Quantized Transport of $\nu =2/3$ Fractional Quantum Hall Edge with Disordered Superconducting Proximity

Abstract

Quantum Hall edge states in proximity to a superconductor (SC) usually acquire a non-quantized electron-to-hole conversion probability in transport, due to non-universal SC couplings and disorders. With counter-propagating modes, we show that the situation can be the opposite in the $\nu =2/3$ fractional quantum Hall (FQH) edge states with SC proximity, where disordered SC-couplings can reconstruct the edge states into an infinite set of stable phases with quantized electron-to-hole conversion probability along a long edge. Each phase is dominated by a disordered SC-coupling that tunnels $\pm |q_N|$ Cooper pairs, which can take values $|q_N|=1,4,15$, etc. We predict that this gives rise to a quantized downstream resistance $R_d=h/(2q_N^2{e}^2)$ in an FQH-SC junction, serving as a quantized electrical transport signature beyond the Hall conductance. Higher-order nonlinear transport due to irrelevant Cooper pair tunneling or vortex dissipation is further studied, which becomes dominant when the edge is in a normal phase. Our results apply to both the single-layer state (as a particle-hole conjugate of $\nu =1/3$) and the bilayer Halperin-(112) state, revealing a rich landscape of disorder-stabilized phases in FQH edge states with SC proximity, and may as well apply to fractional Chern insulators recently observed at the same filling.

arXiv commentMain: 4.5 pages, 3 figures; Supplemental Material: 5 sections

References in corpus (78)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Comments on the Sachdev-Ye-Kitaev model
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Topological orders and Edge excitations in FQH states
• Nearly-flat bands with nontrivial topology
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Interfacial mode coupling as the origin of the enhancement of Tc in FeSe films on SrTiO3
• Observation of Fractionally Quantized Anomalous Hall Effect
• Fractional quantum Hall effect in the absence of Landau levels
• Fractional Chern Insulator
• Chiral Topological Superconductor From the Quantum Hall State
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Topological Quantum Computation Based on Chiral Majorana Fermions
• Randomness at the Edge: Theory of Quantum Hall transport at filling $\nu =2/3$
• Observation of fractional Chern insulators in a van der Waals heterostructure
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Protected edge modes without symmetry
• Supercurrent in the quantum Hall regime
• Impurity scattering and transport of fractional Quantum Hall edge state
• Chiral topological superconductor and half-integer conductance plateau from quantum anomalous Hall plateau transition
• Detection of valley polarization in graphene by a superconducting contact
• Inducing Superconducting Correlation in Quantum Hall Edge States
• Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.
• Fractional quantum anomalous Hall states in twisted bilayer MoTe${}_2$ and WSe${}_2$
• Induced superconductivity in high mobility two dimensional electron gas in GaAs heterostructures
• Quantum Hall effect in graphene with superconducting electrodes
• Signatures of Chiral Superconductivity in Rhombohedral Graphene
• Andreev Reflection in Strong Magnetic Fields
• Superconducting proximity effect through graphene from zero field to the Quantum Hall regime
• Edge reconstruction in the fractional quantum Hall regime
• Boundary Degeneracy of Topological Order
• Edge reconstruction in the $\nu =2/3$ fractional quantum Hall state
• Superconducting analogue of the parafermion fractional quantum Hall states
• Composite Edge States in the $\nu =2/3$ Fractional Quantum Hall Regime
• Superconductivity and quantized anomalous Hall in rhombohedral graphene
• Spin-triplet supercurrent carried by quantum Hall edge states through a Josephson junction
• Transport in a disordered $\nu =2/3$ fractional quantum Hall junction
• Interference of chiral Andreev edge states
• Andreev reflection in the fractional quantum Hall state
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• Classification of Disordered Phases of Quantum Hall Edge States
• Andreev reflection and cyclotron motion at superconductor -- normal-metal interfaces
• Synthesizing a Fractional v=2/3 State from Particle and Hole States
• Full control of quantum Hall supercurrent in a side gated graphene Josephson junction
• Cooper pair tunnelling into a Quantum Hall fluid
• Induced superconducting pairing in integer quantum Hall edge states
• Edge State Induced Andreev Oscillation in Quantum Anomalous Hall Insulator-Superconductor Junctions
• Inter-Landau-level Andreev Reflection at the Dirac Point in a Graphene Quantum Hall State Coupled to a NbSe2 Superconductor
• Mechanisms of Andreev reflection in quantum Hall graphene
• Induced superconducting correlations in the quantum anomalous Hall insulator
• Josephson Currents in Quantum Hall Devices
• Superconductivity and fermionic dissipation in quantum Hall edges
• Disorder in Andreev reflection of a quantum Hall edge
• Tuning the Many-body Interactions in a Helical Luttinger Liquid
• Loss and decoherence at the quantum Hall - superconductor interface
• A robust and tunable Luttinger liquid in correlated edge of transition-metal second-order topological insulator Ta${}_2$Pd${}_3$Te${}_5$
• Doping a fractional quantum anomalous Hall insulator
• Multiple Chiral Majorana Fermion Modes and Quantum Transport
• The conductance of superconducting-normal hybrid structures
• Equal-Spin Andreev Reflection in Junctions of Spin-Resolved Quantum Hall Bulk State and Spin-Singlet Superconductor
• Shot noise as a diagnostic in the $\nu =2/3$ fractional quantum Hall edge zoo
• Andreev reflection at the interface with an oxide in the quantum Hall regime
• Coherent-Incoherent Crossover of Charge and Neutral Mode Transport as Evidence for the Disorder-Dominated Fractional Edge Phase
• Edge-induced pairing states in a Josephson junction through a spin-polarized quantum anomalous Hall insulator
• Multiple Mechanisms for Emerging Conductance Plateaus in Fractional Quantum Hall States
• Localization and conductance in fractional quantum Hall edges
• An infrared bootstrap of the Schur index with surface defects
• Distribution of Conductances in Chiral Topological Superconductor Junctions
• Ungappable edge theories with finite dimensional Hilbert spaces
• Integrability of the $\nu =4/3$ fractional quantum Hall edge states