Zero Modes in General Fractional Quantum Hall-Superconductor Hybrid Structures

Non-Abelian zero modes are one of the most promising routes to realize topological quantum computation. Blueprints consists of edges of fractional quantum Hall (FQH) state proximitized by an s-wave superconductor have been proposed to host such zero modes. For instance, in the case with Laughlin FQH edges, the hybrid structure supports parafermion zero modes. In this work, we study the properties of the non-Abelian zero in these hybrid structures formed for a larger class of FQH bulk states, focusing on the Jain and generalized Moore-Read states. While a theory for the properties of such non-Abelian defects for generic topological states is known, our goal is to study the appearance of said defects from the perspective of conformal field theory describing the edge of the FQH state. In addition to determining the topological properties of the zero modes, our approach allows us to study experimental signatures such as the fractional Josephson effect---which distinguishes Pfaffian and particle-hole symmetric Pfaffian states from anti-Pfaffian state---and braiding of zero modes that produces topologically produced operations.