Tomography of zero-energy end modes in topological superconducting wires

Abstract

We characterize the Majorana zero modes in topological superconducting wires with spin-orbit coupling and magnetic field, in terms of the spherical angles of their spin orientation, ϕ, θ and a phase δ, and analyze their transformation under SU(2) rotations. We show that, when the spin-orbit coupling and the magnetic field are perpendicular, ϕ and δ are universal in an appropriate coordinate system. We use these geometric properties to explain the behavior of the Josephson current in junctions of two wires with different orientations of the magnetic field and/or the spin-orbit coupling. We show how to extract from there, the angle θ, hence providing a full description of the Majorana modes.

Nonequilibrium electrical, thermal and spin transport in open quantum systems of topological superconductors, semiconductors and metals

“…We mainly try to reveal many exciting thermal and spin transport features in different junctions of TS, SM, and N wires, which are either less explored or have not been investigated. While the spin transport in the junctions of TS and SM wires are rarely investigated in the past, a systematic study of spin transport can be fruitful in disclosing necessary signatures of Majorana quasiparticles (such as spin polarizations of Majoranas [14]) and the topological nature of the systems [17,40,41]. The obtained expression of spin current here is expected to be useful for further investigation of spin transport.…”

“…There has been a surge of interest in quantized thermal conductances for detecting fractionally charged and neutral modes [10][11][12]. The MBSs in experimentally realized TSs made of hybrid nanowires combining spin-orbit coupled semiconductor and superconductor materials have a non-zero spin polarization [13,14]. Therefore, such systems' spin transport is expected to provide valuable information about the systems' MBSs and topological properties [15][16][17].…”