### Applications of the Pfaffian State to Topological Phases

Alexander Sirota
Fractional topological insulators are electronic topological phases in $(3+1)$ dimensions enriched by time reversal and charge $U(1)$ conservation symmetries. The most straightforward series of fermionic fractional topological insulators is analyzed where their bulk quasiparticles consist of deconfined partons that carry fractional electric charges in integral units of $e^\ast=e/(2n+1)$ and couple to a discrete $\mathbb{Z}_{2n+1}$ gauge theory. This thesis proposes massive symmetry preserving or breaking fractional topological insulator surface states. By combining the long-ranged entangled bulk...
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