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.

5 pages + supplemental material, 3+6 figures

References in corpus (15)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Scaling of Majorana Zero-Bias Conductance Peaks
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Flux-induced topological superconductivity in full-shell nanowires
• Fractional topological superconductors with fractionalized Majorana fermions
• Epitaxial Pb on InAs nanowires
• Interaction effects on proximity-induced superconductivity in semiconducting nanowires
• Localizing fractional quasiparticles on graphene quantum hall antidots
• Signatures of Topological Superconductivity and Parafermion Zero Modes in Fractional Quantum Hall Edges
• Transmission Amplitude through a Coulomb blockaded Majorana Wire
• Insulating regime of an underdamped current-biased Josephson junction supporting ${\mathbb{Z}}_3$ and ${\mathbb{Z}}_4$ parafermions
• Quantum dots as parafermion detectors

Cited by in corpus (12)

• 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