## 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.

Original language | English (US) |
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Pages (from-to) | 12386-12390 |

Number of pages | 5 |

Journal | Proceedings of the National Academy of Sciences of the United States of America |

Volume | 113 |

Issue number | 44 |

DOIs | |

State | Published - Nov 1 2016 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- General

## Keywords

- 5/2 fractional quantum Hall state
- Edge-current tunneling
- Fractional quantum Hall effect
- Non-Abelian statistics
- Quantum point contact