Fractional charge and spin states in topological insulator constrictions

We theoretically investigate the properties of two-dimensional topological insulator constrictions both in the integer and fractional regimes. In the presence of a perpendicular magnetic field, the constriction functions as a spin filter with near-perfect efficiency and can be switched by electric fields only. Domain walls between different topological phases can be created in the constriction as an interface between tunneling, magnetic fields, charge density wave, or electron-electron interaction dominated regions. These domain walls host non-Abelian bound states with fractional charge and spin and result in degenerate ground states with parafermions. If a proximity gap is induced bound states give rise to an exotic Josephson current with 8 pi periodicity.