Parafermionic modes in topological systems
Dr. Michele Burrello (Max-Planck-Institut für Quantenoptik, Garching)

Recent works show that, in particular topological systems, it may be possible to fractionalize Majorana zero modes to obtain more exotic anyons called parafermions.
In this talk I will first review some aspects of the Majorana zero modes appearing in topological superconductors, then I will describe how parafermionic zero modes arise at the interface between a superconductor and a ferromagnet along the edge of a fractional topological insulator (FTI) and I will examine their properties.
Finally I will address the physics of two-dimensional arrays of interacting parafermionic modes. The geometry of the underlying topological insulators is strictly related to the topological characteristics of these systems. In a geometry where the length of the FTI edges is independent on the system size, the array has a topologically ordered phase, giving rise to a qudit toric code Hamiltonian in perturbation theory. In a geometry where the length of the edges scales instead with system size, an exact duality maps the system to an Abelian lattice gauge theory without topological order.