Zero Modes in Fractional Topological Superconductors

One-dimensional fractional topological superconductors (FTSCs) arise from hybrid structures including edge states of a topologically ordered system and an s-wave superconductor. Zero modes with non-Abelian statistics localize at the ends when putting these FTSCs on finite intervals. These zero modes exhibit parafermionic statistics for the Laughlin fractional quantum Hall (FQH) bulk. Here we find zero modes from a topologically ordered bulk using anyon condensation and generalize the zero mode algebra in the edge theory perspective. We study specific bulk systems such as Jain sequence FQH states at different fillings and generalized Moore-Read FQH states. We identify the topological properties of the zero modes in these FTSCs and study experimental signatures such as the fractional Josephson effect, which can distinguish Pfaffian and particle-hole symmetric Pfaffian states from anti-Pfaffian states.