Field-Induced Percolation and Nonequlibrium Phase Behavior in Binary Mixtures with Differential Diffusivity

Active matter consists of agents that consume local energy to generate autonomous motion or exert forces, leading to dynamics fundamentally out of thermal equilibrium. We study a binary mixture of "hot" and "cold" particles differing only in their random motion or diffusivity, where this local energy contrast drives sustained non-equilibrium behavior. Under an external sinusoidal field, the interplay between diffusivity differences and field strength produces varied collective dynamics: passive particles form dense band-like structures surrounded by active ones. Reentrant behavior, where demixing disappears at both low and high densities, arises even when both species respond identically to the field, a feature not previously reported. Over time, clusters grow and align along the field, forming phase-separated bands, with a field-driven percolation transition at specific densities calculated by finite-size scaling. These results provide insights into tunable self-organization in soft matter, with potential applications in microfluidics and biomedical systems.