Robust fractional quantum Hall states and continuous quantum phase transitions in a half-filled bilayer graphene Landau level

TL;DR

This paper reports the discovery of a robust nonabelian fractional quantum Hall state in bilayer graphene, with larger energy gaps and tunable phase transitions, advancing the pursuit of topological quantum computing.

Contribution

It demonstrates a new, stable nonabelian quantum Hall phase in bilayer graphene with larger energy gaps and controllable phase transitions, providing evidence for nonabelian anyons.

Findings

Observation of a robust, incompressible even-denominator fractional quantum Hall state.

Numerical simulations suggest the state is in the Pfaffian phase hosting nonabelian anyons.

Magnetic and electric fields tune phase transitions and valley polarization, revealing a continuous transition and an intermediate phase.

Abstract

Nonabelian anyons offer the prospect of storing quantum information in a topological qubit protected from decoherence, with the degree of protection determined by the energy gap separating the topological vacuum from its low lying excitations. Originally proposed to occur in quantum wells in high magnetic fields, experimental systems thought to harbor nonabelian anyons range from p-wave superfluids to superconducting systems with strong spin orbit coupling. However, all of these systems are characterized by small energy gaps, and despite several decades of experimental work, definitive evidence for nonabelian anyons remains elusive. Here, we report the observation of arobust, incompressible even-denominator fractional quantum Hall phase in a new generation of dual-gated, hexagonal boron nitride encapsulated bilayer graphene samples. Numerical simulations suggest that this state is in the Pfaffian phase and hosts nonabelian anyons, and the measured energy gaps are several times larger than those observed in other systems. Moreover, the unique electronic structure of bilayer graphene endows the electron system with two new control parameters. Magnetic field continuously tunes the effective electron interactions, changing the even-denominator gap non-monotonically and consistent with predictions that a transition between the Pfaffian phase and the composite Fermi liquid (CFL) occurs just beyond the experimentally explored magnetic field range. Electric field, meanwhile, tunes crossings between levels from different valleys. By directly measuring the valley polarization, we observe a continuous transition from an incompressible to a compressible phase at half-filling mediated by an unexpected incompressible, yet polarizable, intermediate phase. Valley conservation implies this phase is an electrical insulator with gapless neutral excitations.