### Séminaire de groupe

Parafermions in time-reversal invariant topological insulators |

Thomas Schmidt |

Université de Luxembourg |

mercredi 10 juin 2015 , 14h00 |

Salle de séminaire du groupe de Physique Statistique |

Topological insulators are band insulators whose conduction and valence bands are characterised by a nontrivial topological invariant. As a consequence, they host robust metallic states at the interfaces with topologically trivial insulators or the vacuum. In the past years, TIs have been experimentally realized in two-dimensional and three-dimensional systems, and several theoretical predictions have been confirmed, e.g., the existence of edge states in two-dimensional TIs and the helical spin structure of surface states of three-dimensional TIs. We investigate the effect of superconductivity on the helical edge states of two-dimensional topological insulators. In the noninteracting limit, it was shown several years ago that this can lead to the emergence of Majorana bound states at the ends of the edge state, and a $4\pi$ periodic Josephson effect was proposed as a possible experimental signature. In contrast, our theory focuses on systems with electron-electron interactions. We show that 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. <br><br> [1] Christoph P. Orth, Rakesh P. Tiwari, Tobias Meng, Thomas L. Schmidt, Non-Abelian parafermions in time-reversal invariant interacting helical systems, Phys. Rev. B <b>91</b>, 081406(R) (2015) |