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SUMMARY:Z4 parafermions in time-reversal invariant topological insulators 
 - Prof. Thomas Schmidt\, University of Luxembourg
DTSTART:20150618T131500Z
DTEND:20150618T141500Z
UID:TALK58516@talks.cam.ac.uk
CONTACT:Gareth Conduit
DESCRIPTION:We investigate the effect of superconductivity on the helical 
 edge states of two-dimensional topological insulators. In the noninteracti
 ng limit\, it was shown several years ago that this can lead to the emerge
 nce of Majorana bound states at the ends of the edge state\, and a 4\\pi p
 eriodic Josephson effect was proposed as a possible experimental signature
 .\n\nIn contrast\, our theory focuses on systems with electron-electron in
 teractions. We show that the interplay between bulk spin-orbit coupling an
 d electron-electron interactions produces umklapp scattering in the helica
 l 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.\n\nWe 
 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 Josep
 hson current with 8pi 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 s
 how how braiding can be implemented in topological insulator systems.\n\n[
 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 91\, 081406(R) (2015).
LOCATION:TCM Seminar Room\, Cavendish Laboratory
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