Shell formation and two-dimensional nanofriction in three-dimensional ion Coulomb crystals

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 prior work that used 2D ion crystals to investigate one-dimensional nanofriction and orientational melting, we leverage this foundation to extend friction studies from linear ion chains and planar rings to 3D shell structures. Using molecular-dynamics simulations, we first map shell formation as a function of ion number N and the trapping aspect ratio, yielding a simple relation that can aid ion-number estimation in experiments. We compute a Peierls-Nabarro-type potential for the rotation of the outer shell against the static inner core, by treating the angle of rotation as a collective coordinate. We find that changing N by just one can alter the effective rotational barrier by up to a factor of ∼7, while in extreme cases changing N by a few can modify the barrier by up to a factor of ∼60. We quantify a geometric commensurability measure and show that the barrier reflects a system-dependent interplay between the intershell interaction, the structural response of the outer shell, and the confining potential of the trap. Using dynamical simulations, we apply rotational torques to the outer shell and identify pinned, stick-slip, and smooth-sliding regimes whose depinning thresholds depend sensitively on ion number, inner-shell geometry, and trap aspect ratio, with some configurations exhibiting hysteresis due to torque-induced metastable states. We find that spatially varying coupling to the inner-core corrugation can create coexisting fast- and slow-moving domains within the rotating outer shell, realizing multidimensional friction where intrashell shear and intershell nanofriction act simultaneously. Our results highlight the utility of self-organized ion Coulomb crystals as model systems for 2D nanofriction and open up possibilities for stabilizing complex systems and developing ultra-low-friction nanomechanical systems, such as ion-based nanorotors and torque sensors.