Some interfaces between two different topologically ordered systems can be gapped. In earlier work it was shown that such gapped interfaces can themselves be effective one-dimensional topological systems that possess localized topological modes in open boundary geometries. Here we focus on how this occurs in the context of an interface between two single-component Laughlin states of opposite chirality, with filling fractions ${\nu }_1=1/p$ and ${\nu }_2=1/p{n}^2$. While one type of interface in such systems was previously studied, we show that allowing for edge reconstruction effects opens up a wide variety of possible gapped interfaces depending on the number of divisors of $n.$ We apply a complementary description of the ${\nu }_2=1/p{n}^2$ system in terms of Laughlin states coupled to a discrete gauge ${\mathbb{Z}}_n$ field. This enables us to identify possible interfaces to the ${\nu }_1$ system based on complete or partial confinement of this gauge field. We determine the tunneling properties, the ground-state degeneracy, and the nature of the non-Abelian zero modes of each interface in order to physically distinguish them.

• Received 8 November 2018

DOI:https://doi.org/10.1103/PhysRevB.99.155134