Renormalization effects in spin-polarized metallic wires proximitized by a superconductor: A scattering approach

TL;DR

This paper develops a scattering approach to explain how coupling to a superconductor renormalizes the properties of spin-polarized metallic wires, affecting Majorana states and their velocities, regardless of interface transparency.

Contribution

It introduces a semiclassical scattering method to analyze renormalization effects in superconductor-normal metal systems, highlighting the role of double Andreev reflections and interface transparency.

Findings

Renormalization of propagation velocity due to Andreev reflections.

Effects persist without a proximity-induced minigap.

Renormalization occurs for various interface transparencies.

Abstract

Spin-polarized normal-metal wires coupled to a superconductor can host Majorana states at their ends. These decay into the bulk and are protected by a minigap in the spectrum. Previous studies have found that strong coupling between the superconductor and the normal-metal wire renormalizes the properties of this low-energy phase. Here, we develop a semiclassical scattering approach to explain these renormalization effects. We show that a renormalization of the propagation velocity in the normal wire originates from double Andreev reflection processes at the superconductor interface and that it continues to exist in the absence of a proximity-induced minigap in the normal-metal wire. We also show that the renormalization effects exist for arbitrary transparency of the normal-metal--superconductor interface, provided the superconductor coherence length is sufficiently long in comparison to the thickness of the normal metal.