Probing nanofriction and Aubry-type signatures in a finite self-organized system

ARTICLE Received 22 Nov 2016 | Accepted 23 Mar 2017 | Published 15 May 2017 DOI: 10.1038/ncomms15364 OPEN Probing nanofriction and Aubry-type signatures in a finite self-organized system J. Kiethe1, R. Nigmatullin2,3, D. Kalincev1, T. Schmirander1 & T.E. Mehlstäubler1 Friction in ordered atomistic layers plays a central role in various nanoscale systems ranging from nanomachines to biological systems. It governs transport properties, wear and dissipation. Defects and incommensurate lattice constants markedly change these properties. Recently, experimental systems have become accessible to probe the dynamics of nanofriction. Here, we present a model system consisting of laser-cooled ions in which nanofriction and transport processes in self-organized systems with back action can be studied with atomic resolution. We show that in a system with local defects resulting in incommensurate layers, there is a transition from sticking to sliding with Aubry-type signatures. We demonstrate spectroscopic measurements of the soft vibrational mode driving this transition and a measurement of the order parameter. We show numerically that both exhibit critical scaling near the transition point. Our studies demonstrate a simple, well-controlled system in which friction in self-organized structures can be studied from classical- to quantum-regimes. 1 Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany. 2 Complex Systems Research Group, Faculty of Engineering and IT, The University of Sydney, Sydney, New South Wales 2006, Australia. 3 Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK. Correspondence and requests for materials should be addressed to T.E.M. (email: ). NATURE COMMUNICATIONS | 8:15364 | DOI: 10.1038/ncomms15364 | www.nature.com/naturecommunications 1 ARTICLE D NATURE COMMUNICATIONS | DOI: 10.1038/ncomms15364 ry friction is the resistance to the relative movement of two solid layers. It is responsible for many phenomena such as earthquakes, wear or crack propagation and is of enormous practical and technological impact1. According to Amontons and Coulomb, friction between solids is proportional to the normal force but independent of the contact areas. This intriguing result was explained by realizing that macroscopic objects touch at asperities that are deformed2. A different signature occurs when atomically flat surfaces slide against each other, as for example encountered in micro- or nanoelectromechanical systems or biological molecular motors1,3,4. At this nanoscale level the friction is no longer described by the Amontons-Coulomb law. For this, mathematical models were developed which are simple enough to be analysed analytically and yet should capture the salient features of the friction phenomena. As the sliding atomic layers are in contact with a thermal environment, dry friction phenomena are a problem of non-equilibrium statistical mechanics as well as nonlinear dynamics5. One of the most successful models describing friction phenomena is the Frenkel–Kontorova (FK) model6. It consists of a chain of coupled particles sliding over a static periodic potential, which mimics a rigid undeformable substrate. The analysis of this model has revealed highly nontrivial, nonlinear dynamics such as the creation of kinks and anti-kinks, which facilitate the sliding. For an infinite system with incommensurate lattice periodicities, this model displays the celebrated Aubry transition7, where the sliding motion becomes frictionless, due to the competition of different interaction energies in the atomic many-body system. In solid-state systems, this superlubric regime has been demonstrated in nanocontacts of graphene and gold surfaces8–11. In finite systems a smooth-sliding regime with finite dissipation exists instead of the superlubric phase. An Aubry-type transition with a symmetry breaking signature occurs, when the system changes from the smooth-sliding to stick-slip regime12,13. With the advent of atomic and friction force microscopes and microbalances it became possible to study individual sliding junctions at the atomistic level14–17. These techniques have identified many friction phenomena at the nanoscale, but many key aspects of friction dynamics are not yet well understood due to the lack of probes that characterize the contact surfaces directly and in situ1. Laser-cooled and trapped ions have been proposed to emulate nanocontacts and to provide insights into the dynamics of friction processes18–20. In this scenario, the FK model is emulated by a chain of ions trapped in the harmonic potential of an ion trap, which is overlapped with an optical standing wave mimicking the corrugation potential. Signatures of an Aubry-type transition, that is, fragmentation and symmetry breaking of the periodic configuration of the ion chain, have been predicted, when the optical lattice depth increases above a critical value19. Another signature of the Aubry transition is the existence of a soft mode, that is, a vibrational mode whose frequency approaches zero at the critical point and drives the transition from pinned to sliding motion12. Such behaviour is also predicted for finite chains of ions in an external optical corrugation potential21. Recently, Bylinskii et al.22 succeeded in cooling up to five ions into an optical lattice and demonstrated the onset of reduced friction and dissipation in a coupled atomic many-body system. In this experiment, the symmetry breaking Aubry-type transition has been observed for the first time with microscopic resolution23, together with velocity effects in the stick-slip motion24. Another synthetic system, in which the microscopic processes of friction have become accessible, are colloidal monolayers driven across external optical potentials25. All these systems aim to emulate the 2 classical FK model, where a layer of interacting particles slides over a fixed rigid corrugation potential. Here we report on the microscopic and spectroscopic control of a system without an externally imposed corrugation potential but consisting of two deformable back acting atomic layers, whose relative motion exhibits the phenomena of nanoscale friction. This system has similarities to a refined microscopic model of friction, which replaces the rigid substrate by a deformable substrate monolayer pinned to a solid body26. In particular, we investigate static friction under the influence of a structural defect and demonstrate physical properties of the system, which are common to finite incommensurate systems. We use a structural defect (kink) in an ion Coulomb crystal27 to create a local disturbance in the ion spacing in the upper and lower chain, and demonstrate an Aubry-type transition when the interatomic spacing of the layers is varied. We show, using numerical calculations, that the soft mode frequency exhibits a power law scaling behaviour in the vicinity of the critical point, where the system becomes s (...truncated)