Superconducting spin properties of Majorana nanowires and the associated spin-orbit coupling driven transverse supercurrent

Abstract

It is difficult to unambiguously confirm the existence of Majorana zero modes (MZMs) due to the absence of smoking-gun signatures in charge transport measurements. Recent studies suggest that the spin degree of freedom of MZMs may provide an alternative detection method. We study the spin properties of the superconducting state in Majorana nanowires and the associated unconventional Josephson effect with realistic experimental parameters taken from Zhang et al., Nature (London) 556, 74 (2018). We start from a general discussion of the polarized spin-triplet pairing, characterized by the superconducting spin polarization, which is fundamentally different from the spin polarization of electrons. For a superconducting thin film with in-plane polarized spin-triplet pairing, an out-of-plane electric field can lead to the spin-obit coupling which generates a supercurrent perpendicular to both the superconducting spin polarization and the electric field, so we name this phenomena as spin-orbit coupling driven transverse supercurrent (SOCDTS). In a Majorana nanowire, the regime with finite superconducting spin polarization almost coincides with the helical regime, which includes the topological regime. We further study the effects of polarized spin-triplet pairing in two types of Josephson junctions. One dramatic finding is that SOC can induce an anomalous supercurrent at zero phase difference only in the U-shape junction, which has been proposed as a basic ingredient of scalable topological quantum computation with the system in the topological regime. This can be viewed as a consequence of the SOCDTS. Our work reveals that the unique superconducting spin properties of MZMs can affect the unusual topological Josephson effect and is indeed helpful for detecting MZMs.

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