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 ${\mathbb{Z}}_n$ 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 ("quasi-particles") of a fractional quantum Hall bulk at filling factor $\nu =1/m$ (for odd integer $m$) incident upon the interface of a superconductor, and in the presence of back-scattering. 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 a UV fixed point of perfect normal reflection towards an IR 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 quasi-particle to an emergent parafermion zero mode at the superconductor interface. These results are fortified by an exact solution.

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Cited by in corpus (11)

• Andreev reflection in the fractional quantum Hall state
• Superconductivity and fermionic dissipation in quantum Hall edges
• Readout of parafermionic states by transport measurements
• Current correlations of Cooper-pair tunneling into a quantum Hall system
• Dynamical topological excitations in parafermion chains
• Measuring topological entanglement entropy using Maxwell relations
• Quantum dots as parafermion detectors
• Dynamics of parafermionic states in transport measurements
• Assessing bound states in a one-dimensional topological superconductor: Majorana versus Tamm
• Can Majorana zero modes in quantum Hall edges survive edge reconstruction?
• Parafermionic representation of Potts-based cluster chain