  We present an exhaustive study of Andreev crystals (ACs) --
quasi-one-dimensional superconducting wires with a periodic distribution of
magnetic regions. The exchange field in these regions is assumed to be much
smaller than the Fermi energy. Hence, the transport through the magnetic region
can be described within the quasiclassical approximation. In the first part of
the paper, by assuming that the separation between the magnetic regions is
larger than the coherence length, we derive the effective nearest-neighbour
tight-binding equations for ACs with a helical magnetic configuration. The
spectrum within the gap of the host superconductor shows a pair of
energy-symmetric bands. By increasing the strength of the magnetic impurities
in ferromagnetic ACs, these bands cross without interacting. However, in any
other helical configuration, there is a value of the magnetic strength at which
the bands touch each other, forming a Dirac point. Further increase of the
magnetic strength leads to a system with an inverted gap. We study junctions
between ACs with inverted spectrum and show that junctions between
(anti)ferromagnetic ACs (always) never exhibit bound states at the interface.
In the second part, we extend our analysis beyond the nearest-neighbour
approximation by solving the Eilenberger equation for infinite and junctions
between semi-infinite ACs with collinear magnetization. From the obtained
quasiclassical Green functions, we compute the local density of states and the
local spin polarization in anti- and ferromagnetic ACs. We show that these
junctions may exhibit bound states at the interface and fractionalization of
the surface spin polarization.
