  In the large N limit cold dense nuclear matter must be in a lattice phase.
This applies also to holographic models of hadron physics. In a class of such
models, like the generalized Sakai-Sugimoto model, baryons take the form of
instantons of the effective flavor gauge theory that resides on probe flavor
branes. In this paper we study the phase structure of baryonic crystals by
analyzing discrete periodic configurations of such instantons. We find that
instanton configurations exhibit a series of "popcorn" transitions upon
increasing the density. Through these transitions normal (3D) lattices expand
into the transverse dimension, eventually becoming a higher dimensional (4D)
multi-layer lattice at large densities.
  We consider 3D lattices of zero size instantons as well as 1D periodic chains
of finite size instantons, which serve as toy models of the full holographic
systems. In particular, for the finite-size case we determine solutions of the
corresponding ADHM equations for both a straight chain and for a 2D zigzag
configuration where instantons pop up into the holographic dimension. At low
density the system takes the form of an "abelian anti-ferromagnetic" straight
periodic chain. Above a critical density there is a second order phase
transition into a zigzag structure. An even higher density yields a rich phase
space characterized by the formation of multi-layer zigzag structures. The
finite size of the lattices in the transverse dimension is a signal of an
emerging Fermi sea of quarks. We thus propose that the popcorn transitions
indicate the onset of the "quarkyonic" phase of the cold dense nuclear matter.
