nucleation of vortices in superconductors in confined geometries
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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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
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Nucleation of vortices and anti-vortices
1. Characteristics of system
2. Nucleation of vortices
3. Physical boundary conditions
4. Characteristics of vortex interaction
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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. B 65, 140501 (2002).V.A. Schweigert et al., Phys. Rev. Lett. 81, 2783 (1998).S. Okayasu et al., IEEE 15 (2), 696 (2005).
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Total flux = LΦ0
Grigorieva et al., Phys. Rev. Lett. 96, 077005 (2006)
Applied H
Baelus et al.: predictions different from observations[Phys. Rev. B 69, 0645061 (2004)]
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Theories at T = 0K
Experiments at finite T ≠ 0K
This study: extension of previous work to include
multi-rings and finite temperatures
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Model
H = Hk = Aapp
d
R < λ2/d = Λ, d << rc
H~Hc1
R
Local field B ~ H
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T = 0K
H < Hc1: Meissner effect
H > Hc1: Vortices penetrate
Flux Φv = qΦ0 , Φ0 = hc/2e
H
rxBHBG 3222 d)()(8
1
H
js = -(c/42)A js = -(c/42)(A-Av)
js
js
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Method of images
ri
r’i = (R2/r)ri
Boundary condition: normal component of js vanishes
image anti-vortex
Φi = qΦ0
Φi (r)= qΦ0 /2r
Av = [Φi (r-ri) - Φi (r-r'i)]θ
Φi -Φi
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Hr1
r2
L > 0 vortex L < 0 anti-vortex r1 < r2
LΦ0
N1 vortices qΦ0
N2 vortices qΦ0
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T = 0 K
02 / RHh
),()0,(')0,('
ln2ln2ln4
),,(
211221
2211212
2
NNgNgNgLh
zqLNzqLNr
RNq
hNNLg
c
Gibbs free Energy
zi = ri/R
Gd
tLNg 20
2)(16),,(
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1
12
4222
2222
)/(sin4
)/2cos(21ln
2)1(
)1ln(ln)1(ln)0,('
iiii
ii
iiiiiii
N
n
c
Nn
zNnzqNzqhN
zqNzqNNr
RqNNg
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1
1
1
1
222
2 1
212121
212121
2112 ))//(2cos(2
))//(2cos(21ln),(
N
m
N
n NmNnzzzz
NmNnzzzzqNNg
α
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Finite temperature T ≠ 0K
TSTGG )0(
)lnlnlnln
ln2ln2(),,(),,,(
2121
2121
NNzz
r
RtNNLgtNNLg
c
Gibbs free energy S=Entropy
220
/)(16 dTktB
Dimensionless Gibbs free energy:
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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
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Results: t = 0 (T = 0K)
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Results: t = 0.14 (T = 1.8K)
H=60 Oe h=20.5
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Vortex Configurations with 90
– (0,2,7)
* * (1,8)
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Total flux = 90
(L,N1,N2)=(0,2,7) at t = 0.14
(L,N)=(1,8) at t = 0
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Vortex Configurations with 100
– (1,9)
* * (0,2,8)
- - (0,3,7)
H = 60 Oe h = 20.5
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Total flux = 100
(L,N1,N2)=(0,3,7)t = 0.14
(L,N1,N2)=(0,2,8)t = 0.14
(L,N)=(1,9)t = 0
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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