Readout of parafermionic states by transport measurements

Abstract

Recent experiments have demonstrated the possibility of inducing superconducting pairing into counterpropagating fractional quantum Hall edge modes. This paves the way for the realization of localized parafermionic modes, non-Abelian anyons that share fractional charges in a nonlocal way. We show that, for a pair of isolated parafermions, this joint degree of freedom can be read by conductance measurements across standard metallic electrodes. We propose two complementary setups. We investigate first the transport through a grounded superconductor hosting two interacting parafermions. In the low-energy limit, its conductance peaks reveal their shared fractional charge yielding a three-state telegraph noise for weak quasiparticle poisoning. We then examine the two-terminal electron conductance of a blockaded fractional topological superconductor, which displays a characteristic $e/3$ periodicity of its zero-bias peaks in the deep topological regime, thus signalling the presence of parafermionic modes.

arXiv comment5 pages + supplemental material, 3+6 figures

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• Evidence for chiral supercurrent in quantum Hall Josephson junctions
• Superconductivity and fermionic dissipation in quantum Hall edges
• Anomalous periodicity and parafermion hybridization in superconducting qubits
• Dynamics of parafermionic states in transport measurements
• Chirality-selective proximity effect between chiral $p$-wave superconductors and quantum Hall insulators
• Quantum computation with hybrid parafermion-spin qubits
• Signatures of Parafermion Zero Modes in Fractional Quantum Hall-Superconductor Heterostructures
• Overlap of parafermionic zero modes at a finite distance
• Can Majorana zero modes in quantum Hall edges survive edge reconstruction?
• Phases of Quasi-One-Dimensional Fractional Quantum (Anomalous) Hall - Superconductor Heterostructures
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor
• Triple Antidot Molecules