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

Topological superconductors are prime candidates for the implementation of topological-quantum-computation ideas because they can support non-Abelian excitations such as Majorana fermions. We go beyond the low-energy effective-model descriptions of Majorana bound states (MBSs) to derive nonequilibrium transport properties of wire geometries of these systems in the presence of arbitrarily large applied voltages. Our approach involves quantum Langevin equations and nonequilibrium 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 nontopological excitations, predict how the behavior compares for an increasing number of odd versus 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.