et al., Phys. Rev. Lett. 96, 077005 (2006) Total flux = LΦ0 Applied H Baelus et al.: predictions different from observations [Phys. Rev. B69, 0645061 (2004)]

  5. Theories at T = 0K • Experiments at finite T ≠0K This study: extension of previous work to include multi-rings and finite temperatures

  6. Model H = Hk = Aapp R H~Hc1 d Local field B ~ H R < λ2/d = Λ, d << rc

  7. H H T = 0K H >Hc1: Vortices penetrate Flux Φv = qΦ0 ,Φ0 = hc/2e H < Hc1: Meissnereffect js js js = -(c/42)A js = -(c/42)(A-Av)

  8. Boundary condition: normal component of jsvanishes Method of images r’i = (R2/r)ri image anti-vortex ri Φi (r)= qΦ0 /2r Φi -Φi Φi= qΦ0 Av = [Φi (r-ri) - Φi (r-r'i)]θ

  9. LΦ0 N2 vortices qΦ0 H r1 r2 r1 < r2 N1 vortices qΦ0 L > 0 vortex L < 0 anti-vortex

  10. T = 0 K Gibbs free Energy zi = ri/R

  11. α

  12. Finite temperature T ≠ 0K Gibbs free energy S=Entropy Dimensionless Gibbs free energy:

  13. Minimise g(L,N1,N2,t) with respect to z1, z2 • Grigorieva: Nb R ~ 1.5nm, 0 ~ 100nm Tc ~ 9.1K, tc ~ 0.7 T ~ 1.8K, t ~ 0.14 (L, N1):a central vortex of flux LΦ0 at centre, N1 vortices (Φ0) on ring z1 (L,N1,N2):a central vortex, N1 vortices on z1 and N2 on z2

  14. Results: t = 0 (T = 0K)

  15. Results: t = 0.14 (T = 1.8K) H=60 Oe h=20.5

  16. Vortex Configurations with 90 – (0,2,7) * * (1,8)

  17. Total flux = 90 (L,N1,N2)=(0,2,7) at t = 0.14 (L,N)=(1,8) at t = 0

  18. Vortex Configurations with 100 – (1,9) - - (0,3,7) H = 60 Oe h = 20.5 * * (0,2,8)

  19. Total flux = 100 (L,N)=(1,9) t = 0 (L,N1,N2)=(0,2,8) t = 0.14 (L,N1,N2)=(0,3,7) t = 0.14

  20. Conclusions and Remarks • Modified theory to include temperature • Results at t = 0.14 in very good agreement with experiments of Grigorieva + her group • Extension to > 2 rings/shells • Underlying physics mechanisms

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