Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states

Abstract

Numerical studies by Wójs, Yi and Quinn have suggested that an unconventional fractional quantum Hall effect is plausible at filling factors $\nu =$ 1/3 and 1/5, provided the interparticle interaction has an unusual form for which the energy of two fermions in the relative angular momentum three channel dominates. The interaction between composite fermions in the second $\Lambda$ level (composite fermion analog of the electronic Landau level) satisfies this property, and recent studies have supported unconventional fractional quantum Hall effect of composite fermions at ${\nu }^{\ast }=$ 4/3 and 5/3, which manifests as fractional quantum Hall effect of electrons at $\nu =$ 4/11, 4/13, 5/13, and 5/17. I investigate in this article the nature of the fractional quantum Hall states at $\nu =$ 4/5, 5/7, 6/17, and 6/7, which correspond to composite fermions at ${\nu }^{\ast }=$ 4/3, 5/3 and 6/5, and find that all these fractional quantum Hall states are conventional. The underlying reason is that the interaction between composite fermions depends substantially on both the number and the direction of the vortices attached to the electrons. I also study in detail the states with different spin polarizations at 6/17 and 6/7 and predict the critical Zeeman energies for the spin phase transitions between them. I calculate the excitation gaps at 4/5, 5/7, 6/7, and 6/17 and compare them against recent experiments.

18 pages, 13 figures, changed title, minor changes in text, published version

References in corpus (13)

• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Spinful Composite Fermions in a Negative Effective Field
• Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study
• Microscopic theory of the quantum Hall hierarchy
• Fractional Quantum Hall Effect at Landau Level Filling nu=4/11
• Landau Level Quantization on the Sphere
• Phase Diagram of Fractional Quantum Hall Effect of Composite Fermions in Multi-Component Systems
• Observation of Incompressibility at $\nu =4/11$ and $\nu =5/13$
• Spin-Polarization of Composite Fermions and Particle-Hole Symmetry Breaking
• Fractional Quantum Hall Effect and Wigner Crystal of Two-Flux Composite Fermions
• Hierarchy wave functions--from conformal correlators to Tao-Thouless states
• Possible realization of a chiral p-wave paired state in a two component system

Cited by in corpus (16)

• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Composite fermion pairing induced by Landau level mixing
• Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect
• Theoretical phase diagram of two-component composite fermions in double layer graphene
• 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
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Unconventional Filling Factor 4/11: A Closed-Form Ground State Wave Function
• The composite fermion theory revisited: a microscopic derivation without Landau level projection
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
• Nonlinear transport of Wigner solid phase surrounding the two-flux composite fermion liquid
• Composite fermions and parton wavefunctions in twisted graphene on hexagonal boron nitride
• Cascade of fractional quantum Hall states in 2D system
• Topological Protection in a Landau Flat Band at $\nu =7/11$, a Candidate Filling Factor for Unconventional Correlations