Symmetry Protected and Topologically Protected Crossed Andreev Reflection

TL;DR

This paper investigates how symmetry-protected crossed Andreev reflection can be used to identify Majorana modes in multiband 1D topological superconductors, demonstrating robustness against certain disorders and clarifying the role of chiral symmetry.

Contribution

It introduces the concept of symmetry-protected CAR in multiband topological superconductors and distinguishes the effects of magnetic and non-magnetic disorders on Majorana and Andreev bound states.

Findings

Symmetry-protected CAR is stable against non-magnetic disorder.

Magnetic disorder destroys CAR from Andreev bound states but not from Majorana modes.

Majorana modes enable topologically protected CAR in realistic systems.

Abstract

Crossed Andreev reflection (CAR) is considered to probe the non-locality of the Majorana quasiparticles in topological superconductors. We propose here to study the CAR in multiband one-dimensional (1D) topological superconductors which may or may not have chiral symmetries, and show how the CAR can be applied to identify Majorana modes in such systems. In particular, for a multiband 1D topological superconductor with approximate chiral symmetry, both the multiple Majorana and low-energy Andreev bound modes can drive the nearly zero-bias CAR, which is shown to be protected by the chiral symmetry and is stable against non-magnetic disorder scatterings. The emergence of symmetry protected CAR makes it hard to identify exotic Majorana fermions out of low-energy Andreev bound states. It is interesting that the magnetic disorders, which break chiral symmetry, can fully kill the non-locality of low-energy Andreev bound states, while cannot affect the Majorana modes, leading to the topologically protected CAR which is solely contributed by the Marjorana modes. The experimentally relevant systems, including the semiconductor nanowires and the Fe chains in the top of an $s$-wave superconductor, have been considered.