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Fractional Phases and Non-Abelian Anyons in Quantum Wires (FracWire)
Start date: Aug 1, 2013, End date: Jul 31, 2017 PROJECT  FINISHED 

I propose to explore how strong interactions between electrons moving in a one dimensional wire with spin-orbit coupling lead to creation of novel fractional helical phases that carry particles with fractional charges. This allows situations where, similar to the fractional quantum Hall effect, the charge fractionalization leads to conductance with quantized fractional numbers of the von Klitzingconductance e^2/h.Recently, it was shown both theoretically and experimentally that when a (non-interacting) wire is put in proximity to a superconductor, zero energy Majorana fermion states are formed at the wire ends. These observations attract a lot of attention as in contrast to the known particles, fermions or bosons, when the zero Majoranas state are exchanged the state of the system is modified - forming the seed requirement for a reliable topological quantum computer. I will study situations where the interacting system is proximity-coupled to a superconductor, in which fractional Majorana bound states (similar to the ones discussed on edges of fractional quantum Hall systems in proximity to a superconductor) may be stabilized. Having in mind real experimental realization of the novel phases we discuss how disorder destabilizes these fractional phases.In addition to the novel phases that I propose to explore, and the detailed description of their experimental consequences, this proposal forms a new theoretical platform for construction of novel states of matter. Based on this idea I plan to study how combination of more than one (interacting) wire in proximity to a superconductor may lead to the fractional states forming a universal quantum computer.
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