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

TL;DR

This paper investigates the competition between Abelian and non-Abelian fractional quantum Hall states at filling factor 5/2 using edge-current-tunneling experiments, revealing a confinement-dependent transition relevant for quantum computing.

Contribution

It demonstrates that confinement tuning in quantum point contacts can induce a transition between Abelian and non-Abelian 5/2 states, highlighting the importance of confinement in topological quantum states.

Findings

Evidence of competition between Abelian and non-Abelian states at 5/2

Observation of a transition from Abelian to non-Abelian state with confinement tuning

Implication that the non-Abelian 5/2 state is intrinsically stable but confinement-dependent

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.