Valley Isospin Controlled Fractional Quantum Hall States in Bilayer Graphene

Abstract

A two-dimensional electron system placed in a magnetic field develops Landau levels, where strong Coulomb interactions lead to the appearance of many-body correlated ground states. Quantum numbers similar to the electron spin enable the understanding and control of complex ground state order and collective excitations. Owing to its spin, valley and orbital degrees of freedom, Bernal-stacked bilayer graphene offers a rich platform to pursue correlated phenomena in two dimensions. In this work, we fabricate dual-gated Bernal-stacked bilayer graphene devices and demonstrate unprecedented fine control over its valley isospin degrees of freedom using a perpendicular electric field. Higher sample quality enables us to probe regimes obscured by disorder in previous studies. We present evidence for a new even-denominator fractional quantum Hall state at filling factor ν = 5/2. The 5/2 state is found to be spontaneously valley polarized in the limit of vanishing valley Zeeman splitting, consistent with a theoretical prediction made regarding the spin polarization of the Moore-Read state. In the vicinity of the even-denominator fractional quantum Hall states, we observe the appearance of the predicted Levin-Halperin daughter states of the Moore-Read Pfaffian wave function at ν= 3/2, 7/2, and -1/2 and of the anti-Pfaffian at ν= 5/2. These observations suggest the breaking of particle-hole symmetry in bilayer graphene. We construct a comprehensive valley polarization phase diagram for the Jain sequence fractional states surrounding filling factor 3/2. These results are well explained by a two-component composite fermion model, further demonstrating the SU(2) nature of the valley isospin in bilayer graphene. Our experiment paves the path for future efforts of manipulating the valley isospin in bilayer graphene to engineer exotic topological orders and quantum information processes.

24 pages, 14 figures. The changes reported in the erratum are included in the latest version

References in corpus (19)

• Non-Abelian Anyons and Topological Quantum Computation
• The electronic properties of bilayer graphene
• Fractional statistics in anyon collisions
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Tunable Fractional Quantum Hall Phases in Bilayer Graphene
• Even denominator fractional quantum Hall state in bilayer graphene
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• The Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width
• Spin polarization of the $\nu =5/2$ quantum Hall state
• Novel method distinguishing between competing topological orders
• Tilt-Induced Anisotropic to Isotropic Phase Transition at $\nu =5/2$
• Contrasting Behavior of the 5/2 and 7/3 Fractional Quantum Hall Effect in a Tilted Field
• Density dependence of valley polarization energy for composite fermions
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Metallic Phase and Temperature Dependence of the $\nu =0$ Quantum Hall State in Bilayer Graphene
• Finite-thickness effect and spin polarization of the even-denominator fractional quantum Hall states
• Competing quantum Hall phases in the second Landau level in low density limit

Cited by in corpus (50)

• High-Temperature Quantum Valley Hall Effect with Quantized Resistance and a Topological Switch
• Energy gap of the even-denominator fractional quantum Hall state in bilayer graphene
• Anyon braiding and telegraph noise in a graphene interferometer
• Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Higher vortexability: zero field realization of higher Landau levels
• High-Resolution Tunneling Spectroscopy of Fractional Quantum Hall States
• Composite fermion pairing induced by Landau level mixing
• Thermal conductance and noise of Majorana modes along interfaced $\nu =5/2$ fractional quantum Hall states
• Strongly coupled edge states in a graphene quantum Hall interferometer
• Topological phase transition between composite-fermion and Pfaffian daughter states near ν = 1/2 FQHS
• Fractional Quantum Hall State at Filling Factor $\nu =1/4$ in Ultra-High-Quality GaAs 2D Hole Systems
• Aharonov-Bohm oscillations in bilayer graphene edge state Fabry-Pérot interferometers
• Aharonov-Bohm interference and the evolution of phase jumps in fractional quantum Hall Fabry-Perot interferometers based on bi-layer graphene
• Fingerprints of anti-Pfaffian topological order in quantum point contact transport
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Identifying the topological order of quantized half-filled Landau levels through their daughter states
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Phase diagram of the $\nu =2$ quantum Hall state in bilayer graphene
• Interplay of valley, layer and band topology towards interacting quantum phases in moiré bilayer graphene
• Valley polarization, magnetization, and superconductivity in bilayer graphene near the van Hove singularity
• Valley-tunable, even-denominator fractional quantum Hall state in the lowest Landau level of an anisotropic system
• Highly-Anisotropic Even-Denominator Fractional Quantum Hall State in an Orbitally-Coupled Half-Filled Landau Level
• Competing Laughlin state and Wigner crystal in bilayer graphene
• Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene
• Ultraclean two-dimensional hole systems with mobilities exceeding 10${}^7$ cm${}^2$/Vs
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Two-component parton fractional quantum Hall state in graphene
• Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene
• Probing the fractional quantum Hall phases in valley-layer locked bilayer MoS${}_2$
• Probing valley phenomena with gate-defined valley splitters
• Fractional quantum Hall state at $\nu =1/2$ with energy gap up to 6 K, and possible transition from one- to two-component state
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Interaction-driven quantum phase transitions between topological and crystalline orders of electrons
• Non-Abelian phases from the condensation of Abelian anyons
• Nematic Enhancement of Superconductivity in Multilayer Graphene via Quantum Geometry
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Probing fractional quantum Hall effect by photoluminescence
• Even-denominator fractional quantum Hall states with spontaneously broken rotational symmetry
• Strongly interacting Hofstadter states in magic-angle twisted bilayer graphene
• Hexagonal boron nitride/bilayer graphene moiré superlattices in the Dirac-material family: energy-band engineering and carrier doping by dual gating
• Interlayer phase coherence and composite fermions
• Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States
• Interlayer exciton condensates between second Landau level orbitals in double bilayer graphene
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor
• Residual quantum coherent electron transport in doped graphene leads
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene
• Topological Protection in a Landau Flat Band at $\nu =7/11$, a Candidate Filling Factor for Unconventional Correlations