Non-Abelian parafermions in time-reversal-invariant interacting helical systems

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 t...

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Bibliographic Details
Published in:Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2015-02, Vol.91 (8), Article 081406
Main Authors: Orth, Christoph P., Tiwari, Rakesh P., Meng, Tobias, Schmidt, Thomas L.
Format: Article
Language:English
Subjects:
Braiding
Condensed matter
Helical
Insulators
Liquids
Scattering
Statistics
Superconductivity
Topology
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Summary: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 sub(4) parafermions. We determine their braiding statistics and show how braiding can be implemented in topological insulator systems.
ISSN:1098-0121
1550-235X
DOI:10.1103/PhysRevB.91.081406