L. -A. Rüffert

Self-organized three-dimensional (3D) ion Coulomb crystals in linear Paul traps naturally form concentric shells that provide a curved, atomically resolved interface for studying two-dimensional (2D) nanofriction. Building on earlier studies of one-dimensional nanofriction and orientational melting in 2D ion crystals, we extend friction studies from linear chains and planar rings to 3D shell structures. Using molecular-dynamics simulations, we map shell formation as a function of ion number N and trap aspect ratio and obtain a simple scaling relation that can aid ion-number estimation in experiments. We compute a Peierls-Nabarro-type potential for rotating the outer shell against a static inner core, using the rotation angle as a collective coordinate. Changing N by one can alter the effective rotational barrier by up to a factor of ~7, while changes by only a few ions can lead to variations up to a factor of ~60. Combining geometric commensurability analysis with energy decomposition, we show that the barrier is governed by a system-dependent interplay between inter-shell interaction, outer-shell response and trap confinement. Dynamical simulations with applied torques reveal pinned, stick-slip and smooth-sliding regimes with depinning thresholds that depend on ion number, inner-shell geometry and trap aspect ratio. Some configurations show hysteresis due to torque-induced metastable states. We further find that spatially varying coupling to the inner-core corrugation can create coexisting fast and slow domains within the rotating outer shell, realizing multidimensional friction in which intra-shell shear and inter-shell nanofriction act simultaneously. Our results establish self-organized ion Coulomb crystals as model systems for 2D nanofriction and suggest routes toward ion-based nanorotors, torque sensors and ultra-low-friction nanomechanical systems.

Trapped ion systems constitute a well controllable scenario for the study and emulation of nanofriction, and in particular of Frenkel-Kontorova-like models. This is in particular the case when a topological defect is created in a zigzag ion Coulomb crystal, which results in an Aubry transition from free sliding to pinned phase as a function of the trap aspect ratio. We explore the quantum effects of the Aubry transition by means of an effective simplified model, in which the defect is treated like a single quantum particle that experiences an effective Peierls-Nabarro potential and a position-dependent mass. We demonstrate the relevance of quantum tunneling in a finite range of aspect ratios close the critical point, showing that the quantum effects may be observed in the kink dynamics for sufficiently low temperatures. Finally, we discuss the requirements to reveal quantum effects at the Aubry transition in future experiments on trapped ions.