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Extrinsic Defects and Possible New Experimental Probes of Topological Order

Topologically ordered states, such as the fractional quantum Hall (FQH) states, are quantum states of matter with various exotic properties, including quasiparticles with fractional quantum numbers and fractional statistics, and robust topology-dependent ground state degeneracies. In this talk, I will describe a new aspect of topological states: their extrinsic defects. These include extrinsically imposed point-like or line-like defects that couple to the topological properties of the state in non-trivial ways. The extrinsic point defects localize topologically protected "parafermion" zero modes, which generalize the notion of Majorana fermion zero modes, and provide a new direction for realizing non-Abelian quantum statistics and topological quantum computation. The line defects allow direct quantum mechanical coupling between electrons and fractionalized anyons, leading to new ways to probe fractionalization. After describing the conceptual framework, I will focus on a specific set of experimental proposals, using conventional bilayer FQH states, to detect parafermion zero modes and to directly observe the long-predicted topological ground state degeneracy of FQH states. In the end I will comment on other ways in which extrinsic defects provide a new window into fractionalization.