Quasi One-Dimensional Vortex Flow Driven Through Mesoscopic Channels

R. Besseling, T. Sorop,

P. H. KesKamerlingh Onnes Laboratory, Leiden University

Nobuhito Kokubo

Institute of Materials Science, University of Tsukuba

Pinning force for vortices

Fp = Jc B

J ｃJ

E

Driving force

velo

cit

y

Electric field due to vortex motion

vBE

E

Vortex flow

Baarle et al APL 2003

BJF

Driving force for vorticesJ

H

Dissipations in normal core

v = F

BS Formula for 1D chain

BaldB

ldbRc

nfDf

1

2

01

l

1D Bardeen Stephen(BS) Formula

BabB

B

cn

f

1

2

0

0

Vortex density B:

Bab 0

BS Formula for flux flow resistivity

a

b

b

Flow

1D Vortex Flow in Twin Boundaries

A. Gurevich PRL, PRB 2002

a

HR f

b

Abrikosov Josephson vortex

IV Curves in Twin Boundaries

Outline of This Talk

Vortex flow channel device

A short summary of previous results

New results•A kink anomaly in IV characteristics•ML experiments

Summary of this talk

J

JH

Weak pinning a-NbGe layer

Strong pinning NbN layer

Mesoscopic Vortex Flow Channels

SEM picture (w=650nm)

0.2 – 1m

w <

Matching Effects

w=230 nm

0 0.4 0.8 1.20

1.0

2.0

~c66(B)

F p (

106 N

/m3 )

0H (T)

experimentaldata

/w 66cFp

J

w

The shear modulus of vortex lattice c66

f

Mismatch conditionMatching condition

b

a

Mode Locking Experiments : Model

Coherent flow, average velocity ‘v’ in pinning potential

a: particle spacing // vv

aSimplified picture

Force

vMLVe

loc

ity

Lattice Mode : fint = v/a

I= Idc + Irf sin(2ft )

ML occurs : fint = p f(vML = p a f)

Flow direction

Mode Locking Experiments: Result

BvE

avff /int

abB /0

weff

b

a

b

wn eff

fnV pc 01

f=6MHz

Irf=0

Large Irf

p=1

p=2

p=3

T<<Tc(NbGe)

w=230nm

PRL 88,247004 (2002)

Vortex density

Oscillation in Fc is closely related with the flow configurations in channels

Field Evolution of n and Fc

Field History in Channels

Field up (FU) modeH is ramped up after ZFC• Field Focusing in channels

A decoration image in channels in a field of 50mT taken by N. Saha,

NbN

Quasi 1D flow properties

Field down (FD) modeH is ramped down after applying a large field (>Hc2 of NbGe)

Conventional 2D FF behavior

NbN

Field History of Ic & IV Curves

H*

Flow Resistance

HRd

H < H* 1D like vortex flow

Low I

High I

f (MHz) (= v/a)

A kink anomaly mark a dynamic change in flow configuration

DC

n = 3

n = 5

Dynamic Change in Flow Structure

f = fint = v/a at p=1

H*

Lower R.F. branch : n Higher R.F. branch: n+2

Quasi 1D flow Properties

constant n

HRd H < H*

Quasi 1D flow propertiesn = 4

n = 5 High RFB

Low RFB

H*

H > H*

Conventional (2D) Flux Flow

HRd

H* : 1D - 2D flow transition

Field profile in a channel

FD

Mobile

FU

Mobile

Summary

• Mesoscopic channel system provides very rich physical properties

• Field history changes the vortex dynamics in channels

• Quasi-1D motion (square root dependence on field with constant flow configurations)

• Dynamic change in flow configurations

• Transition from quasi1D to 2D flow properties