Theoretical Search for Nested Quantum Hall Effect of Composite Fermions

Abstract

Almost all quantum Hall effect to date can be understood as {\em integral} quantum Hall effect of appropriate particles, namely electrons or composite fermions. This paper investigates theoretically the feasibility of nested states of composite fermions which would lead to a quantum Hall effect that cannot be understood as integral quantum Hall effect of composite fermions. The weak residual interaction between composite fermions will play a crucial role in the establishment of such quantum Hall states by opening a gap in a partially filled composite-fermion level. To treat the problem of interacting composite fermions, we develop a powerful method that allows us to obtain the low energy spectra at composite fermion fillings of ${\nu }^{\ast }=n+\bar{\nu }$ without making any assumption regarding the structure of composite fermions in the topmost partially filled level. The method is exact aside from neglecting the composite-fermion Landau level mixing, and enables us to study rather large systems, for example, 24 particles at a total flux of 62 $hc/e$, for which the dimension of the lowest Landau level Hilbert space is $\sim 10^{17}$. We have investigated, for fully spin polarized composite fermions, several filling factors between 1/3 and 2/5 using this approach. The results indicate that any possible incompressibility at these fractions is likely to have a fundamentally different origin than that considered earlier.

14 pages, 16 figures

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• Fractional Quantum Hall Effect in Graphene: Quantitative Comparison between Theory and Experiment
• State Counting for Excited Bands of the Fractional Quantum Hall Effect: Exclusion Rules for Bound Excitons
• Role of exciton screening in the 7/3 fractional quantum Hall effect
• Ground State Phase Diagram of 2D Electrons in High Magnetic Field
• Phase Diagram of Fractional Quantum Hall Effect of Composite Fermions in Multi-Component Systems
• Enigmatic 4/11 State: A Prototype for Unconventional Fractional Quantum Hall Effect
• Microscopic origin of the next generation fractional quantum Hall effect
• Spontaneous polarization of composite fermions in the $n=1$ Landau level of graphene
• Second Generation of Composite Fermions in the Hamiltonian Theory
• Fermion Chern Simons Theory of Hierarchical Fractional Quantum Hall States
• Composite fermion theory of correlated electrons in semiconductor quantum dots in high magnetic fields
• Possible Anti-Pfaffian Pairing of Composite Fermions in the Lowest Landau Level
• Testing the topological nature of the fractional quantum Hall edge
• Understanding the 5/2 Fractional Quantum Hall Effect without the Pfaffian Wave Function
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• Interplay between fractional quantum Hall liquid and crystal phases at low filling
• Positions of the magnetoroton minima in the fractional quantum Hall effect
• Composite Fermions on a Torus
• Higher Energy Composite Fermion Levels in the Fractional Quantum Hall Effect
• A note contrasting two microscopic theories of the fractional quantum Hall effect
• Two-dimensional electron system in high magnetic fields: Wigner crystal vs. composite-fermion liquid
• Partially spin polarized quantum Hall effect in the filling factor range 1/3 < nu < 2/5
• Possible Reentrance of the Fractional Quantum Hall Effect in the Lowest Landau Level
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Composite-fermion crystallites in quantum dots
• Quasihole condensates in quantum Hall liquids
• Fractionally charged skyrmions in fractional quantum Hall effect
• Spin phase diagram of the nu_e=4/11 composite fermion liquid
• Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states
• Semiconductor quantum dots in high magnetic fields: The composite-fermion view
• Change in the character of quasiparticles without gap collapse in a model of fractional quantum Hall effect
• Transition from Free to Interacting Composite Fermions away from $\nu$=1/3
• The Hierarchy of Incompressible Fractional Quantum Hall States
• On the self-similarity in quantum Hall systems
• Possible realization of a chiral p-wave paired state in a two component system
• Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect
• Second Generation of Moore-Read Quasiholes in a Composite Fermion Liquid
• Neutral Collective Modes in Spin-Polarized Fractional Quantum Hall States at Filling Factors 1/3, 2/5, 3/7, and 4/9
• 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
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• Pair-distribution functions of correlated composite fermions
• Incompressible States of the Interacting Composite Fermions in Negative Effective Magnetic Fields at $\nu =4/13$, 5/17, and 3/10
• Fermionic Chern-Simons Theory of SU(4) Fractional Quantum Hall Effect
• Flavor altering excitations of composite fermions
• Anomalously low magnetoroton energies of the unconventional fractional quantum Hall states of composite fermions
• States of interacting composite fermions at Landau level fillig $\nu =2+3/8$
• Local density of states and particle entanglement in topological quantum fluids
• Fingerprints of Composite Fermion Lambda Levels in Scanning Tunneling Microscopy
• Microscopic study of the 2/5 fractional quantum Hall edge
• Numerical studies of the Pfaffian model of the nu=5/2 fractional quantum Hall effect
• Unconventional Filling Factor 4/11: A Closed-Form Ground State Wave Function
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• Novel Families of Fractional Quantum Hall States : A Berry Phase Approach
• Composite fermions in the neighborhood of $\nu =1/3$
• Two-fluid theory of composite bosons and fermions and the quantum Hall proximity effect
• Residual interactions and correlations among Laughlin quasiparticles: Novel hierarchy states
• Double roton-minima in bosonic fractional quantum Hall states
• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere
• Probing fractional quantum Hall effect by photoluminescence
• Charge and Statistics of Quasiholes in Pfaffian States of Composite Fermion Excitations
• Topological Protection in a Landau Flat Band at $\nu =7/11$, a Candidate Filling Factor for Unconventional Correlations