Superconductivity and fermionic dissipation in quantum Hall edges

Abstract

Proximity-induced superconductivity in fractional quantum Hall edges is a prerequisite to proposed realizations of parafermion zero-modes. A recent experimental work [Gül et al., Phys. Rev. X 12, 021057 (2022)] provided evidence for such coupling, in the form of a crossed Andreev reflection signal, in which electrons enter a superconductor from one chiral mode and are reflected as holes to another, counter-propagating chiral mode. Remarkably, while the probability for crossed Andreev reflection was small, it was stronger for $\nu =1/3$ fractional quantum Hall edges than for integer ones. We theoretically explain these findings, including the relative strengths of the signals in the two cases and their qualitatively different temperature dependencies. An essential part of our model is the coupling of the edge modes to normal states in the cores of Abrikosov vortices induced by the magnetic field, which provide a fermionic bath. We find that the stronger crossed Andreev reflection in the fractional case originates from the suppression of electronic tunneling between the fermionic bath and the fractional quantum Hall edges. Our theory shows that the mere observation of crossed Andreev reflection signal does not necessarily imply the presence of localized parafermion zero-modes, and suggests ways to identify their presence from the behavior of this signal in the low temperature regime.

5+11 pages, 4+1 figures. Short (12:22) video explanation of model and main results at https://www.youtube.com/watch?v=h0rS7TyUUMI

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• Thermoelectric processes of quantum normal-superconductor interfaces
• Dynamics of parafermionic states in transport measurements
• SU(4) Symmetry Breaking and Induced Superconductivity in Graphene Quantum Hall Edges
• Non-local transport measurements in hybrid quantum Hall - superconducting devices
• Heat-charge separation in a hybrid superconducting quantum Hall setup
• Transparent Graphene-Superconductor Interfaces: Quantum Hall and Zero Field Regimes
• Chirality-selective proximity effect between chiral $p$-wave superconductors and quantum Hall insulators
• On-Demand and Tunable Andreev-Conversion of Single-Electron Charge Pulses
• Floquet-Nambu theory of electron quantum optics with superconductors
• Wigner representation of Andreev-reflected charge pulses
• Quantum computation with hybrid parafermion-spin qubits
• Signatures of Parafermion Zero Modes in Fractional Quantum Hall-Superconductor Heterostructures
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor
• Vortex Pinning in Niobium covered by a thin polycrystalline Gold
• Revealing Superconducting Chiral Edge Modes via Resistance Distributions
• Quantized Transport of $\nu =2/3$ Fractional Quantum Hall Edge with Disordered Superconducting Proximity
• Can Majorana zero modes in quantum Hall edges survive edge reconstruction?