Disorder‐Driven Ionic Mobility Edge and Localization‐Driven Dendrite Formation in Solid Electrolytes

ABSTRACT Dendrite formation in solid electrolytes remains a central obstacle to reliable solid‐state batteries, yet its microscopic origin is debated. A unified framework is presented in which dendrites emerge from disorder‐driven localization of ionic transport. A disorder parameter σ _E , defined by the variance of migration energy barriers, controls the topology of the percolation backbone above the ionic mobility edge Ec . While Ec is set by the mean barrier and remains invariant under σ _E , increasing disorder depletes active conducting pathways, driving a transition from extended conduction to localized transport. This connectivity transition produces filamentary current channels under applied bias; the resulting flux focusing and electric‐field amplification at filament tips provide a direct mechanism for dendrite nucleation. Subsequent growth follows transport‐limited diffusion‐limited aggregation dynamics, yielding fractal morphologies with D _f ≈ 1.7. The critical current density follows j _crit = j ₀ exp(−σ _{E , eff} / k _B T ), linking microscopic energy‐landscape statistics to macroscopic electrochemical stability. The resulting disorder–current phase diagram reveals a nonequilibrium transition between stable and dendritic regimes. These results establish transport localization as a fundamental transport‐mediated mechanism of dendrite formation, indicating that narrowing the distribution of migration barriers, reducing the mean barrier alone, is key to stable solid electrolytes.