Interaction Enabled Topological Crystalline Phases

TL;DR

This paper introduces a general mechanism for creating interaction-enabled topological phases in fermionic systems, highlighting how interactions can induce non-trivial crystalline topological states that are trivial in free-fermion models.

Contribution

It proposes a novel mechanism for interaction-enabled topological phases, especially in crystalline systems, and interprets these phases as mean-field charge-4e superconductors arising from complex interactions.

Findings

Interaction enables topological phases absent in free-fermion models.

Crystalline defects host non-Abelian anyon bound states.

Systems can be viewed as charge-4e superconductors.

Abstract

In this article we provide a general mechanism for generating interaction-enabled fermionic topological phases. We illustrate the mechanism with crystalline symmetry-protected topological phases in 1D and 2D. These non-trivial phases require interactions for their existence and, in the cases we consider, the free-fermion classification yields only a trivial phase. Similar to the interpretation of the Kitaev Majorana wire as a mean-field p-wave superconductor Hamiltonian arising from an interacting model with quartic interactions, we show that our systems can be interpreted as "mean-field" charge-$4e$ superconductors arising, e.g., from an interacting model with eight-body interactions, or through another physical mechanism. The quartet superconducting nature allows for the teleportation of full Cooper pairs, and in 2D for interesting semiclassical crystalline defects with non-Abelian anyon boundstates.