Fractional Quantum Hall Effect at $\nu =2+4/9$

Abstract

Motivated by two independent experiments revealing a resistance minimum at the Landau level (LL) filling factor $\nu =2+4/9$, characteristic of the fractional quantum Hall effect (FQHE) and suggesting electron condensation into a yet unknown quantum liquid, we propose that this state likely belongs in a parton sequence, put forth recently to understand the emergence of FQHE at $\nu =2+6/13$. While the $\nu =2+4/9$ state proposed here directly follows three simpler parton states, all known to occur in the second LL, it is topologically distinct from the Jain composite fermion (CF) state which occurs at the same $\nu =4/9$ filling of the lowest LL. We predict experimentally measurable properties of the $4/9$ parton state that can reveal its underlying topological structure and definitively distinguish it from the $4/9$ Jain CF state.

15 pages, 13 figures (includes supplemental material), published version

References in corpus (52)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Topological orders and Edge excitations in FQH states
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Observation of half-integer thermal Hall conductance
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Quantized Thermal Transport in the Fractional Quantum Hall Effect
• Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases
• Observation of neutral modes in the fractional quantum Hall regime
• Observed Quantization of Anyonic Heat Flow
• Nonconventional odd denominator fractional quantum Hall states in the second Landau level
• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Finite Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wavefunction Overlap and Topological Degeneracy
• Fractional Quantum Hall Effect in the Second Landau Level
• Composite Fermions and Broken Symmetries in Graphene
• Even denominator fractional quantum Hall states in higher Landau levels of graphene
• High quality magnetotransport in graphene using the edge-free Corbino geometry
• Fibonacci anyons and charge density order in the 12/5 and 13/5 plateaus
• Proliferation of neutral modes in fractional quantum Hall states
• Parton construction of a wave function in the anti-Pfaffian phase
• Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two dimensional electron layers: finite-thickness effects
• Characterizing Neutral Modes of Fractional States in the Second Landau Level
• The nature of composite fermions and the role of particle hole symmetry: A microscopic account
• Spinful Composite Fermions in a Negative Effective Field
• Fractional Quantum Hall Effect in Graphene: Quantitative Comparison between Theory and Experiment
• Non-Abelian quantized Hall states of electrons at filling factors 12/5 and 13/5 in the first excited Landau level
• Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study
• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
• Competing states for the fractional quantum Hall effect in the 1/3-filled second Landau level
• Luttinger theorem for the strongly correlated Fermi liquid of composite fermions
• The Fractional Quantum Hall States at $\nu =13/5$ and $12/5$ and their Non-Abelian Nature
• Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells
• Classification of Disordered Phases of Quantum Hall Edge States
• Role of exciton screening in the 7/3 fractional quantum Hall effect
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Fermi-sea-like correlations in a partially filled Landau level
• Transition from Abelian to non-Abelian quantum liquids in the second Landau level
• Spontaneous polarization of composite fermions in the $n=1$ Landau level of graphene
• Abelian and Non-Abelian States in $\nu =2/3$ Bilayer Fractional Quantum Hall Systems
• Competing Topological Orders in the nu=12/5 Quantum Hall State
• Fermi wave vector for the non-fully spin polarized composite-fermion Fermi sea
• Fractional Quantum Hall Effect at $\nu =2+6/13$: The Parton Paradigm for the Second Landau Level
• The enigmatic 12/5 fractional quantum Hall effect
• Quasiholes of 1/3 and 7/3 quantum Hall states: size estimates via exact diagonalization and density-matrix renormalization group
• ${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect
• Tripartite Composite Fermion States
• Increasing the ν = 5 / 2 gap energy: an analysis of MBE growth parameters
• The enigma of the $\nu =2+\frac{3}{8}$ fractional quantum Hall effect
• Anomalous Gap Reversal of the $3+1/3$ and $3+1/5$ Fractional Quantum Hall States
• Finite Temperature Behavior in the Second Landau Level of the Two-dimensional Electron Gas

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• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• Interplay between fractional quantum Hall liquid and crystal phases at low filling
• Transitions from Abelian composite fermion to non-Abelian parton fractional quantum Hall states in the zeroth Landau level of bilayer graphene
• Abelian topological order of $\nu =2/5$ and $3/7$ fractional quantum Hall states in lattice models
• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• Unconventional ${\mathbb{Z}}_n$ parton states at $\nu =7/3$: The role of finite width
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Microscopic Model for Fractional Quantum Hall Nematics
• Composite fermion pairing induced by Landau level mixing
• Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications
• 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
• Fractionalisation and dynamics of anyons at $\nu =n+1/3$ in fractional quantum Hall effect and their experimental signatures
• Revisiting excitation gaps in the fractional quantum Hall effect
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Signatures of Supersymmetry in the $\nu =5/2$ Fractional Quantum Hall Effect
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• 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
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Fractional quantum Hall coexistence phases in higher Landau levels of graphene
• Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene
• A numerical study of bounds in the correlations of fractional quantum Hall states
• Universal Modelling of Oscillations in Fractional Quantum Hall Fluids
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• 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
• Ordering the topological order in the fractional quantum Hall effect
• Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States
• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Crossover from Integer to Fractional Quantum Hall Effect
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene