Families of Gapped Interfaces Between Fractional Quantum Hall States

Some interfaces between two different topologically ordered systems can be gapped. In earlier work it has been 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, and with filling fractions $\nu_1=1/p$ and $\nu_2=1/pn^2$. While one type of interface in such systems has been 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 $\nu_2=1/pn^2$ 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, ground state degeneracy, and the nature of the non-Abelian zero modes of each interface in order to physically distinguish them.