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

作者：Orth Christoph P^*; Tiwari Rakesh P; Meng Tobias; Schmidt Thomas L

来源：Physical Review B, 2015, 91(8): 081406.

DOI：10.1103/PhysRevB.91.081406

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.

• 出版日期2015-2-25