Competing ν= 5/2 fractional quantum Hall states in confined geometry

Abstract

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current-tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state, but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state, but also for the design of future topological quantum computation devices.

References in corpus (21)

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• Rapid collapse of spin waves in non-uniform phases of the second Landau level
• Influence of device geometry on tunneling in ν=5/2 quantum Hall liquid
• Tilt Induced Localization and Delocalization in the Second Landau Level
• Experimental constraints and a possible quantum Hall state at $\nu =5/2$
• Enhancement of the $\nu =5/2$ Fractional Quantum Hall State in a Small In-Plane Magnetic Field

Cited by in corpus (22)

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• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
• Partial equilibration of integer and fractional edge channels in the thermal quantum Hall effect
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Edge Probes of Topological Order
• 3/2 Fractional Quantum Hall Plateau in Confined Two-Dimensional Electron Gas
• Competing charge density waves probed by non-linear transport and noise in the second and third Landau levels
• Observation of an anomalous density-dependent energy gap of the $\nu =5/2$ fractional quantum Hall state in the low density regime
• Piezo-driven sample rotation system with ultra-low electron temperature
• Gate-controlled transmission of quantum Hall edge states in bilayer graphene
• Probing quantum phases in ultra-high-mobility two-dimensional electron systems using surface acoustic waves
• Competition of Pairing and Nematicity in the Two-Dimensional Electron Gas
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Low-temperature environments for quantum computation and quantum simulation
• Anomalous quantized plateaus in two-dimensional electron gas with gate confinement
• The Monte Carlo simulation of the topological quantities in FQH systems
• Even-denominator fractional quantum Hall state in conventional triple-gated quantum point contact
• Stability of the 5/2 Fractional Quantum Hall State in a Corbino Disc Sample with In-plane Electric Fields
• Edge Induced Topological Phase Transition of the Quantum Hall state at Half Filling
• Anomalous acousto-current within the quantum Hall plateaus