Fractional Quantum Hall Hierarchy and the Second Landau Level

Abstract

We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the nu = 5/2 Moore-Read state, we construct new explicit trial wavefunctions to describe the fractional quantum Hall effect in the second Landau level. The resulting hierarchy of states, which reproduces the filling fractions of all observed Hall conductance plateaus in the second Landau level, is characterized by electron pairing in the ground state and an excitation spectrum that includes non-Abelian anyons of the Ising type. We propose this as a unifying picture in which p-wave pairing characterizes the fractional quantum Hall effect in the second Landau level.

10 pages; v2: many additional details and discussion included to help clarify the original results, including a composite fermion type formulation of some of the states; v3: minor corrections

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• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Observation of the e/3 Fractionally Charged Laughlin Quasiparticles
• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
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• Towards identification of a non-abelian state: observation of a quarter of electron charge at $\nu =5/2$ quantum Hall state
• Proposed experiments to probe the non-abelian ν=5/2 quantum Hall state
• Quantized Thermal Transport in the Fractional Quantum Hall Effect
• Measurement-Only Topological Quantum Computation
• Exact Quantization of Even-Denominator Fractional Quantum Hall State at $\nu$=5/2 Landau Level Filling Factor
• Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases
• Insulating and Fractional Quantum Hall States in the N=1 Landau Level
• Universal Quantum Computation with the nu=5/2 Fractional Quantum Hall State
• A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Fractional Quantum Hall Effect of Composite Fermions
• 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
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• Edge states and tunneling of non-Abelian quasiparticles in the nu=5/2 quantum Hall state and p+ip superconductors
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• Intrinsic Gap of the nu=5/2 Fractional Quantum Hall State
• Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2
• Possibility of p-wave pairing of composite fermions at $\nu =1/2$
• Numerical study of charge and statistics of Laughlin quasi-particles
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Cited by in corpus (106)

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• From Luttinger liquid to non-Abelian quantum Hall states
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• Topological flat band models with arbitrary Chern numbers
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States
• A theory of topological edges and domain walls
• The non-Abelian Interferometer
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• Tunneling of anyonic Majorana excitations in topological superconductors
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Fibonacci anyons and charge density order in the 12/5 and 13/5 plateaus
• Fractional charge and fractional statistics in the quantum Hall effects
• Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
• Measurement-Only Topological Quantum Computation via Anyonic Interferometry
• Parton construction of a wave function in the anti-Pfaffian phase
• Characterizing Neutral Modes of Fractional States in the Second Landau Level
• Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States
• Experimental probe of topological orders and edge excitations in the second Landau level
• Synthetic Topological Qubits in Conventional Bilayer Quantum Hall Systems
• Implementing arbitrary phase gates with Ising anyons
• Projective Ribbon Permutation Statistics: a Remnant of non-Abelian Braiding in Higher Dimensions
• Measurement-Only Topological Quantum Computation via Tunable Interactions
• Competing states for the fractional quantum Hall effect in the 1/3-filled second Landau level
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Quasi-Topological Phases of Matter and Topological Protection
• The Fractional Quantum Hall States at $\nu =13/5$ and $12/5$ and their Non-Abelian Nature
• Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states
• Two-dimensional quantum liquids from interacting non-Abelian anyons
• Metaplectic Anyons, Majorana Zero Modes, and their Computational Power
• Collective states of non-abelian quasiparticles in a magnetic field
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Splitting the Topological Degeneracy of non-Abelian Anyons
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• Transition from Abelian to non-Abelian quantum liquids in the second Landau level
• Influence of device geometry on tunneling in ν=5/2 quantum Hall liquid
• Abelian and Non-Abelian States in $\nu =2/3$ Bilayer Fractional Quantum Hall Systems
• Hall Viscosity of Hierarchical Quantum Hall States
• Competing Topological Orders in the nu=12/5 Quantum Hall State
• Competing Abelian and non-Abelian topological orders in $\nu =1/3+1/3$ quantum Hall bilayers
• Numerical Calculation of the Neutral Fermion Gap at $\nu =5/2$
• Quantum Hall quasielectrons - Abelian and non-Abelian
• Thermoelectric probe for neutral edge modes in the fractional quantum Hall regime
• The enigmatic 12/5 fractional quantum Hall effect
• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• Quasiparticles and excitons for the Pfaffian quantum Hall state
• Coulomb Blockade Doppelgangers in Quantum Hall States
• Tripartite Composite Fermion States
• Condensing non-Abelian quasiparticles
• Quantum Hall hierarchy from coupled wires
• Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise
• Emergent particle-hole symmetry in spinful bosonic quantum Hall systems
• Non-Abelian phases in two-component $\nu =2/3$ fractional quantum Hall states: Emergence of Fibonacci anyons
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Quantum spin ladders of non-Abelian anyons
• The enigma of the $\nu =2+\frac{3}{8}$ fractional quantum Hall effect
• Quasihole condensates in quantum Hall liquids
• Partition Functions of Non-Abelian Quantum Hall States
• Composite Fermion states on the torus
• A general approach to quantum Hall hierarchies
• Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states
• Anomalous Gap Reversal of the $3+1/3$ and $3+1/5$ Fractional Quantum Hall States
• S3 Quantum Hall Wavefunctions
• Entanglement Entropy of Generalized Moore-Read Fractional Quantum Hall State Interfaces
• Complete spin phase diagram of the fractional quantum Hall liquid
• One-dimensional itinerant interacting non-Abelian anyons
• Energy projection and modified Laughlin states
• Entanglement Measures for Quasi-Two-Dimensional Fractional Quantum Hall States
• Fractionalization of itinerant anyons in one dimensional chains
• Matrix product state representation of quasielectron wave functions
• Gapped Excitations of unconventional FQHE states in the Second Landau Level
• Hierarchy construction and non-Abelian families of generic topological orders
• Fluctuation theorems without time-reversal symmetry
• Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots
• Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State
• Hierarchical Nature of the Quantum Hall Effects
• Identifying the topological order of quantized half-filled Landau levels through their daughter states
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Gauging U(1) symmetry in (2+1)d topological phases
• Screening properties and phase transitions in unconventional plasmas for Ising-type quantum Hall states
• Particle-hole Asymmetry of Fractional Quantum Hall States in the Second Landau Level of a Two-dimensional Hole System
• Identifying non-Abelian anyons with upstream noise
• Stability of the k=3 Read-Rezayi state in chiral two-dimensional systems with tunable interactions
• Chern-Simons-Higgs transitions out of Topological Superconducting Phases
• Freezing of an unconventional two-dimensional plasma
• Tunnelling current through fractional quantum Hall interferometers
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• Twisted Interferometry
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