We investigate 1D quantum systems that support Majorana bound states at interfaces between topologically distinct regions. In particular, we show that there exists a duality between particle-hole and spin degrees of freedom in certain spin-orbit-coupled 1D platforms such as topological insulator edges. This duality results in a spin analog of previously explored “fractional Josephson effects”—that is, the spin current flowing across a magnetic junction exhibits 4π periodicity in the relative magnetic field angle across the junction. Furthermore, the interplay between the particle-hole and spin degrees of freedom results in unconventional magneto-Josephson effects, such that the Josephson charge current is a function of the magnetic field orientation with periodicity 4π.
