Free Majorana Fermions with Superconducting Quantum Wires and a Magnetic Impurity

TL;DR

This paper models free Majorana fermions arising from a magnetic impurity in a superconducting wire system, demonstrating their wavefunctions, pairing, and potential realization in superconducting setups.

Contribution

It introduces a theoretical framework for free Majorana fermions generated by magnetic impurities in superconducting wires, with detailed wavefunction and pairing analysis.

Findings

Identification of two zero-energy Majorana fermions of magnetic origin

Derivation of the edge wavefunction for the Majorana bound state

Proposal for realizing free Majorana fermions with magnetic impurities bridging superconductors

Abstract

Through the two-channel Kondo model, I address a magnetic spin-1/2 impurity interacting with a bound state of spin origin at the edge in a Luther-Emery liquid showing a spin gap in the bulk. The system presents two zero-energy Majorana fermions of magnetic origin, one on the impurity site and one at the edge. I derive the wavefunction at the edge for the produced zero-energy Majorana fermion bound state within the same formalism as topological interfaces. I present alternative versions of the quantum field theory revealing the specific pairing of the Majorana fermions in the bulk. I address local physical responses. I develop the idea that this model can be realized with a magnetic impurity bridging the gap between two s-wave superconducting wires. I show the protection of the zero-energy Majorana fermions that will be referred to as free Majorana fermions.