Gap inversion in quasi-one-dimensional Andreev crystals

We study a periodic arrangement of magnetic regions in one-dimensional superconducting wire. Due to the local exchange field, each region supports Andreev bound states that hybridize forming Bloch bands subgap spectrum what we call crystal (AC). As an illustration, ACs with ferromagnetic and antiferromagnetic alignment are considered. relate spectral asymmetry index spin-resolved Hamiltonian spin polarization identify it as observable quantifies closing reopening excitation gap. In particular, exhibit sequence gapped phases separated by gapless Dirac phase boundaries. Heterojunctions between neighboring support spin-polarized at interface. close analogy charge fractionalization systems mass inversion, find interface spin.