---

I will present recent progress on Majorana fermions and other exotic excitations with non-Abelian braid statistics that can emerge in condensed matter systems. These excitations have attracted wide attention recently, also because of their potential applications in topological quantum computing. Majorana fermion zero-modes and their generalizations, parafermions, can emerge in nanowires and atomic chains in the presence of spin orbit interaction or spatially periodic magnetic fields, in RKKY systems forming intrinsic spin helices, in topological insulators, and typically in the presence of superconductivity. I will discuss some candidate materials such as semiconducting Rashba nanowires and atomic magnetic chains and show some recent experimental progress. Finally, I plan to discuss parafermions, which, in contrast to Majorana fermions, can emerge only in the presence of strong electron-electron interactions and have a more powerful braid statistics that enables entanglement and in particular exact CNOT gates by braiding alone (without the need of any measurements).

---

Daniel Loss, University of Basel
TP seminar room 0.03
Contact: Alexander Altland