Non-Abelian parafermions in time-reversal-invariant interacting helical systems
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Contributors
Abstract
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 8π periodicity. Moreover, the bound states, which are protected by time-reversal symmetry, are fourfold degenerate and can be described as Z4 parafermions. We determine their braiding statistics and show how braiding can be implemented in topological insulator systems.
Details
Original language | English |
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Article number | 081406 |
Journal | Physical Review B - Condensed Matter and Materials Physics |
Volume | 91 |
Issue number | 8 |
Publication status | Published - 25 Feb 2015 |
Peer-reviewed | Yes |