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Non-Abelian Anyons and Topological Quantum Computation
Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of
Observation of half-integer thermal Hall conductance
TLDR
Measurements of the thermal Hall conductance in the first excited Landau level of the quantum Hall effect show the existence of a state with non-Abelian excitations and perform topological unitary transformations when braided, which can be useful for topological quantum computation.
Topological Superconductivity in a Planar Josephson Junction
We consider a two-dimensional electron gas with strong spin-orbit coupling contacted by two superconducting leads, forming a Josephson junction. We show that in the presence of an in-plane Zeeman
Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors
Proposed experiments to probe the non-Abelian nu = 5/2 quantum hall state.
TLDR
The non-Abelian nature of quasiparticles in the fractional quantum Hall state at nu = 5/2 is tested and analogous effects in the thermodynamic properties of closed systems are found.
Fractional topological insulators.
TLDR
Generalizations of two-dimensional topological insulators which can be realized in interacting, time reversal invariant electron systems, which contain excitations with fractional charge and statistics in addition to protected edge modes are analyzed.
Observation of a quarter of an electron charge at the ν = 5/2 quantum Hall state
TLDR
Data is reported on shot noise generated by partitioning edge currents in the ν = 5/2 state, consistent with the charge of the quasiparticle being e/4, and inconsistent with other possible values, such as e/2 and e.
Theory of the Fabry-Perot quantum Hall interferometer
We analyze interference phenomena in the quantum-Hall analog of the Fabry-Perot interferometer, exploring the roles of the Aharonov-Bohm effect, Coulomb interactions, and fractional statistics on the
Non-Abelian states of matter
TLDR
Experimental studies attempt to identify non-Abelian states in systems that manifest the fractional quantum Hall effect, if such states can be identified, they may become useful for quantum computation.
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