Parafermionic generalization of the topological Kondo effect

TL;DR

This paper introduces a novel parafermionic generalization of the topological Kondo effect, exploring a new class of quantum impurity problems with potential experimental realizations in fractional quantum Hall systems.

Contribution

It extends the topological Kondo effect to parafermionic zero modes and fractional edge states, revealing a new class of quantum impurity problems beyond the traditional Kondo paradigm.

Findings

Linear conductance shows similar behavior to the Majorana case.

At strong coupling, currents are isotropically partitioned with universal scattering.

Device can operate as a noiseless current extractor.

Abstract

We propose and study a parafermionic generalization of the topological Kondo effect. The latter has been predicted to arise for a Coulomb-blockaded mesoscopic topological superconductor (Majorana box), where at least three normal leads are tunnel-coupled to different Majorana zero modes on the box. The Majorana states represent a quantum impurity spin that is partially screened due to cotunneling processes between leads, with a stable non-Fermi liquid ground state. Our theory studies a generalization where (i) Majorana states are replaced by topologically protected parafermionic zero modes, (ii) charging effects again define a spin-like quantum impurity on the resulting parafermion box, and (iii) normal leads are substituted by fractional edge states. In this multi-terminal problem, different fractional edge leads couple only via the parafermion box. We show that although the linear conductance tensor exhibits similar behavior as in the Majorana case, both at weak and strong coupling, our parafermionic generalization is actually not a Kondo problem but defines a rich new class of quantum impurity problems. At the strong-coupling fixed point, a current injected through a reference lead will be isotropically partitioned into outgoing currents in all other leads, together with a universal negative current scattered into the reference lead. The device can thus be operated as current extractor, where the current partitioning is noiseless at the fixed point. We describe a fractional quantum Hall setup proximitized by superconductors and ferromagnets, which could allow for an experimental realization in the near future.