Obtaining non-abelian anyons is one of the major goals within the field of topological states of matter. The simplest of these anyons, Majorana bound states, have been proposed as candidates for implementing topological quantum computation relying on its non-abelian statistics. Parafermions can be regarded as ZN generalizations of the Z2-symmetric Majorana bound states. They have a richer non-abelian exchange statistics compared to Majorana bound states and would thus offer advantages for quantum computation. In contrast to Majorana bound states, parafermions usually require strong interactions between electrons and have been proposed to exist, for instance, in fractional quantum Hall insulators with induced superconductivity. In this project, we intend to use bosonization and related tools such as the renormalization group and sine-Gordon theory to study effective low-energy models that host parafermions. In particular, we are interested in how a finite system size and the system geometry affect parafermionic zero modes. These effects should give rise, for instance, to oscillations of the bound-state energy, a well-known phenomenon in the physics of Majorana bound states. These topics are important for current experiments investigating the interplay between fractional quantum Hall states and superconductivity, and will help in the quest to find parafermions.
News published in Agência FAPESP Newsletter about the scholarship: