Majorana fermions in an out-of-equilibrium topological superconducting wire: an exact microscopic transport analysis of a p-wave open chain coupled to normal leads

TL;DR

This paper provides an exact microscopic analysis of non-equilibrium transport in topological superconducting wires supporting Majorana fermions, revealing how spectral weight and topological phase transitions influence observable properties.

Contribution

It extends beyond low-energy models to include high-energy effects, modeling realistic lead coupling and analyzing the evolution across the topological quantum phase transition.

Findings

Spectral weight in Majorana bound states can be significantly large.

The spectral weight decreases continuously to zero at the topological quantum phase transition.

The study offers insights for experimental detection of Majorana fermions.

Abstract

Topological superconductors are prime candidates for the implementation of topological-quantum-computation ideas because they can support non-Abelian excitations like Majorana fermions. We go beyond the low-energy effective-model descriptions of Majorana bound states (MBSs), to derive non-equilibrium transport properties of wire geometries of these systems in the presence of arbitrarily large applied voltages. Our approach involves quantum Langevin equations and non-equilibrium Green's functions. By virtue of a full microscopic calculation we are able to model the tunnel coupling between the superconducting wire and the metallic leads realistically; study the role of high-energy non-topological excitations; predict how the behavior compares for increasing number of odd vs. even number of sites; and study the evolution across the topological quantum phase transition (QPT). We find that the normalized spectral weight in the MBSs can be remarkably large and goes to zero continuously at the topological QPT. Our results have concrete implications for the experimental search and study of MBSs.