Na Nanosca scale sti stick ck-sl slip p fricti ction stu - PowerPoint PPT Presentation

Na Nanosca scale sti stick ck-sl slip p fricti ction stu studi died d with th tr trappe pped d ions s Al Alex exei ei Bylinsk skii Dorian Gangl gloff Ian Counts ts Honggi ggi Jeon Wo Wonho Jhe Jhe ( (Seoul Seoul) Vlada dan Vuleti ti ć Massa ssach chuse setts tts Insti stitu tute te of Tech chnology gy MIT-Harvard d Cente ter for Ultr traco cold d Ato toms s

Outl tline • Ion-trap emulator of friction with cold trapped ions • Single-asperity, single-atom friction (Prandtl- Tomlinson model 1928) • Thermolubricity, velocity dependence of friction • From few- to many-particle friction (Frenkel- Kontorova model 1938) • Superlubricity and the Aubry transition (Aubry 1983) • Friction in multistable potentials

Frict rictio ion at the nanosca scale le • Spectacular advances • Molecular dynamics simulations with thousands of atoms at the surface layer. • Atomic force microscopy friction can measure atomic- scale friction. A. Socoliuc, R. Bennewitz, E. Gnecco, and E. Meyer, PRL 92 , 134301 (2004). force

Ion-cr crysta stal fricti ction emulato tor Pioneering theoretical proposals by Shepelyansky, Vanossi & Tosatti, Haeffner and others I. Garcıa-Mata, O. V. Zhirov, D. L. Shepelyansky, Eur. Phys. J. D 41 , 325 (2006). A. Benassi, A. Vanossi, E. Tosatti, Nat. Commun. 2 , 236 (2011). D. Mandelli, A. Vanossi, E. Tosatti, Phys. Rev. B 87 , 195418 (2013). T. Pruttivarasin, M. Ramm, I. Talukdar, A. Kreuter, H. Haeffner, New J. Phys. 13 , 075012 (2011).

Our ion fricti ction sy syste stem d~0.5 n m a Theory ¡proposals: ¡ support chain a • Benassi, ¡A., ¡Vanossi, ¡A., ¡& ¡ substrate Tosa5, ¡E. ¡(2011). ¡ Nature ¡ Communica.ons , ¡ 2 , ¡236 ¡ ¡ • García-­‑Mata, ¡I., ¡Zhirov, ¡O. ¡V., ¡& ¡ b ion trap (support) Shepelyansky, ¡D. ¡L. ¡(2006). ¡ The ¡ European ¡Physical ¡Journal ¡D , ¡ 41(2), ¡325–330 ¡(2006) ¡ d~5 µ m • Pru5varasin, ¡T., ¡Ramm, ¡M., ¡ Talukdar, ¡I., ¡Kreuter, ¡A., ¡& ¡ Häffner, ¡H. ¡ New ¡Journal ¡of ¡ Yb+ ion chain optical lattice Physics , ¡ 13 (7), ¡075012 ¡(2011) ¡ a=185nm (substrate)

Our ion fricti ction sy syste stem Karpa, Bylinskii, Gangloff, Cetina, & Vuletic, Suppression of Ion Transport due to Long-Lived Subwavelength Localization by an Optical Lattice. PRL 111 , 163002 (2013).

Ion cr crysta stal fricti ction emulato tor Position and track each atom • with sub-lattice-site resolution Control all microscopic • parameters: Temperature, potential depth, lattice period, atom number, velocity, atom position, time resolved tracking.

Subw bwavelength gth po posi siti tion tr track cking g 600 fitted curve 185 nm 500 fluorescence Collected counts/s 400 300 200 100 0 8 9 10 11 12 13 14 15 16 DC electrode voltage (V) x F ∝ sin 4 ( x )

Single-particle friction: Prandtl-Tomlinson model

Singl gle-pa parti ticl cle mode del for nanofricti ction movie Stick-slip friction L. Prandtl, Z. Angew. Math. Mech. 8 , 85 (1928); G. A. Tomlinson, Philos. Mag. 7 , 905 (1929).

Sti tick ck-sl slip p fricti ction with th ions s in opti ptica cal latti ttice ce Ion imaging with 3 µ m • resolution (sufficient to resolve neighboring ions) Sub-lattice site resolution • via position dependent ion fluorescence (~20 nm for 100ms integration time, lattice spacing 185 nm)

Time- and d latti ttice ce-si site te-reso solved d si singl gle-ion de dete tecti ction Hysteresis loop measures friction

Fricti ction measu surement t with th si singl gle ato tom Friction ∝ normal load Prandtl- Tomlinson model Solid line: Prandtl-Tomlinson model � = ​(​#↓%&'' /​#↓'*& L. Prandtl, Z. Angew. Math. Mech. 8 , 85 (1928); G. A. Tomlinson, Philos. Mag. 7 , 905 (1929). A. Bylinskii, D. Gangloff, and V. Vuleti ć , Science 348 , 1115 (2015).

Dependence of friction on velocity v F s M

Veloci city tu tuning g of fricti ction High T Low T Low T High T or high v or low v Low temperature High temperature U B or high velocity: or low velocity: Non-equilibrium, Near equilibrium, atom stuck in Boltzmann factors metastable state Trap position: 1 2 3 1 2 3 Friction is reduced Fluorescence 2F s by temperature. 2 F 2 F How much depends 2 F on velocity Trap position Jinesh, Krylov, Valk, Dienwiebel, & Frenken, Phys. Rev. B 78 , 155440 (2008).

Thermolubr brici city ty Thermal activation reduces friction force as ion follows global potential minimum. movie Experiment and theory in real friction: Speed Dependence of Atomic Stick-Slip Friction in Optimally Matched Experiments and Molecular Dynamics Simulations Li, Dong, Perez, Martini, and Carpick, Phys. Rev. Lett. 106 , 126101

Four veloci city ty regi gimes s of fricti ction D. Gangloff, A. Bylinskii, I. Counts, W. Jhe, and V. Vuleti ć , Nat. Phys. 11 , 915 (2015).

Dependence of friction on surface: Structural friction M F s

Many-p Ma y-part rticle icle mo model l of frict rictio ion η = 2 π 2 a 2 U/K d g/K a (mod 1) = ω 2 L /ω 2 0 X = F app d K K g U a + Prandtl-Tomlinson Frenkel-Kontorova (1928) (1938)

Fricti ction with th se several ions: s: match tched d ca case se Same as single-ion friction for each ion: large friction. All ions slip simultaneously. movie

Match tched d and d mism smatch tched d configu co gurati tions s Mismatched q=1 Matched q=1 Matching parameter Shown is phase of unperturbed ion position relative to optical lattice.

Fricti ction with th se several ions: s: mism smatch tched d Nearly vanishing friction: Superlubricity. A. Bylinskii, D. Gangloff, and V. Vuleti ć , Science movie 348 , 1115-1118 (2015).

Transi siti tion from match tched d to to mism smatch tched d regi gime - - - T=0 ____ T > 0 2 ions 3 ions 6 ions A. Bylinskii, D. Gangloff, and V. Vuleti ć , Science 348 , 1115 (2015).

Match Ma ched vs. vs. misma mismatch ched ch chain ins s d a (mod 1) = 0 d a a (mod 1) = 1 d d 2 a Essence of superlubricity: near-zero friction persists for finite spring constant.

Match tched d and d mism smatch tched d fricti ction for tw two ions s matched mismatched D. Gangloff, A. Bylinskii, I. Counts, W. Jhe, and V. Vuleti ć , Nature Physics (2015).

Two-ion match tching g de depe pende dence ce of fricti ction: “su supe perlubr brici city ty” ” “Superlubricity”: K. Shinjo, M. Hirano, Surf. Sci. 283, 473 (1993).

Supe perlubr brici city ty in real fricti ction • Dienwiebel, M. et al. Superlubricity of graphite. Phys. Rev. Lett. 92 , 126101 (2004).

Transpo sport t via kinks: s: sy synch chrony Peierls-Nabarro potential for two ions Polar plot representation of slipping times (2 ions) Polar plot representation of slipping times (5 ions) Synchrony

Transpo sport t via kinks: s: sy synch chrony commensurate- incommensurate transition incommensurate commensurate Synchronous transport Transport via kinks Weak dependence of friction on matching Strong dependence on matching

Nanofriction and Aubry transition

Sta tati tic c Aubr bry tr transi siti tion Infinite chain Maximally incommensurate d/a mod 1 = Golden Ratio What happens as periodic corrugating potential is increased? Atoms suddenly localize in periodic potential at some criticial potential depth. Aubry, S. Exact models with a complete devil’s staircase. Journal of Physics C: Solid State Physics 16 , 2497 (1983). Aubry, S. & Le Daeron, P. The discrete Frenkel-Kontorova model and its extensions. Physica D: Nonlinear Phenomena 8 , 381–422 (1983).

An Analyt lyticit icity y bre reakin king x pinned mod a 0.5 Potential 0 U < U c maximum -0.5 x init mod a -0.5 0.5 0 Fractal structure: gaps in position space on every scale Aubry, S. Exact models with a complete devil’s staircase. Journal of Physics C: Solid State Physics 16 , 2497 (1983).

Aubr bry tr transi siti tion Position relative to lattice Final position Primary gap secondary gap Initial position Aubry transition: smooth distribution of positions (for infinite chain) breaks up into fractal distribution. Highest critical potential for (d/a) mod 1 =(1+ √ 5)/2 (Golden Ratio)

Finite te Aubr bry tr transi siti tion Position relative to lattice Gaps correspond to bistable hysteresis loops in friction. Aubry sliding-to-pinned analycity breaking transition is transition from superlubricity to stick-slip friction.

Aubr bry tr transi siti tion in finite te ch chain Primary gap for one ion (avoiding potential maximum) corresponds to secondary gap for next ion.

Obse bservati tion of pr primary and d se seco conda dary ga gaps ps in th three-ion ch chain 0.7 Primary gap Δ x 0 0.07 Δ x Secondary gap 0 A. Bylinskii, D. Gangloff, I. Counts, V. Vuletic, Nat. Mat. (2016).