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Majorana fermions (MFs), particles identifiable with their
own anti-particles, were first introduced by E. Majorana in high
energy physics. In its condensed matter analog, MFs are understood as
localized topological quasiparticles bound to order parameter defects
in superconductors with non-Abelian braiding statistics that could be
useful for topological quantum computation. Following our proposal, a
number of experimental groups have recently claimed to have realized
MFs in semiconductor-superconductor heterostructures. In this talk I
will describe this story along with its most recent developments. I
will also touch upon our ongoing work on topological superconductors
and more recently, on topological Mott insulators, that could be
realized using cold atom systems in artificial optical lattices. |