Superconducting vortex avalanches
D. Shantsev
Åge A. F. Olsen,
D. Denisov, V. Yurchenko,
Y. M. Galperin, T. H. Johansen
AMCS (COMPLEX) group
Department of Physics
University of Oslo
Norway
Vortices in Superconductors
Vortex lattice
A. A. Abrikosov
2003
(published 1957)
Hc2
Normal state
Mixed state
(vortex matter)
Hc1
Type II
Meissner state
Temperature
Tc
Vortices are driven by Lorentz force and
their motion creates electric field E ~ dB/dt
Lorentz
force
F = j F0
Vortices get pinned by tiny defects
and start moving only if
Lorentz force > Pinning force
Ba
Lorentz
force
current
J
• Resistance is zero only due to pinning
• Stronger pinning => larger currents
pinning
force
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
Trapped field magnets
High-current cables
Jc
Record trapped field:
17 Tesla
~100 times better than Cu wire
Self-organized criticality for vortex avalanches in Nb
E. Altshuler et al.
Phys. Rev. B 70, 140505 (2004)
Power-law
Avalanche size (number of vortices)
Statistics of vortex avalanches
Reference
Geometry
Material
Sensor
Avalanche
type
Avalanche
distribution
Heiden &
Rochlin
PRL (1968)
Hollow
cylinder
Pb-In
Coil
Off the
edge
Exponential
Field et al
PRL (1995)
Hollow
cylinder
Nb-Ti
Coil
Off the
edge
(slow ramps)
Zieve et al
PRB (1996)
Planar
YBCO
crystal
1 Hall
probe
Internal
Peaked
Ring
Nb
film
2 Hall
probes
Off the
edge &
internal
Peaked or
Power law
Nowak et al
PRB (1997)
Aegerter
PRE (1998)
Behnia et al
PRB (2000)
Planar
Planar
BSCCO
crystal
SQUID
Nb
film
Hall probe
arrang.
Off the
edge
Internal
Power law
(dep. on T)
Exp or
Power law
(dep. on T & t)
Peaked or
Power Law
(dep. on H & T)
Table from Altshuler&Johansen, RMP 2004
T-effect ?
E ~ dB/dt
Vortex motion
dissipates energy,
J*E
Local Temperature
Increases
velocity
positive
feedback
current
It is easier for vortices
to overcome pinning barriers
+kT
Vortices move
faster
Thermal avalanches
Shape of dendritic avalanches
Size of small avalanches
H
THEORY
0.8
Ba = 2Bc
0.4
0.2
Ba = Bc
0.0
-1.5
-1.0
-0.5
x/w
0.0
before jump
after jump
50
Flux density B (mT)
B / 0 jcd
1.0
0.6
dynamic
criterion
EXPERIMENT
before jump
after jump
1.2
Uniform
jumps
40
Fingering
adiabatic criterion
Hadiab
Dendrites
30
20
Ba=11.6mT
S
10
t
a
b
l
e
Ba=5.6mT
edge
0
-100
0
100
distance (m)
Phys. Rev. B 72, 024541 (2005)
200
Ec/n
Ec
Phys. Rev. B 70, 224502 (2004)
Phys. Rev. B 73, 014512 (2006)
Threshold fields for dendritic avalanches
Anistropic dendritic avalanches
Phys. Rev. Lett. 97, 077002 (2006)
Phys. Rev. ? (200?)
E
Phys. Rev. Lett. 98, 117001 (2006)
How to determine T without measuring T ?
MgB2 ring
Some avalanches perforate the ring:
they connect the outer and inner edges
and can bring FLUX into the hole
Flux in the hole
Every step:
a perforating
avalanche
Applied field
Stage 1:
Stage 2:
Propagation of the tip
Heated resistive channel
DF
current
Speed: ~100 km/s (P. Leiderer)
Time: ~ 10 ns
current
• Decrease of current
• Injection of flux into the hole
I
L = 4 nH
 J 2 dTc3
h0
 Tmax 3 (Tmax  T0 )
Temperature evolution in the heated channel:
T
100 K ~2.5Tc
t
WRONG
I
I=0
Perforation reduces the total current in the ring
by just ~15%
Distribution of current density in the ring
perforation-induced
change
inner
radius
outer
radius
Conclusions
Types of vortex avalanches:
1. non-thermal (power-law size distribution): SOC
2. thermal (peaked size distribution):
their size, topology and threshold fields are in agreement with theory
Rings: two-stage avalanches
1. tip crosses the ring
2. 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)
Superconductor has “internal” magnetic nanostructure
magnetic field lines
Vortex lattice
seen at the superconductor surface
superconductor
F0
flux quantum
50 nm
(at 1 Tesla)
vortex core
x ~ 10 nm
J
B(r)
l
2003 Nobel prize to
Alexei Abrikosov
for prediction of Vortices
r1
Φ
r0
J