Spin and Majorana polarization in topological superconducting wires

TL;DR

This paper investigates the spin textures and polarization properties of Majorana bound states in a 1D topological superconductor with spin-orbit coupling, proposing new order parameters for topological phase transitions.

Contribution

It introduces the concepts of Majorana polarization and density as local order parameters, linking spin textures to topological phases in superconducting wires.

Findings

Majorana states exhibit spin polarization dependent on SOC components

Majorana polarization correlates with transverse spin polarization

Proposes spin-polarized density of states as a detection method

Abstract

We study a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in proximity of a superconductor. Using both analytical and numerical techniques we calculate the electronic spin texture of the Majorana end states. We find that the spin polarization of these states depends on the relative magnitude of the Rashba and Dresselhaus SOC components. Moreover, we define and calculate a local "Majorana polarization" and "Majorana density" and argue that they can be used as order parameters to characterize the topological transition between the trivial system and the system exhibiting Majorana bound modes. We find that the local "Majorana polarization" is correlated to the transverse spin polarization, and we propose to test the presence of Majorana fermions in a 1D system by a spin-polarized density of states measurement.