Gap inversion in one-dimensional Andreev crystals

TL;DR

This paper investigates the spectral properties and topological phases of one-dimensional Andreev crystals with magnetic regions, revealing gap inversion phenomena, spin polarization effects, and fractionalized interface states.

Contribution

It introduces the concept of gap inversion in Andreev crystals and relates spectral asymmetry to observable spin polarization, providing new insights into topological phases in superconducting systems.

Findings

Antiferromagnetic ACs exhibit gapped and gapless phases separated by Dirac points.

Heterojunctions support spin-polarized bound states at interfaces.

Interface spin fractionalization occurs analogous to charge fractionalization in Dirac systems.

Abstract

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