  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.
