Single-file diffusion of charged particles on a devil’s staircase

Abstract Controlling how particles diffuse through low-dimensional materials, where long-range repulsion couples every particle to every other, is central to ionic conductors, intercalation compounds, and many confined transport systems. Yet how such repulsion shapes diffusion at realistic temperatures has remained poorly understood, because the ordered states it stabilizes and the rare hops that govern motion are difficult to treat analytically or to sample numerically. Here we show, by combining large-scale simulations with a theoretical framework, that diffusion is sharply suppressed at a hierarchy of commensurate densities forming a devil’s staircase, most prominently at one-half, one-third, and two-thirds filling, and that random defects destabilize these ordered states and restore transport. To explain this, we represent particle configurations as evenly spaced building blocks whose rearrangements map the complex interacting system onto a simple symmetric exclusion process. Our results provide a unified, quantitative account of diffusion suppression in long-range interacting materials.