Topological Phases in the Zeroth Landau Level of Bilayer Graphene

Abstract

We analyze the phase diagram of the zeroth Landau level of bilayer graphene, taking into account the realistic effects of screening of the Coulomb interaction and the strong mixing between two degenerate sublevels. We identify robust quantum Hall states at filling factors ν=-1, -4/3, -5/3, -8/5, -1/2, and discuss the nature of their ground states, collective excitations, and relation to the more familiar states in GaAs using a tractable model. In particular, we present evidence that the ν=-1/2 state, which was recently reported experimentally, is non-Abelian, and described by either the Moore-Read Pfaffian wave function or its particle-hole conjugate, while ruling out other candidates such as the 331 state.

4.5 pages, 5 figures

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Cited by in corpus (36)

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• Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene
• Tunable Fractional Quantum Hall Phases in Bilayer Graphene
• Even denominator fractional quantum Hall state in bilayer graphene
• Observation of even denominator fractional quantum Hall effect in suspended bilayer graphene
• Electron-Hole Asymmetric Integer and Fractional Quantum Hall Effect in Bilayer Graphene
• Direct measurement of discrete valley and orbital quantum numbers in a multicomponent quantum Hall system
• Valley Isospin Controlled Fractional Quantum Hall States in Bilayer Graphene
• The Effects of Landau level mixing on the fractional quantum Hall effect in monolayer Graphene
• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
• Insulating state in tetralayers reveals an even-odd interaction effect in multilayer graphene
• Higher Landau-Level Analogs and Signatures of Non-Abelian States in Twisted Bilayer MoTe${}_2$
• Robust fractional quantum Hall effect and composite fermions in the $N=2$ Landau level in bilayer graphene
• Microscopic pairing mechanism, order parameter, and disorder sensitivity in moiré superlattices: Applications to twisted double-bilayer graphene
• Energy gap of the even-denominator fractional quantum Hall state in bilayer graphene
• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Understanding the Missing Fractional Quantum Hall States in ZnO
• Interaction-induced insulating state in thick multilayer graphene
• Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene
• Energy gaps and layer polarization of integer and fractional quantum Hall states in bilayer graphene
• The Pfaffian state in an electron gas with small Landau level gaps
• Landau quantization of multilayer graphene on a Haldane sphere
• Phase diagram of a graphene bilayer in the zero-energy Landau level
• Evidence for a topological "exciton Fermi sea" in bilayer graphene
• Bootstrapping the Quantum Hall problem
• Gully quantum Hall ferromagnetism in biased trilayer graphene
• Phase diagram of the $\nu =2$ quantum Hall state in bilayer graphene
• Landau Levels of Bilayer Graphene in a WSe${}_2$/Bilayer Graphene van der Waals Heterostructure
• Competing Laughlin state and Wigner crystal in bilayer graphene
• Quantum Hall ferroelectric helix in bilayer graphene
• PH Pfaffian intra and inter correlations in the quantum Hall bilayer
• Time-reversal odd transport in bilayer graphene: Hall conductivity and Hall viscosity
• Non-Abelian topological order with SO(5)${}_1$ chiral edge states
• Fractional quantum Hall effect in bilayer graphene beyond the single Landau level approximation