  The competition between thermal fluctuations and potential forces is the
foundation of our understanding of phase transitions and matter in equilibrium.
Driving matter out of equilibrium allows for a new class of interactions which
are neither attractive nor repulsive but transverse. The existence of such
transverse forces immediately raises the question of how they interfere with
basic principles of material self-organization. Despite a recent surge of
interest, this question remains open. Here, we show that activating transverse
forces by homogeneous rotation of colloidal units generically turns otherwise
quiescent solids into a crystal whorl state dynamically shaped by
self-propelled dislocations. Simulations of both a minimal model and a full
hydrodynamics model establish the generic nature of the chaotic dynamics of
these self-kneading polycrystals. Using a continuum theory, we explain how odd
and Hall stresses conspire to destabilize chiral crystals from within. This
chiral instability produces dislocations that are unbound by their
self-propulsion. Their proliferation eventually leads to a crystalline whorl
state out of reach of equilibrium matter.

Soft Condensed Matter