Exotic bound states in low dimensions: Majorana fermions and parafermions

Jelena Klinovaja

University of Basel

Exotic bound states in one-dimensional condensed matter systems have attracted wide attention due to their promise of non-Abelian statistics useful for topological quantum computing. For example, Majorana fermions can emerge in a variety of setups in which either standard or synthetic spin-orbit interaction is present. Here, candidate materials are semiconducting Rashba nanowires [1-2],  graphene nanoribbons [3], atomic magnetic chains or magnetic semiconductors [4]. At the same time, much effort is invested in identifying systems that host even more exotic quasiparticles than Majorana fermions that obey non-Abelian statistics of the Fibonacci type. Generating such quasiparticles is a crucial step towards a more powerful braid statistics that enables universal topological quantum computing. I will present results on time-reversal invariant parafermions. This setup consists of two quantum wires with Rashba spin-orbit interactions coupled to an s-wave superconductor, in the presence of strong electron-electron interactions [5].

[1]  J. Klinovaja and D. Loss, Phys. Rev. B 86, 085408 (2012).
[2]  D. Rainis, L. Trifunovic, J. Klinovaja, and D. Loss, Phys. Rev. B 87, 024515 (2013).
[3]  J. Klinovaja and D. Loss, Phys. Rev. X 3, 011008 (2013); J. Klinovaja and D. Loss, Phys. Rev. B 88, 075404 (2013).
[4]  J. Klinovaja, P. Stano, A. Yazdani, and D. Loss, Phys. Rev. Lett. 111, 186805 (2013).
[5]  J. Klinovaja and D. Loss, Phys. Rev. B 90, 045118 (2014).