Unified analysis of Topological Defects in 2D systems of Active and Passive disks

We have carried out a comprehensive quantitative analysis of localized and extended topological defects in the steady state of 2D passive and active repulsive Brownian disk systems. Both in and out-of-equilibrium, solid-hexatic melting is driven by the unbinding of dislocations, in quantitative agreement with the KTHNY singularity. Instead, although disclinations dissociate as soon as the liquid phase appears, they are not free, but rather always grouped together or with other more complex defect structures. Extended clusters of defects largely dominate below the solid-hexatic critical line. The latter percolate in the liquid phase very close to the hexatic-liquid transition, both for continuous and discontinuous transitions, in the homogeneous liquid regime. At critical percolation the clusters of defects are fractal with statistical and geometric properties that, within our numerical accuracy, are independent of the activity and compatible with the universality class of uncorrelated critical percolation. We show that the disclinations are not free, but rather always very near more complex defect structures.