  The low energy limit of QCD admits (crystals of) superconducting Baryonic
tubes at finite density. We begin with the Maxwell-gauged Skyrme model in
(3+1)-dimensions (which is the low energy limit of QCD in the leading order of
the large N expansion). We construct an ansatz able to reduce the seven coupled
field equations in a sector of high Baryonic charge to just one linear
Schrodinger-like equation with an effective potential (which can be computed
explicitly) periodic in the two spatial directions orthogonal to the axis of
the tubes. The solutions represent ordered arrays of Baryonic superconducting
tubes as (most of) the Baryonic charge and total energy is concentrated in the
tube-shaped regions. They carry a persistent current (which vanishes outside
the tubes) even in the limit of vanishing U(1) gauge field: such a current
cannot be deformed continuously to zero as it is tied to the topological
charge. Then, we discuss the subleading corrections in the 't Hooft expansion
to the Skyrme model (called usually \mathcal{L}_{6}$, $\mathcal{L}_{8}$ and so
on). Remarkably, the very same ansatz allows to construct analytically these
crystals of superconducting Baryonic tubes at any order in the 't Hooft
expansion. Thus, no matter how many subleading terms are included, these
ordered arrays of gauged solitons are described by the same ansatz and keep
their main properties manifesting a universal character. On the other hand, the
subleading terms can affect the stability properties of the configurations
setting lower bounds on the allowed Baryon density.
