Predicted signatures of topological superconductivity and parafermion zero modes in fractional quantum Hall edges

Abstract

Parafermion zero modes are exotic emergent excitations that can be considered as Zn generalizations of Majorana fermions. Present in fractional quantum Hall-superconductor hybrid systems, among others, they can serve as potential building blocks in fault-tolerant topological quantum computing. We propose a system that reveals noise and current signatures indicative of parafermion zero modes. The system is comprised of the edge excitations (“quasiparticles”) of a fractional quantum Hall bulk at filling factor ν=1/m (for odd integer m) incident upon the interface of a superconductor, and in the presence of backscattering. Using perturbative calculations, we derive the current that propagates away from this structure, and its corresponding noise correlation function. Renormalization group analysis reveals a flow from an ultraviolet fixed point of perfect normal reflection towards an infrared fixed point of perfect Andreev reflection. The power law dependence of the differential conductance near these fixed points is determined by m. We find that behavior at these two limits is physically distinguishable; whereas near perfect Andreev reflection, the system deviates from equilibrium via tunneling of Cooper pairs between the two edges, near perfect normal reflection this is done via tunneling of a single quasiparticle to an emergent parafermion zero mode at the superconductor interface. These results are fortified by an exact solution.

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