Emergence and melting of active vortex crystals

Melting of two-dimensional (2D) equilibrium crystals, from superconducting vortex lattices to colloidal structures, is a complex phenomenon characterized by the sequential loss of positional and orientational order. Whereas melting processes in passive systems are typically triggered by external heat injection, active matter crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Emergent crystal-like order has been observed in recent experiments on suspensions of swimming sperm cells, fast-moving bacteria, Janus colloids, and in embryonic tissues. Yet, despite recent progress in the theoretical description of such systems, the non-equilibrium physics of active crystallization and melting processes is not well understood. Here, we establish the emergence and investigate the melting of self-organized vortex crystals in 2D active fluids using an experimentally validated generalized Toner-Tu theory. Performing hydrodynamic simulations at an unprecedented scale, we identify two distinctly different melting scenarios: a hysteretic discontinuous phase transition and melting through an intermediary hexatic phase, both of which can be controlled by self-propulsion and active stresses. Our analysis further reveals intriguing transient features of active vortex crystals including meta-stable superstructures of opposite spin polarity. Generally, these results highlight the differences and similarities between crystalline phases in active fluids and their equilibrium counterparts.