The search Majorana fermions and non-Abelian statistics in semiconductor-superconductor systems.
This event is part of the Condensed Matter Theory Seminar Series.
Majorana fermions are hitherto unobserved exotic excitations, which are
their own anti-particles. Despite the nomenclature, Majorana fermions are neither fermions nor bosons but have novel exchange statistics that categorizes them as non-Abelian anyons. Non-Abelian anyons are associated with a ground state degeneracy of the entire system, which cannot be broken by any external fields. Observing such a topologically robust ground state degeneracy would not only be a fundamental breakthrough in physics, but could also be used to create topological quantum computers which are free of the decoherence problem. I will describe our work which suggests that topological superconductors containing Majoranas are fairly generic and a large class of spin-orbit coupled systems can be used to realize Majorana fermions. Possible experimental tests of these ideas range from simple tunneling experiments to test the existence of zero-energy Majorana states to explicit demonstration of non-Abelian statistics through tunneling coupled nanowire arrays and interferometry. Finally, we will discuss how the spin-orbit coupled models motivate an intrinsically number conserving microscopic model of a topological superconductor mediated by attractive interactions, which supports Majorana fermions. The bosonization approach used to study this one-dimensional model makes transparent the connection between the topological order described by Majorana fermions and the emergent Ising order in such spin-orbit coupled superconductors.