Non-Abelian quantum order in spin-orbit-coupled semiconductors: Search for topological Majorana particles in solid-state systems

@article{Sau2010NonAbelianQO,
  title={Non-Abelian quantum order in spin-orbit-coupled semiconductors: Search for topological Majorana particles in solid-state systems},
  author={Jay Deep Sau and Sumanta Tewari and R. M. Lutchyn and Tudor D Stanescu and Sankar Das Sarma},
  journal={Physical Review B},
  year={2010},
  volume={82},
  pages={214509}
}
We show that an ordinary semiconducting thin film with spin-orbit coupling can, under ap- propriate circumstances, be in a quantum topologically ordered state supporting exotic Majorana excitations which follow non-Abelian statistics. The key to the quantum topological order is the coexistence of spin-orbit coupling with proximity-induced s-wave superconductivity and an externally-induced Zeeman coupling of the spins. For the Zeeman coupling below a critical value, the system is a non… 
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  • T. Stanescu, S. Tewari
  • Physics
    Journal of physics. Condensed matter : an Institute of Physics journal
  • 2013
TLDR
This review provides an update on the current status of the search for Majorana fermions in semiconductor nanowires by focusing on the recent developments, in particular the period following the first reports of experimental signatures consistent with the realization of Majorana bound states in semiconducting nanowire-superconductor hybrid structures.
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References

Fractional statistics and anyon superconductivity
The occurrence of fractional statistics has been discovered in more and more quantum field theory models, including some of the most geometrical and canonical ones. In a remarkable case, the