Emergent smectic order in simple active particle models

Novel "smectic-P" behavior, in which self-propelled particles form rows and move on average along them, occurs generically within the orientationally-ordered phase of simple models that we simulate. Both apolar (head-tail symmetric) and polar (head-tail asymmetric) models with aligning and repulsive interactions exhibit slow algebraic decay of smectic order with system size up to some finite length scale, after which faster decay occurs. In the apolar case, this scale is that of an undulation instability of the rows. In the polar case, this instability is absent, but traveling fluctuations disrupt the rows in large systems and motion and smectic order may spontaneously globally rotate. These observations agree with a new hydrodynamic theory which we present here. Variants of our models also exhibit active smectic "A" and "C" order, with motion orthogonal and oblique to the layers respectively.