1. 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 A. MAEDA Y. INOUE H. KITANO T. UMETSU IWV-10, Mumbai, India, Jan 9-15, 2005 JAERI S. OKAYASU Frontier Research System, RIKEN S. SAVELEV F. NORI CRIEPI I. TSUKADA

2. 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

3. 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 driving force 0 ＦCＦC ＦCＦC ＦkＦk staticmoving F k depends on velocity at low velocities Amontons-Coulomb’s friction friction in reality ・・・ friction driving force 0 ＦCＦC ＦｃＦｃ staticmoving Massive blocks

4. 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 F k, (> static friction), is independent of velocity. ・ (3) is invalid at low velocities (velocity dependent) larger velocity dependence for clean surfaces ・ finite F k even for zero normal reaction Not always valid ・ any relationship between F k and F s ? ・ any relationship between F k and F s ? scaling law between F k and F s （ thick paper ： Heslot (1994) ） scaling law between F k and F s （ thick paper ： Heslot (1994) ） Good model systems are necessary, with which systematic experiment is available in a repeated manner universal property?

5. 1 D model for clean surfaces clean surface(normal) dirty surface ・ clean surface finite F k even for zero F s ・ disordered surface less velocity dependent similar to Amontons-Coulomb’s law numerical solution for the above equation F k as a function of velocity Microscopic formulation of friction steady state summing up for all atoms time averaged friction: sum of interatomic (pinning) forces eq. motion for a lower atom i ← a displacement of upper atom i: u i, mass m a ← b displacement of lower atom j v j, mass m b eq. motion for an upper atom i dissipation from a representative DF to others H. Matsukawa and H. Fukuyama: PRB 49, 17286 (1994)

6. Model systems for friction study in quantum condensate in solids Charge-density wave (CDW) Vortex lattice of superconductor u i : displacement of i-th electron in the CDW m: mass of the i-th electron F p : pinning force for i-th electron u i : displacement of i-th vortex in the lattice m: mass of the i-th vortex in the lattice F p : pinning force for i-th vortex B 1D 2D

7. (a) many internal degrees of freedom (b) nonlinearity (c) random pinning (d) finite threshold friction (critical current density J c ) (e) finite kinetic friction in moving state (flux flow) Driven vortices of superconductor J E JcJc energy dissipation 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

8. Expressing solid-solid friction in terms of vortex motion Driving force J ×Φ 0 viscous force η direction of vortex motion kinetic friction F FRIC （ pinning force ） I -V measurement and viscosity, , measurement can deduce kinetic friction Flux flow resistivity necessary to make correspondence with theory J: current density  : resistivity  0 : flux quantum

9. Sliding charge-density waves (CDWs) kinetic friction driving electric field for CDW conductivity at electric field E conductivity in the infinite field limit electronic charge I-V measurement and measurement can deduce kinetic friction

11. microscopic understanding of solid-solid friction using driven vortices of high-T c 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 superconductors in terms of physics of friction and vice versa

12. (1) thin films (PLD) (I. Tsukada (CRIEPI)) compare F k among samples with different pinning # dc14 ・・・ pristine T c =31 K # dc 6 ・・・ irradiated by ion T c =30 K (2) bulk crystal ( FZ method) B Φ =3T columnar defects (S. Okayasu (JAERI)) Samples Cuprate superconductor : La 2-x Sr x CuO 4 (x=0.16) achieve high current densities (velocities) for viscosity measurement by microwave technique 200 MeV Iodine

13. Y.Tuchiya et al PRB 63 184517 (2001). A.Maeda et al Physica C 362 (2001) 127-134  * ～ 1×10 -7 Ns/m 2 （ 4.5K) Vortex viscosity and electronic structure of QP in the core LSCO (x=0.15) (moderately clean) moderately clean nature rather generic in HTSC (doping, material) T. Umetsu et al unpublished.

14. LSCO films stronger pinning at low temperatures in irradiated samples effect of irradiation I-V measured with using short pulses

15. F k (v) （ up to ～ 1 km/s ） 4) smaller F k in irradiated samples 3) F k saturates and decreases inconsistent with the behavior at low velocities ? pristine3T irradiated 2) very much different from the Amontons-Coulomb behavior 1) F k changes with B and T in a reproducible manner good as a model system similar to “clean surface” existence of a peak in F k (v) Data points with crosses denote pulsed measurements

16. 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

17. Numerical simulation for 1D vortex array at finite temperatures S. Savel’ev and F. Nori a peak

18. LSCO films Pinning did not increase R below H = 1 T matching effect (B  =3T)?

19. “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 Ｔ irradiated pristine

20. S. Savel’ev and F. Nori

21. Analytical formula Solution of Fokker-Planck equation driving forrce potential height typical length scale of the potential viscosity ・ similar F k (v) behavior as the experimental data ・ maximum F k around at a velocity v satisfying Q/l ～  v

22. A peak in the kinetic friction F k (v) velocity at the peak S. Savel’ev and F. Nori in good agreement with experiment Potential energy plays an important role for F k (v).

23. Estimate Q and l by a collective pinning theory G. Blatter et al. Rev. Mod. Phys. 66 (1994) 1125. pristine irradiated effective radius of columnar defects crossover field gives good agreement !

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

25. Effect of dimension and disorder (T=0 K result) 1D-CDW 2D F-K model T. Kawaguchi and H. Matsukawa: PRB 61 (2000) R16346. F k (v) largely dependent on dimension and disorder H. Matsukawa: JPSJ 57 (1988) 3463.

26. Physical origin of the peak v FkFk static kinetic changing parameters change transition between static and kinetic regime increasing magnetic field increasing temperature decreasing system size (macro to micro) broaden the transition

27. N strongly coupled system collective coordinate new stochastic variable effective temperature (L : system size)

28. Conclusion discuss kinetic friction by investigating dynamics of VL in high-T c SC and CDW reproducible control of “interaction between interfaces”by B, T etc promising : vortices of high-T c superconductors, CDWs as good model systems for investigating physics of friction ・ systematic investigation of size effect ・ waiting time dependence ・ scaling between F s and F k ? 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 F s and F k (b) provide a link between microscopic and macroscopic friction Future perspective The peak is a broadened transition between F s and F k

29. New concepts proposed in driven vortex system plasticity static channels dynamic reordering etc.

30. C. J. Olson et al., PRL 81, 3757 (1998). P. Le Doussal & T. Giamarchi, PRB 57, 11356 (1998). Dynamic Phase diagram of driven vortices