Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene

Abstract

The current proposals for producing non-Abelian anyons and Majorana particles, which are neither fermions nor bosons, are primarily based on the realization of topological superconductivity in two dimensions. We show theoretically that the unique Landau level structure of bilayer graphene provides a new possible avenue for achieving such exotic particles. Specifically, we demonstrate the feasibility of a "parton" fractional quantum Hall (FQH) state, which supports non-Abelian particles without the usual topological superconductivity. Furthermore, we advance this state as the fundamental explanation of the puzzling $1/2$ FQH effect observed in bilayer graphene [Kim {\em et al.}, Nano Lett. {\bf 15}, 7445 (2015)], and predict that it will also occur in trilayer graphene. We indicate experimental signatures that differentiate the parton state from other candidate non-Abelian FQH states and predict that a transverse electric field can induce a topological quantum phase transition between two distinct non-Abelian FQH states.

6 pages, 2 figures

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Cited by in corpus (53)

• Even denominator fractional quantum Hall state in bilayer graphene
• Even denominator fractional quantum Hall states in higher Landau levels of graphene
• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Fractional charge and fractional statistics in the quantum Hall effects
• Parton construction of a wave function in the anti-Pfaffian phase
• Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells
• Tensor network representations of parton wave functions
• Fractional Quantum Hall Effect at $\nu =2+6/13$: The Parton Paradigm for the Second Landau Level
• Fractional Quantum Hall Effect at $\nu =2+4/9$
• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• ${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect
• Transitions from Abelian composite fermion to non-Abelian parton fractional quantum Hall states in the zeroth Landau level of bilayer graphene
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Entangled Pauli Principles: the DNA of Quantum Hall Fluids
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Unconventional ${\mathbb{Z}}_n$ parton states at $\nu =7/3$: The role of finite width
• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• Metallic Phase and Temperature Dependence of the $\nu =0$ Quantum Hall State in Bilayer Graphene
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Local two-body parent Hamiltonians for the entire Jain sequence
• Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene
• Composite fermion pairing induced by Landau level mixing
• Real-space entanglement spectra of parton states in fractional quantum Hall systems
• Theoretical phase diagram of two-component composite fermions in double layer graphene
• Majorana braiding gates for topological superconductors in a one dimensional geometry
• Parton wave function for the fractional quantum Hall effect at $\nu =6/17$
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
• Landau level diagram and the continuous rotational symmetry breaking in trilayer graphene
• Composite fermions in Fock space: Operator algebra, recursion relations, and order parameters
• Local density of states and particle entanglement in topological quantum fluids
• Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• PH-Pfaffian order in a translationally and rotationally invariant system
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• An Exactly Solvable Model for Strongly Interacting Electrons in a Magnetic Field
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• Two-component parton fractional quantum Hall state in graphene
• From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization
• Very high-energy collective states of partons in fractional quantum Hall liquids
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
• Adiabatic Continuity of the Spinful Quantum Hall States
• Exactly Solvable Hamiltonian for Non-Abelian Quasiparticles
• Interaction-driven quantum phase transitions between topological and crystalline orders of electrons
• Linking infinite bond-dimension matrix product states with frustration-free Hamiltonians
• Non-Abelian topological order with SO(5)${}_1$ chiral edge states
• Composite fermions and parton wavefunctions in twisted graphene on hexagonal boron nitride
• Crossover from Integer to Fractional Quantum Hall Effect