Reference : Non-Abelian parafermions in time-reversal invariant interacting helical systems
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Physics
Non-Abelian parafermions in time-reversal invariant interacting helical systems
Orth, Christoph P. [> >]
Tiwari, Rakesh P. [> >]
Meng, Tobias [> >]
Schmidt, Thomas mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Physics and Materials Science Research Unit > ; University of Basel > Department of Physics]
Physical Review. B
[en] The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional topological insulator. If the chemical potential is at the Dirac point, umklapp scattering can open a gap in the edge state spectrum even if the system is time-reversal invariant. We determine the zero-energy bound states at the interfaces between a section of a helical liquid which is gapped out by the superconducting proximity effect and a section gapped out by umklapp scattering. We show that these interfaces pin charges which are multiples of $e/2$, giving rise to a Josephson current with $8\pi$ periodicity. Moreover, the bound states, which are protected by time-reversal symmetry, are fourfold degenerate and can be described as $Z_4$ parafermions. We determine their braiding statistics and show how braiding can be implemented in topological insulator systems.
arXiv:1405.4353 [cond-mat.mes-hall]

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