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

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.

Robust Fractional Quantum Hall States in Bilayer Graphene

The paper examines incompressible even-denominator fractional quantum Hall (FQH) states observed in bilayer graphene under high magnetic fields. The phenomenon of fractional quantum Hall effect is crucial in the study of condensed matter systems, and the presence of these states in bilayer graphene provides insights into the dynamics of nonabelian anyons and novel quantum phases. While bilayer graphene has been explored previously for fractional quantum Hall phases, the robustness of the even-denominator states and their nontrivial characteristics now emerging mandates a closer evaluation.

Key Findings

• Observation of FQH Phases: The study reports robust even-denominator FQH phases, particularly focusing on hexagonal boron nitride encapsulated bilayer graphene samples. This architectural combination is pivotal for achieving higher energy gaps than those observed in traditional semiconductor systems.

• Nonabelian Pfaffian Phase: Numerical simulations consistent with the experimental observations suggest that the studied FQH state corresponds to the Pfaffian phase, theoretically hosting nonabelian anyons. These anyons are significant for topologically protected qubits in quantum computing, offering decoherence resistance.

• Energy Gap Measurements: The study observes larger thermodynamic and transport energy gaps compared to former FQH systems. This increase suggests potential improvements in application and understanding of quantum Hall states, with notable implications for determining quantum phase transitions.

• Control Parameters and Phase Transitions: The unique electronic structure of bilayer graphene enables the tuning of effective electron interactions through magnetic and electric fields, leading to a transition between Pfaffian phase and composite Fermi liquid (CFL). The study notes a continuous transition mediated by an intermediate incompressible phase possessing polarizable characteristics.

Implications

The findings have substantial implications for both theoretical advancements and practical implementations in quantum technologies.

• Quantum Information Processing: Nonabelian anyons are pivotal for quantum computing, potentially leading to fault-tolerant systems through topological protection. The improved energy gaps here can bolster information retention capabilities in quantum systems.

• Controlled Quantum States: Bilayer graphene allows manipulation of quantum phases via external fields, offering insights into electron interaction dynamics and possible development of tunable quantum devices.

• Future Quantum Hall Research: The impressive energy gaps open avenues for studying quantum states at higher and more variable magnetic fields, aiding research on nontrivial phases like the paired Pfaffian states.

• Interferometric Experiments: Given the large energy gap and reduced bulk-edge coupling, bilayer graphene appears particularly suited for interferometric detection of nonabelian statistics, marking an essential step towards empirical validation of these anyons' existence.

Outlook on Future Research

Drawing from the robustness of observed phases and the tuning potential of bilayer graphene, the study hints at intriguing prospects in quantum research:

• Exploration Across Magnetic Fields: A deeper investigation into magnetic field effects can unravel further nuances in quantum state transitions, especially concerning the dynamic interplay between Pfaffian and CFL phases.

• Lower Temperature Measurements: Such assessments could reinforce the existent topological states, advancing understanding of foundational quantum mechanics.

• Nonabelian Statistics: Developing more sophisticated methods to delineate and measure nonabelian anyon statistics within the observed states could provide conclusive evidence supporting theoretical models.

The examination of bilayer graphene presents compelling evidence for exploring quantum states that are not only theoretically fascinating but hold essential practical promise for future technology. As research continues to unfold, we expect more breakthroughs in harnessing the peculiarities of nonabelian anyons and pushing the boundaries of quantum computational possibilities.