Majorana spintronics

We propose a systematic magnetic-flux-free approach to detect, manipulate, and braid Majorana fermions in a semiconductor-nanowire-based topological Josephson junction by utilizing the Majorana spin degree of freedom. We find an intrinsic pi-phase difference between spin-triplet pairings enforced by the Majorana zero modes (MZMs) at the two ends of a one-dimensional spinful topological superconductor. This pi phase is identified to be a spin-dependent superconducting phase, referred to as the spin phase, which we show to be tunable by controlling spin-orbit coupling strength via electric gates. This electric controllable spin phase not only affects the coupling energy between MZMs but also leads to a fractional Josephson effect in the absence of any applied magnetic flux, which enables the efficient topological qubit readout. We thus propose an all-electrically controlled superconductor-semiconductor hybrid circuit to manipulate MZMs and to detect their non-Abelian braiding statistics properties. Our work on spin properties of topological Josephson effects potentially opens up a new thrust for spintronic applications with Majorana-based semiconductor quantum circuits.LPS-MPO-CMTC; Microsoft Q; National Natural Science Foundation of China [11574008]; Thousand-Young-Talent Program of ChinaSCI(E)ARTICLE19