Abstract: We study Dirac plasmons and their damping in spatially separated N-layer graphene structures at finite doping and temperatures. The plasmon spectrum consists of one optical excitation with square-root dispersion and N – 1 acoustical excitations with linear dispersion, which are undamped at zero temperature and finite doping within a triangular energy region outside the electron-hole continuum. In the long-wavelength limit the energy and weight of the optical plasmon modes increase, respectively, as the square root and linearly with N in agreement with recent experimental findings. The energy and weight of the upper-lying acoustical branches also increase with N. This increase is strongest for the uppermost acoustical mode, and we find that its energy can exceed at some value of momentum the plasmon energy in an individual graphene sheet. Meanwhile, the energy of the low-lying acoustical branches decreases weakly with N as compared with the single acoustical mode in double-layer graphene structures. Our numerical calculations provide a detailed understanding of the overall behavior of the wave-vector dependence of the optical and acoustical multilayer plasmon modes and show how their dispersion and damping are modified as a function of temperature, interlayer spacing, and inlayer carrier density in (un)balanced graphene multilayer structures. DOI: 10.1103/PhysRevB.87.085401

Abstract: The physical properties of clays and micas can be controlled by exchanging ions in the crystal lattice. Atomically thin materials can have superior properties in a range of membrane applications, yet the ion-exchange process itself remains largely unexplored in few-layer crystals. Here we use atomic-resolution scanning transmission electron microscopy to study the dynamics of ion exchange and reveal individual ion binding sites in atomically thin and artificially restacked clays and micas. We find that the ion diffusion coefficient for the interlayer space of atomically thin samples is up to 10(4) times larger than in bulk crystals and approaches its value in free water. Samples where no bulk exchange is expected display fast exchange at restacked interfaces, where the exchanged ions arrange in islands with dimensions controlled by the moire superlattice dimensions. We attribute the fast ion diffusion to enhanced interlayer expandability resulting from weaker interlayer binding forces in both atomically thin and restacked materials. This work provides atomic scale insights into ion diffusion in highly confined spaces and suggests strategies to design exfoliated clay membranes with enhanced performance. Layered clays are of interest for membranes and many other applications but their ion-exchange dynamics remain unexplored in atomically thin materials. Here, using electron microscopy, it is found that the ion diffusion for few-layer two-dimensional clays approaches that of free water and that superlattice cation islands can form in twisted and restacked materials.