Spectral properties of Andreev crystals

TL;DR

This paper thoroughly investigates the spectral properties of Andreev crystals, revealing how magnetic configurations influence their band structure, bound states, and spin polarization, with implications for superconducting spintronics.

Contribution

It provides a detailed theoretical analysis of Andreev crystals with various magnetic configurations, deriving effective models and exploring their spectral and interface properties.

Findings

In ferromagnetic ACs, bands cross without interaction as magnetic strength increases.

In helical ACs, bands can touch at Dirac points, leading to inverted gaps.

Junctions between ACs can host bound states and exhibit spin polarization fractionalization.

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-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.