Majorana spintronics

Xin Liu, Xiaopeng Li, Dong-Ling Deng, Xiong-Jun Liu, S. Das Sarma

Published 2016-02-25Version 1

Josephson effect is a fascinating macroscopic quantum phenomenon that plays a vital role in many practical applications of superconductivity. Josephson currents in a conventional Josephson junction are usually controlled by tuning a magnetic flux, which couples to the charge degree of freedom of electrons through the Josephson effect. Here, we propose a systematic {\it magnetic-flux-free} approach to control the Josephson effect in semiconductor nanowires by utilizing the spin degree of freedom of Cooper pairs. An intrinsic $\pi$ phase difference is demonstrated between spin-triplet pairings enforced by the Majorana zero modes (MZMs) at the two ends of a one-dimensional spinful topological superconductor, which has been demonstrated to occur in semiconductor nanowires with spin-orbit coupling (SOC). This $\pi$ phase is identified to be a spin-dependent superconducting phase, referred to as {\it spin-phase}, and can be further tuned via electric gates which control the SOC strength. A finite topological Josephson current, whose direction measures the fermion parity, is shown to arise, which can be tuned by varying the SOC strength in the absence of any magnetic flux in the superconducting circuit. We further show that the SOC controlled spin-phase affects the coupling energy between MZMs, which we propose as an all electrically controlled superconductor-semiconductor hybrid circuit to manipulate MZMs and to detect their non-Abelian braiding statistics properties. Our work provides insights into the spin properties of topological Josephson effects and opens new potential spintronic applications in Majorana-based semiconductor quantum circuits.