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