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Sparse Cyclic Excitations Explain the Low Ionic Conductivity of Stoichiometric Li$_{7}$La$_{3}$Zr$_{2}$O$_{12}$

We have performed long time-scale molecular dynamics simulations of the cubic and tetragonal phases of the solid lithium-ion--electrolyte Li$_{7}$La$_{3}$Zr$_{2}$O$_{12}$ (LLZO), using a first-principles parameterised interatomic potential. Collective lithium transport was analysed by identifying dynamical excitations; persistent ion displacements over distances comparable to the separation between lithium sites, and string-like clusters of ions that undergo cooperative motion. We find that dynamical excitations in c-LLZO are frequent, with participating lithium numbers following an exponential distribution, mirroring the dynamics of fragile glasses. In contrast, excitations in t-LLZO are both temporally and spatially sparse, consisting preferentially of highly concerted lithium motion around closed loops. This qualitative difference is explained as a consequence of lithium ordering in t-LLZO, and provides a mechanistic basis for the much lower ionic conductivity of t-LLZO compared to c-LLZO.