Detecting and braiding higher-order Majorana corner states through their spin degree of freedom

Abstract

We uncover the transverse Majorana spin polarization of a class of higher-order topological superconductors. ``Transverse'' means that the spin polarization of the Majorana zero modes is perpendicular instead of parallel with the applied magnetic field. With this novel Majorana spin property, we predict the spin-selective Andreev reflection occurs at lead polarization perpendicular to the applied magnetic field, in sharp contrast to that in the Majorana nanowire and vortex system. The induced topological Josephson ${\ensuremath{\phi}}_{0}$ junction shows the qualitative difference from the topologically trivial Josephson ${\ensuremath{\phi}}_{0}$ junction and provides benefits in constructing all electronically controlled Majorana networks for braiding. We thus provide a comprehensive scheme for probing non-Abelian statistics in this class of higher-order topological superconductors with transverse Majorana spin texture.