Signatures of parafermionic modes in superconductor-fractional quantum Hall heterostructures

With recent developments in the experimental control of graphene-based fractional quantum Hall systems, it has now been demonstrated possible to induce superconducting pairing between counterpropagating fractional edge modes. Theoretical works predict that such systems could host parafermionic modes; non-Abelian anyons which share a fractional charge in a nonlocal way. These modes could be exploited for topological quantum computing.

In this talk I will propose setups, based on recent experiments, that allow for readout of the topologically protected charge shared by a pair of isolated parafermions. These involve conductance measurements through metallic leads. I will also discuss the possible quasiparticle poisoning which can lead to a three-state telegraph noise characteristic for Z₆ parafermions and can be treated with the Lindblad formalism and the quantum jump approach. The above investigations are relevant to study more complex systems with more than two parafermions which are required for quantum computing. In particular, a minimal setup of four modes is necessary to investigate their associativity fusion rules.