Spectral properties of Andreev crystals

Abstract

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-neighbor 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-neighbor approximation by solving the Eilenberger equation for infinite ACs 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.

Gap inversion in quasi-one-dimensional Andreev crystals

“…This is indeed confirmed by the exact numerical solution of Eq. ( 4) 34 In conclusion, we show that the spin polarization of a gapped system with collinear magnetization can only change upon gap closing. This occurs in Andreev crystals for which we present a complete study of their spectral properties for ferromagnetic and antiferromagnetic configurations.…”

Yu-Shiba-Rusinov states in two-dimensional superconductors with arbitrary Fermi contours

“…The results demonstrate how the low-symmetric square-and hexagon-shaped FCs lead to a slower decay of the YSR states. Such a decay is similar to the 1D situation, and suggests the use of superconductors with a square-shaped FC for the realization of one-dimensional Andreev crystals [57,58] by placing chains of magnetic defects along the direction parallel to the symmetry axis of the square.…”