SNS junctions in nanowires with spin-orbit coupling: role of confinement and helicity on the sub-gap spectrum

TL;DR

This paper investigates how confinement and helicity influence the sub-gap spectrum and transport properties of SNS nanowire junctions with strong spin-orbit coupling, revealing zero-energy states and their evolution into Majorana modes.

Contribution

It provides a detailed analysis of the role of confinement and helicity in shaping sub-gap states and transport features in nanowire SNS junctions with spin-orbit coupling, including the emergence of Majorana states.

Findings

Fabry-Perot resonances and Fano dips in conductance due to contact scattering.

Helical gaps with half-quantum conductance and oscillations in the normal regime.

Zero-energy parity-protected states evolving into Majorana bound states beyond critical Zeeman field.

Abstract

We study normal transport and the sub-gap spectrum of superconductor-normal-superconductor (SNS) junctions made of semiconducting nanowires with strong Rashba spin-orbit coupling. We focus, in particular, on the role of confinement effects in long ballistic junctions. In the normal regime, scattering at the two contacts gives rise to two distinct features in conductance, Fabry-Perot resonances and Fano dips. The latter arise in the presence of a strong Zeeman field $B$ that removes a spin sector in the leads (\emph{helical} leads), but not in the central region. Conversely, a helical central region between non-helical leads exhibits helical gaps of half-quantum conductance, with superimposed helical Fabry-Perot oscillations. These normal features translate into distinct subgap states when the leads become superconducting. In particular, Fabry-Perot resonances within the helical gap become parity-protected zero-energy states (parity crossings), well below the critical field $B_c$ at which the superconducting leads become topological. As a function of Zeeman field or Fermi energy, these zero-modes oscillate around zero energy, forming characteristic loops, which evolve continuously into Majorana bound states as $B$ exceeds $B_c$. The relation with the physics of parity crossings of Yu-Shiba-Rusinov bound states is discussed.