Superconducting vortex avalanches D. Shantsev Åge A. F. Olsen, D. Denisov, V. Yurchenko, Y. M....
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Transcript of Superconducting vortex avalanches D. Shantsev Åge A. F. Olsen, D. Denisov, V. Yurchenko, Y. M....
Superconducting vortex avalanches
D. Shantsev Åge A. F. Olsen,
D. Denisov, V. Yurchenko, Y. M. Galperin, T. H. Johansen
AMCS (COMPLEX) groupDepartment of Physics
University of OsloNorway
Temperature TTcc
Mixed state(vortex matter)
Meissner state
Normal state
HHc1c1
HHc2c2
Type II
Vortex lattice
A. A. Abrikosov
(published 1957)
20032003
Vortices in Superconductors
Lorentz forceF = j
Vortices are driven by Lorentz force andtheir motion creates electric field E ~ dB/dt
Ba
J
pinningforce
Lorentzforce
Vortices get pinned by tiny defects and start moving only if
Lorentz force > Pinning force
• Resistance is zero only due to pinning• Stronger pinning => larger currents
current
Critical state
Vortices :• driven inside due to applied field• get pinned by tiny inhomogeneities => Metastable critical state
Picture: R.Wijngarden
Avalanches ?
“Applied” Motivation to study vortex avalanches
The slope of the vortex pile - the critical current density Jc – is the key parameter for many applications of superconductors
Jc
Trapped field magnets
Record trapped field: 17 Tesla
~100 times better than Cu wire
High-current cables
Power-law
Avalanche size (number of vortices) N
um
ber
of
avala
nch
es
E. Altshuler et al.
Self-organized criticality for vortex avalanches in Nb
Phys. Rev. B 70, 140505 (2004)
Peaked or
Power Law(dep. on H & T)
InternalHall probe
arrang.
Nb
filmPlanar
Behnia et al
PRB (2000)
Exp or
Power law
(dep. on T & t)
Off the
edgeSQUID
BSCCO
crystalPlanar
Aegerter
PRE (1998)
Peaked or
Power law(dep. on T)
Off the
edge &
internal
2 Hall
probes
Nb
filmRing
Nowak et al
PRB (1997)
PeakedInternal1 Hall
probe
YBCO
crystalPlanar
Zieve et al
PRB (1996)
Power law(slow ramps)
Off the
edgeCoilNb-Ti
Hollow
cylinder
Field et al
PRL (1995)
ExponentialOff the
edgeCoilPb-In
Hollow
cylinder
Heiden & Rochlin
PRL (1968)
Avalanche
distribution
Avalanche
typeSensorMaterialGeometryReference
Statistics of vortex avalanches
T-effect ?
Table from Altshuler&Johansen, RMP 2004
current
velocity
E ~ dB/dt Vortex motiondissipates energy,
J*E
Local TemperatureIncreases
+kT
It is easier for vortices to overcome pinning barriers
Vortices movefaster
positivefeedback
-1.5 -1.0 -0.5 0.00.0
0.2
0.4
0.6
0.8
1.0
1.2
Ba = 2Bc
Ba = Bc
before jump after jump
B /
0
j cd
x / w-100 0 100 200
0
10
20
30
40
50 before jump after jump
Ba=5.6mTFlu
x de
nsity
B (
mT
)
distance (m)
Ba=11.6mT
edge
Thermal avalanches
THEORY EXPERIMENT
Phys. Rev. B 70, 224502 (2004) Phys. Rev. B 73, 014512 (2006)
Phys. Rev. B 72, 024541 (2005)
Size of small avalanches Shape of dendritic avalanches
Dendrites
Threshold fields for dendritic avalanches
Phys. Rev. Lett. 97, 077002 (2006) Phys. Rev. ? (200?)
Anistropic dendritic avalanches
Phys. Rev. Lett. 98, 117001 (2006)
MgB2 ring
How to determine T without measuring T ?
Some avalanches perforate the ring:
they connect the outer and inner edgesand can bring FLUX into the hole
Flu
x in
the
hol
e
Applied field
Every step: a perforating
avalanche
current
Stage 1:Propagation of the tip
Speed: ~100 km/s (P. Leiderer)Time: ~ 10 ns
current
Stage 2:Heated resistive channel
• Decrease of current• Injection of flux into the hole
2 33
max max 00
( )cJ dTT T T
h
I
Temperature evolution in the heated channel:
T
t
100 K ~2.5Tc
L = 4 nH
Perforation reduces the total current in the ring by just ~15%
I I = 0
WRONG
Distribution of current density in the ring
outerradius
innerradius
perforation-inducedchange
Types of vortex avalanches:1. non-thermal (power-law size distribution): SOC2. thermal (peaked size distribution):
their size, topology and threshold fields are in agreement with theory
Rings: two-stage avalanches1. tip crosses the ring2. short-lived heated channel transferring flux into the hole
Maximal T during avalanche: • 100 K in MgB2 ring with Tc=40 K
Phys. Rev. B 74, 064506 (2006)Phys. Rev. B ? (cond-mat/0705.0997)
Conclusions
nm
J
B(r)
vortex core
Vortex latticeseen at the superconductor surface
2003 Nobel prize toAlexei Abrikosovfor prediction of Vortices
Superconductor has “internal” magnetic nanostructure
superconductor
magnetic field lines
50 nm (at 1 Tesla)
0 flux quantum
r0
r1
Φ
J