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Non-Abelian topological insulators from an array of quantum wires

We suggest a construction of a large class of topological states using an array of quantum wires. First, we show how to construct a Chern insulator using an array of alternating wires that contain electrons and holes, correlated with an alternating magnetic field. This is supported by semi-classical arguments and a full quantum mechanical treatment of an analogous tight-binding model. We then show how electron-electron interactions can stabilize fractional Chern insulators (Abelian and non-Abelian). In particular, we construct a relatively stable non-Abelian $\mathbb{Z}_{3}$ parafermion state. Our construction is generalized to wires with alternating spin-orbit couplings, which give rise to integer and fractional (Abelian and non-Abelian) topological insulators. The states we construct are effectively two-dimensional, and are therefore less sensitive to disorder than one-dimensional systems. The possibility of experimental realization of our construction is addressed.