Enigmatic 2+6/13 Filling Factor: A Prototype Intermittent Topological State

Abstract

Observation of filling factor 6/13 is one of the surprising fractional quantum Hall states in the second Landau level because, in contrast to the standard wisdom, the fractions ($\nu <1/2$) with lower numerators, namely 4 and 5, have not yet been observed. We find that a state indeed forms at $\nu =6/13$ as an intermittent topological state between two prominent states at $\nu =1/2$ and $\nu =2/5$ with lower numerators. Also, we predict that a state forms at $\nu =5/13$ as an intermittent to $\nu =2/5$ and $\nu =3/8$. Our proposed wave functions for $\nu =6/13$ and $5/13$ have excellent overlaps with the corresponding exact ground state wave functions. The Chern-Simons coupling matrices deduced from the form of these wave functions are analyzed to predict the topological properties, which may be experimentally verified.

References in corpus (40)

• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Observation of half-integer thermal Hall conductance
• Is the Composite Fermion a Dirac Particle?
• Nonconventional odd denominator fractional quantum Hall states in the second Landau level
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Parafermion Hall states from coset projections of abelian conformal theories
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• The Effect of Landau Level-Mixing on the Effective Interaction between Electrons in the fractional quantum Hall regime
• Landau Level Mixing and the Fractional Quantum Hall Effect
• Breaking of Particle-Hole Symmetry by Landau Level Mixing in the nu=5/2 Quantized Hall State
• Particle-hole symmetry without particle-hole symmetry in the quantum Hall effect at ν = 5/2
• More Realistic Hamiltonians for the Fractional Quantum Hall Regime in GaAs and Graphene
• Landau-level-mixing and the ground state of the 5/2 quantum Hall effect
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Parton construction of a wave function in the anti-Pfaffian phase
• The Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width
• Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State
• Novel method distinguishing between competing topological orders
• Landau Level Mixing in the Perturbative Limit
• On the Interpretation of Thermal Conductance of the nu=5/2 Edge
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
• Partial equilibration of integer and fractional edge channels in the thermal quantum Hall effect
• Enigmatic 4/11 State: A Prototype for Unconventional Fractional Quantum Hall Effect
• Non-Abelian states with negative flux: a new series of quantum Hall states
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian
• Partial Equilibration of the Anti-Pfaffian edge due to Majorana Disorder
• Fractional Quantum Hall Effect at $\nu =2+6/13$: The Parton Paradigm for the Second Landau Level
• Partial equilibration of anti-Pfaffian edge modes at $\nu =5/2$
• Energetics of Pfaffian-AntiPfaffian Domains
• Temperature enhancement of thermal Hall conductance quantization
• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• Disorder-driven transition and intermediate phase for $\nu =5/2$ fractional quantum Hall effect
• Finite Temperature Behavior in the Second Landau Level of the Two-dimensional Electron Gas
• An Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength
• Fractional Quantum Hall States of the $\mathcal{A}$ phase in the Second Landau Level
• Reply to "Comment on `Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength' "