IWV-10, Mumbai, India, Jan 9-15, 2005
Nano-scale friction
kinetic friction of solids of
Magnetic flux quanta and Charge-density
－ a new route to microscopic understanding of friction －
Dep. Basic Science,
Univ. Tokyo, Japan
Frontier Research System,
RIKEN
A. MAEDA
Y. INOUE
H. KITANO
T. UMETSU
S. SAVELEV
F. NORI
CRIEPI
I. TSUKADA
JAERI
S. OKAYASU
Outline
1) background：
problems in physics of friction
dynamics of driven vortices of superconductors and CDW
2) purpose of this research
3) experimental
4) kinetic friction as a function of velocity
5) theoretical understanding
6) effect of irradiation of columnar defects
7) comparison of vortex result with CDW systems
8) further discussion
9) conclusion
Physics of friction ・physics not well understood
・importance in application and control
static friction ・・・ rather understood (adhesion mechanism)
kinetic friction ・・・ collapse of Amontons-Coulomb’s law
friction
friction
ＦC
Fk depends on velocity
at low velocities
Ｆｃ
Ｆk
ＦC
ＦC
driving force
0
static
moving
Amontons-Coulomb’s friction
Massive blocks
driving force
0
static
moving
friction in reality・・・
Problems on kinetic friction
Amontons-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.
・finite Fk even for zero normal reaction
Not always valid
・(3) is invalid at low velocities (velocity dependent)
larger velocity dependence for clean surfaces
・any relationship between Fk and Fs?
scaling law between Fk and Fs （thick paper： Heslot (1994)）
d (v)  S (t  D0 / v)
universal property?
Good model systems are necessary, with which
systematic experiment is available in a repeated manner
H. Matsukawa and H. Fukuyama:
PRB 49, 17286 (1994)
Microscopic formulation of friction
←a displacement of upper atom i: ui , mass
←b displacement of lower atom j vj , mass



ma ui  ma ra (ui   ui i )   Fa (ui  u j )   FI



ja
jb
(i , j )
mb vi  mb rb ( vi   vi i )   Fb ( v i  v j )   FI
jb
ja
dissipation from a representative DF to others
steady state
summing up for all atoms
time averaged
ma
mb
eq. motion
for an upper atom i
(ui  v j )  Fex  FG
(i , j )
( v i  u j )  FS ( v j )  FG
eq. motion
for a lower atom i
  FI // (ui  v j ) t  Na Fex
ia jb
t
friction: sum of interatomic (pinning) forces
1 D model for clean surfaces
numerical solution for the above equation
・clean surface
finite Fk even for zero Fs
・disordered surface
less velocity dependent
similar to Amontons-Coulomb’s law
Fk as a function of velocity
clean surface
(normal) dirty surface
Model systems for friction study in quantum condensate in solids
Charge-density wave (CDW)

1D

T  Tc
m ui  m ui   F (ui  u j )   Fp (ui )  Fex
(i )
i, j
i
Fex  eE
ui : displacement of i-th electron in the CDW
・
j    e ui
m: mass of the i-th electron
Fp: pinning force for i-th electron
i
2D
Vortex lattice of superconductor


(m ui ) ui   F (ui  u j )   Fp (ui )  Fex
(i )
i, j
i
Fex  0  j
・
E    0  ui
i
B
0 
h
2e
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
Driven vortices of superconductor
(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)
E
many 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
energy
dissipation
Jc
J
Expressing solid-solid friction in terms of vortex motion
necessary to make correspondence with theory
Fk   P u  J   0  hu


ρ

 J   0 1 
 ρ (ω   ) 
0: flux quantum
J: current density
r: resistivity
ρ (ω  ) 
B 0
η
viscous force η<ｖ>
kinetic friction FFRIC
（pinning force）
Driving force
J ×Φ0
direction of vortex motion
Flux flow resistivity
I -V measurement and viscosity ,h , measurement can deduce kinetic friction
Sliding charge-density waves (CDWs)
kinetic friction
  (E) 
Fk  eE 1 

 

e
electronic charge
E
driving electric field for CDW
 (E)

conductivity at electric field E
conductivity in the infinite field limit
I-V measurement and   measurement can deduce kinetic friction
Purpose of research
microscopic understanding of solid-solid friction
using driven vortices of high-Tc superconductor as a model system
(1) measure kinetic friction in quantum condensates
effect of disorder
compare with other quantum condensate : CDW
(2) theory : numerical simulation and analytical formula
(3) Comparison between the experiments and the theory
re-investigate dynamics of vortices of superconductors
in terms of physics of friction and vice versa
# dc14・・・pristine
# dc 6 ・・・irradiated by ion
(S. Okayasu (JAERI))
Tc=31 K
Tc=30 K
dc-6 ( B = 3 T)
dc-14 (unirradiated)
600
400
200
cm)
achieve high current densities (velocities)
800
200
Resistivity (
(1) thin films (PLD) (I. Tsukada (CRIEPI))
cm)
Cuprate superconductor : La2-xSrxCuO4 (x=0.16)
Resistivity (
Samples
100
0
28
29
30
31
32
33
34
200
300
10-3
Resistivity ( cm)
BΦ=3T columnar defects
for viscosity measurement by microwave technique
50
Temperature (K)
200 MeV Iodine
(2) bulk crystal (FZ method)
100
Temperature (K)
0
0
compare Fk among samples with different pinning
dc-8 ( B = 0.3 T)
dc-6 ( B = 3 T)
dc-14 (unirradiated)
150
10-4
dc14
10-5
5T
-6
10
4T
-7
10
0T
3T
2T
-8
10
1T
0.3T
-9
10
15
18
21
24
27
Temperature (K)
30
33
Vortex viscosity and electronic structure of QP in the core
h*
 0.2
n
h* ～ 1×10-7 Ns/m2 （4.5K)
LSCO (x=0.15)
  h* (moderately clean)   E  0.2
core  GL
E
moderately clean nature rather generic in HTSC (doping, material)
1E-7
1E-8
h
( Ns / m2)
1E-6
1E-9
0.0
LSC 2 GHz
LSC 19 GHz
YBC 19 GHz
BSCCO 19 GHz
0.2
0.4
T. Umetsu et al unpublished.
Y.Tuchiya et al PRB 63 184517 (2001).
0.6
T / Tc
0.8
1.0
A.Maeda et al Physica C 362 (2001)
127-134
Resistivity (W cm)
LSCO
films
Resistivity (W cm)
I-V measured with
using short pulses
10-3
10-4
27 K
10-5
10-7
10-8
10
10
-3
1
10
10-4
10-4
2
10
10
3
10-6
10-7
10-8
unirradiated
4
10
5
10
21 K
10-9 1
10
10
10-3
6
10-4
10-5
10-5
10-6
10-6
10-7
10-7
10-8
10-8
10-9 1
10
2
10
10
3
24 K
10-5
5T
4T
3T
2T
1T
0.3T
3T irradiated
10-6
-9
10-3
4
10
2
J (A/cm )
stronger pinning at low temperatures
in irradiated samples
5
10
103
104
105
106
103
104
2
105
106
18 K
10-9 1
10
10
6
102
102
J (A/cm )
effect of irradiation
Kinetic Friction (10-6 N/m)
（up to ～1 km/s）
1) Fk changes with B and T
in a reproducible manner
good as a model system
similar to “clean surface”
3) Fk saturates and decreases
Kinetic Friction (10-6 N/m)
2) very much different from
the Amontons-Coulomb behavior
8
dc14 ( B  = 0 T )
existence of a peak in Fk(v)
4) smaller Fk in irradiated samples
inconsistent with the behavior
at low velocities ?
Data points with crosses denote
pulsed measurements
24 K
8
6
6
4
4
2
0
0.0
Kinetic Friction (10-6 N/m)
Fk (v)
12
0.3 T
1T
2T
3T
4T
5T
0.5
1.0
Vortex Velocity (km/s)
1.5
2
0
0.0
12
21 K
10
10
8
8
6
6
4
4
2
2
0
0.0
20
0.2
0.4
0.6
0.8
Vortex Velocity (km/s)
0
1.0 0.0
18 K
20
15
10
10
5
5
0.1
0.2
0.3
0.4
Vortex Velocity (km/s)
pristine
24 K
0.3 T
1T
2T
3T
4T
5T
0.5
1.0
Vortex Velocity (km/s)
1.5
21 K
0.2
0.4
0.6
0.8
Vortex Velocity (km/s)
1.0
18 K
15
0
0.0
dc6 ( B  = 3 T )
0
0.5 0.0
0.1
0.2
0.3
0.4
Vortex Velocity (km/s)
3T irradiated
0.5
Minimal model to explain the data : overdamped equation of motion
S. Savel’ev and F. Nori

h xi  
xi


U ( xi )  W ( xi  x j )   Fd  2kBT  (t )
i


xi
h
: position of vortices
U ( xi )
: substrate pinning potential
: viscosity of vortices
W ( xi  x j ) : inter-vortex interaction
Fd
: driving force
 (t )
T
: thermal random force
: temperature
Numerical simulation for 1D vortex array at finite temperatures
S. Savel’ev and F. Nori
2
Q
a peak
Resistivity (W cm)
Resistivity (W cm)
LSCO films
10
-3
10
-4
10
-5
10
-6
10
-7
10
-8
10
-9
27K
24K
21K
18K
4T
1
10
10
-3
10
-4
10
-5
10
-6
10
2
10
3
10
4
10
5
10
6
-7
10
-8
10
-9
-3
10
-4
10
-5
10
-6
10
-7
10
-8
10
-9
27K
24K
21K
10
18K
3T
1
10
2
10
3
10
4
5
10
6
10
-3
10
-4
10
27K
-5
10
3T irradiated
21K
-6
10
24K
10
10
18K
27K
-7
10
unirradiated
21K
2T
1
10
10
-8
10
18K
2
10
3
10
4
10
5
24K
1T
-9
10
6
10
10
J (A/cm2)
Pinning did not increase R below H = 1 T
1
10
2
10
3
4
10
5
10
6
10
J (A/cm2)
matching effect (B=3T)?
101
4T
100 18 K
21 K
-1
10
-2
10
LSCO (x=0.15) film
dc14 ( unirradiated)
dc6 ( 3T irradiated)
24 K
10-3
10-2
10-1
Vortex Velocity (km/s)
100
kinetic friction (10-6 N/m)
kinetic friction (10-6 N/m)
“Inversion” of kinetic friction at intermediate velocities！
101
3T
18 K
100
21 K
-1
10
10-3
friction
sample with strong pinning
higher static friction
lower kinetic friction
more gradual dependence on v
LSCO (x=0.15) film
dc14 ( 0T irradiated)
dc6 ( 3T irradiated)
24 K
10-2
10-1
Vortex Velocity (km/s)
pristine
3Ｔirradiated
velocity
100
S. Savel’ev and F. Nori
Analytical formula
Solution of Fokker-Planck equation
( Fd  4Q /  )
h ( Fd   k BT (T ))
2
v( Fd , T , Q, ) 
2
2
k BTFd (T )  4Q 2 / 
Fk ( Fd , T , Q, ) 
Fd   k BT (T )
Fd
driving forrce
Q
potential height

typical length scale of the potential
h
viscosity
16Q2 cosh(Fd  / 2k BT )  cosh(Q / kBT )
 (T ) 
2
(4Q2  Fd  2 ) sinh(Fd  / 2k BT )
・similar Fk(v) behavior as the experimental data
・maximum Fk around at a velocity v satisfying Q/l～hv
A peak in the kinetic friction Fk(v)
velocity at the peak
jc
vp
jc  0
h
S. Savel’ev and F. Nori
106 A/cm2
0  2.07 107 gauss•cm2
h 107 Ns/m
vp
2 102 m/s
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.
pristine
Q  Hc12/3 Hc 4/3 2
irradiated
Q  Hc 2 2

 rp  
rp  130 A
effective radius of columnar defects
crossover field gives
 Hc 
rp   

H
 c1 
good agreement !
2/3
5
100 A
Vortex lattice in SC vs CDW
using data in A. Maeda et al. JPSJ 59 (1990) 234.
100
10
101
unirradiated
1T
2T
3T
4T
5T
3T irradiated
2
3
4
5
T
T
T
T
Fkin/Fsmax
kinetic friction (10-6 N/m)
2
100
LSCO(x=0.15) film
T = 18 K
10-1 4
10
105
106
2
J (A/cm )
vortex lattice of SC （２Ｄ）
NbSe3 #305
10
30 K
1
0.1
52 K
58 K
1
35 K
47 K
56 K
42 K
57 K
10
100
E/ET
CDW （1Ｄ）
similar behavior despite the difference of dimensionality of collective motion
Thermal effect smears out the difference in dimension ?
Effect of dimension and disorder (T=0 K result)
1D-CDW
2D F-K model
T. Kawaguchi and H. Matsukawa:
PRB 61 (2000) R16346.
H. Matsukawa: JPSJ 57 (1988) 3463.
Fk(v) largely dependent
on dimension and disorder
Physical origin of the peak
Q /  h Fd
Fk
kinetic
static
changing parameters
change transition between
static and kinetic regime
v
broaden the transition
increasing magnetic field
increasing temperature
decreasing system size (macro to micro)
N strongly coupled system
collective coordinate
xmacro
new stochastic variable
xi

i N
 macro  
i
effective temperature
T
Teff  3
L
Teff 
i
N
T
N
(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
theoretical understanding by a simple overdamped model
numerical simulation, analytical results
reproduce almost all the experimental behavior : the peak, defect dependence
The peak is a broadened transition between Fs and Fk
(a) explain the roundness of the crossing of Fs and Fk
(b) provide a link between microscopic and macroscopic friction
Future perspective
・systematic investigation of size effect
・waiting time dependence
・scaling between Fs and Fk ?
New concepts
proposed in
driven vortex system
plasticity
static channels
dynamic reordering
etc.
Dynamic Phase diagram of driven vortices
P. Le Doussal & T. Giamarchi, PRB 57, 11356 (1998).
C. J. Olson et al., PRL 81, 3757 (1998).

Blanco-Canosa et al. PRL 2013, arXiv 2014

resultat de la course des poussins

Studienplan WiSe 2016/17 Vers. 0.5 vom 07.07.16 IE1