Majorana Fermions in spin up and down electronic complexes in spin-orbit coupled array of semiconductor quantum dots in proximity to $s$-type superconductor and in magnetic field

TL;DR

This paper investigates Majorana modes in spinful semiconductor-superconductor nanowires, revealing how inter-chain coupling affects their stability and spectral properties, with implications for quantum computing applications.

Contribution

It introduces a framework using bond Fermion transformation and exact diagonalization to analyze Majorana modes in spinful nanowires, highlighting the effects of inter-chain coupling.

Findings

Zero-energy Majorana modes localize at system boundaries in one effective chain.

Inter-chain coupling lifts parity degeneracy and redistributes spectral weight.

The study provides insights into the stability of Majorana modes in realistic spinful systems.

Abstract

Semiconductor-s-type superconductor nanowires host spinful fermions and cannot be reduced to a single spinless Kitaev chain hosting single Majorana zero mode. Instead, such systems can be converted into two coupled p-wave Kitaev-like chains associated with different spin sectors. Using the bond Fermion transformation and exact diagonalization, we analyze parity resolved spectra and local spectral functions, demonstrating that zero-energy modes strongly localized at the system boundaries emerge only in one effective chain. Inter-chain coupling lifts parity degeneracy and redistributes the low-energy spectral weight, providing a controlled framework to assess the stability of Majorana-like modes in the finite spinful nanowires.