Nano-scale frictionkinetic friction of solids of

Magnetic flux quanta and Charge-density

－ a new route to microscopic understanding of friction

－ Dep. Basic Science,Univ. Tokyo, Japan

A. MAEDAY. INOUE

H. KITANOT. UMETSU

IWV-10, Mumbai, India, Jan 9-15, 2005

JAERIS. OKAYASU

Frontier Research System,RIKEN

S. SAVELEVF. NORI

CRIEPII. TSUKADA

　　　　　　　　　　　　　　　　　 Outline1) 　 background ： problems in physics of friction dynamics of driven vortices of superconductors and CDW2) 　 purpose of this research3) 　 experimental4) 　 kinetic friction as a function of velocity5) theoretical understanding6) 　 effect of irradiation of columnar defects7) 　 comparison of vortex result with CDW systems8) further discussion9) 　 conclusion

Physics of friction ・ physics not well understood・ importance in application and control

static friction 　・・・　 rather understood (adhesion mechanis

m)

kinetic frictionkinetic friction ・・・ ・・・ collapse of Amontons-Coulomb’s lacollapse of Amontons-Coulomb’s la

ww

friction

driving force0

Ｆ C

Ｆ C

Ｆ k

static moving

Fk depends on velocityat low velocities

Amontons-Coulomb’s friction friction in reality ・・・

friction

driving force0

Ｆ C

Ｆｃ

static moving

Massive blocks

Problems on kinetic friction

Amontons-Coulombs’ LawAmontons-Coulombs’ Law　 (1) Friction is independent of apparent contact area.　 (2) Friction is proportional to normal component of reaction.　 (3) Kinetic friction Fk, (> static friction), is independent of velocity.

・ (3) is invalid at low velocities (velocity dependent)　　　 larger velocity dependence for clean surfaces

・ finite Fk even for zero normal reactionNot always valid

・・ any relationship between any relationship between FFkk and and FFss?? 　　

scaling law between scaling law between FFkk and and FFss （（ thick paperthick paper ： ： Heslot (1994)Heslot (1994) ））

Good model systems are necessary, with which systematic experiment is available in a repeated manner

)/()( 0 vDtv Sd universal property?

1 D model for clean surfaces

clean surface (normal) dirty surface

・ clean surface finite Fk even for zero Fs

・ disordered surface less velocity dependent　　 similar to Amontons-Coulomb’s law

numerical solution for the above equation Fk as a function of velocity

Microscopic formulation of friction

ttjii j

FNF exaa b

//I )(

vu steady state

summing up for all atoms

time averaged friction: sum of interatomic (pinning) forces

Gex

),(

Ia

aaaa )()()( FFvuFuuFuuub

jiji

j

ji

jiiii rmm

GS

),(

aIbbb )()()()( FvFuvFvvFvvv

bb

jjiji

jji

jiiii rmm eq. motion

for a lower atom i

　　　　　　　　　　　　　　　　　← a 　 displacement of upper atom i:

　 ui , mass 　 ma

　　　　　　　　　　　　　　　　 ← b 　 displacement of lower atom j

　 vj , mass 　 mb

eq. motion

for an upper atom i

dissipation from a representative DF to others

H. Matsukawa and H. Fukuyama:PRB 49, 17286 (1994)

Model systems for friction study in quantum condensate in solids

Charge-density wave (CDW)

Vortex lattice of superconductor

ex

)(

p,

)()( FuFuuFuu

ii

i

ji

ji

ii mm

( )

p ex,

( ) ( ) ( )i

i i i j i

i j i

m

u u F u u F u F

ui : displacement of i-th electron in the CDW

m: mass of the i-th electron Fp: pinning force for i-th electron 　　　　　　　　　　

EF eex

i

ie・uj

ui : displacement of i-th vortex in the lattice

m: mass of the i-th vortex in the lattice Fp: pinning force for i-th vortex 　　　　　　　　　　

jF 0ex

i

i

・uE 0

cTT

B

e

h

20

1D

2D

　　　　　 (a) many internal degrees of freedom　　　　　 (b) nonlinearity　　　　　 (c) random pinning　　　　　 (d) finite threshold friction (critical current density Jc)　　　　　 (e) finite kinetic friction in moving state (flux flow)

Driven vortices of superconductor

J 　

E 　　

Jc

energydissipation

many advantagesmany advantages

　 ・ change various parameter continuously and repeatedly in a reproducible manner

・ no sample degradation (no wear)

・ comparison with CDW (1 dim)　　 discuss friction and dimension

・ potentially, a good model system of friction study・ expect understanding of kinetic friction in a microscopic level・ bridge friction in macroscopic scale and microscopic scale

Expressing solid-solid friction in terms of vortex motion

Driving force　 J ×Φ0

viscous force η< ｖ >

direction of vortex motion

kinetic friction FFRIC

（ pinning force ）

I -V measurement and viscosity , , measurement can deduce kinetic friction

)(10

0

ωρ

ρJ

JF Pk

　 　 　

uu

η

Bωρ 0)(

Flux flow resistivity

necessary to make correspondence with theory

J: current density: resistivity

0: flux quantum

( )1k

EF eE

Sliding charge-density waves (CDWs)

kinetic friction

E

( )E

driving electric field for CDW

conductivity at electric field E

conductivity in the infinite field limit

e electronic charge

I-V measurement and measurement can deduce kinetic friction

microscopic understanding of solid-solid frictionusing driven vortices of high-Tc superconductor as a model system

Purpose of research

(1) measure kinetic friction in quantum condensates

(2) theory : numerical simulation and analytical formula

(3) Comparison between the experiments and the theory

effect of disorder

compare with other quantum condensate : CDW

re-investigate dynamics of vortices of superconductorsin terms of physics of friction and vice versa

(1) thin films (PLD) 　 (I. Tsukada (CRIEPI))

compare Fk among samples with different pinning

# dc14 ・・・ pristine Tc=31 K# dc 6 ・・・ irradiated by ion Tc=30 K 　

(2) bulk crystal (FZ method)

BΦ=3T columnar defects

(S. Okayasu (JAERI))

Samples Cuprate superconductor : La2-xSrxCuO4 (x=0.16)

achieve high current densities (velocities)

0 100 200 3000

200

400

600

800

28 29 30 31 32 33 340

50

100

150

200

Res

istivi

ty (

cm)

Temperature (K)

dc-8 ( B = 0.3 T) dc-6 ( B = 3 T) dc-14 (unirradiated)

Resi

stiv

ity

(c

m)

Temperature (K)

dc- 6 ( B = 3 T) dc- 14 (unirradiated)

15 18 21 24 27 30 3310- 9

10- 8

10- 7

10- 6

10- 5

10- 4

10- 3

dc14

0.3T

0T

2T1T

3T4T

5T

Resi

stiv

ity

(cm

)

Temperature (K)

for viscosity measurement by microwave technique

200 MeV Iodine

Y.Tuchiya et al PRB 63 184517 (2001).

A.Maeda et al Physica C 362 (2001)

127-134

0.0 0.2 0.4 0.6 0.8 1.01E- 9

1E- 8

1E- 7

1E- 6

(

Ns

/ m

2 )

T / Tc

LSC 2 GHz LSC 19 GHz YBC 19 GHz BSCCO 19 GHz

* ～ 1×10-7 Ns/m2 　

（ 4.5K)

2.0

E

E

Vortex viscosity and electronic structure of QP in the core

LSCO (x=0.15) 2.0*

n

* (moderately clean)

moderately clean nature rather generic in HTSC (doping, material)

T. Umetsu et al unpublished.

core GL

LSCO films

stronger pinning at low temperaturesin irradiated samples effect of irradiation

I-V measured withusing short pulses

Fk (v) （ up to ～ 1 km/s ）

4) smaller Fk in irradiated samples

3) Fk saturates and decreases

inconsistent with the behavior at low velocities ?

pristine 3T irradiated

2) very much different fromthe Amontons-Coulomb behavior

1) Fk changes with B and T in a reproducible manner

good as a model system

similar to “clean surface”

existence of a peak in Fk(v)

Data points with crosses denotepulsed measurements

( ) ( ) 2 ( )i i i j d Bii

x U x W x x F k T tx

ix

( )iU x

( )i jW x x

dF

( )t

T

Minimal model to explain the data : overdamped equation of motion

: position of vortices

: viscosity of vortices

: substrate pinning potential

: inter-vortex interaction

: driving force

: thermal random force

: temperature

S. Savel’ev and F. Nori

Numerical simulation for 1D vortex array at finite temperatures

S. Savel’ev and F. Nori

a peak

Q

2

LSCO films

Pinning did not increase R below H = 1 T matching effect (B=3T)?

10- 3 10- 2 10- 1 10010- 2

10- 1

100

101

LSCO (x=0.15) film dc14 ( unirradiated) dc6 ( 3T irradiated)

21 K

24 K

18 K

4 T

kineti

c f

ricti

on (

10-

6 N/m

)

Vortex Velocity (km/ s)10- 3 10- 2 10- 1 100

10- 1

100

101

LSCO (x=0.15) film dc14 ( 0T irradiated) dc6 ( 3T irradiated)

21 K

24 K

18 K

3 T

kine

tic

fric

tion

(10-6

N/m

)

Vortex Velocity (km/ s)

“Inversion” of kinetic friction at intermediate velocities ！

sample with strong pinning higher static friction lower kinetic friction　 more gradual dependence on v

velocity

friction

3 Ｔirradiated

pristine

S. Savel’ev and F. Nori

Analytical formula

Solution of Fokker-Planck equation

))((

)/4(),,,(

222

TTkF

QFQTFv

Bd

dd

)(

/4)(),,,(

2

TTkF

QTTFkQTFF

Bd

dBdk

)2/sinh()4(

)/cosh()2/cosh(16)(

222

2

TkFFQ

TkQTkFQT

Bdd

BBd

dFQ

driving forrce

potential height

typical length scale of the potential

viscosity

・ similar Fk(v) behavior as the experimental data・ maximum Fk around at a velocity v satisfying Q/l ～ v

A peak in the kinetic friction Fk(v)

0cp

jv

velocity at the peak S. Savel’ev and F. Nori

6 210 A/cmcj 7 2

0 2.07 10 gauss•cm

710 Ns/m 22 10 m/spv

in good agreement with experiment

Potential energy plays an important role for Fk(v).

Estimate Q and l by a collective pinning theory

G. Blatter et al. Rev. Mod. Phys. 66 (1994) 1125.

2/3 4/3 21c cQ H H pristine

irradiated 2 2cQ H pr

130pr Aeffective radius of columnar defects

crossover field gives2/3

1

5 100cp

c

Hr A

H

good agreement !

104 105 10610- 1

100

101

102

LSCO(x=0.15) film T = 18 K

3T irradiated

2 T 3 T 4 T 5 T

kine

tic f

rict

ion (

10-6

N/m

)

unirradiated 1 T 2 T 3 T 4 T 5 T

J (A/ cm2)

Vortex lattice in SC vs CDW 　

vortex lattice of SC （２Ｄ） CDW （ 1 Ｄ）

similar behavior despite the difference of dimensionality of collective motion

Thermal effect smears out the difference in dimension ?

1 10 1000.1

1

10

100

42 K30 K

57 K

58 K

47 K56 K

52 K

35 K

NbSe3 #305

Fki

n/F

smax

E/ ET

using data in A. Maeda et al. JPSJ 59 (1990) 234.

Effect of dimension and disorder (T=0 K result)

1D-CDW 2D F-K model

T. Kawaguchi and H. Matsukawa: PRB 61 (2000) R16346.

Fk(v) largely dependent on dimension and disorder

H. Matsukawa: JPSJ 57 (1988) 3463.

Physical origin of the peak

v

Fk

/ dQ F

static

kinetic changing parameterschange transition between static and kinetic regime

increasing magnetic fieldincreasing temperaturedecreasing system size (macro to micro)

broaden the transition

N strongly coupled system

collective coordinatei

macroi

xx

N

new stochastic variablei

macroi N

effective temperature eff

TT

N

3eff

TT

L (L : system size)

Conclusion

discuss kinetic friction by investigating dynamics of VL in high-Tc SC and CDW

reproducible control of “interaction between interfaces”by B, T etc

promising : vortices of high-Tc superconductors, CDWs

as good model systems for investigating physics of friction

・ systematic investigation of size effect・ waiting time dependence ・ scaling between Fs and Fk ?

theoretical understanding by a simple overdamped model

numerical simulation, analytical results

reproduce almost all the experimental behavior : the peak, defect dependence

(a) explain the roundness of the crossing of Fs and Fk

(b) provide a link between microscopic and macroscopic friction

Future perspective

The peak is a broadened transition between Fs and Fk

New concepts proposed in driven vortex system

plasticitystatic channelsdynamic reordering etc.

C. J. Olson et al., PRL 81, 3757 (1998).

P. Le Doussal & T. Giamarchi, PRB 57, 11356 (1998).

Dynamic Phase diagram of driven vortices