Incompressible States of the Interacting Composite Fermions in Negative Effective Magnetic Fields at $\nu =4/13$, 5/17, and 3/10

Abstract

By developing an algorithm for evaluating the basis states for the composite fermions with negative effective magnetic field, we perform the composite-fermion-diagonalization study for the fully spin-polarized fractional quantum Hall states at the filling factors $\nu =3/10$, 4/13, and 5/17 in the range $2/7<\nu <1/3$. These observed states correspond to partially filled second effective Landau level, for the composite fermions carrying four vortices, with filling factor $\bar{\nu }=1/2$, 1/3, and 2/3 respectively, analogous to the previously studied states of composite fermions with two attached vortices in the range $1/3<\nu <2/5$. We show that the character of these states in the range $2/7<\nu <1/3$ replicates the same for the states in the range $1/3<\nu <2/5$ having identical $\bar{\nu }$: Chiral p-wave pairing with anti-Pfaffian correlation of composite fermions carrying six quantized vortices produces incompressible state at $\nu =3/10$; an unconventional interaction between composite fermions, resulting from the suppression of fermion pairs with relative angular momentum three and producing fractional quantum Hall effect of composite fermions in the second effective Landau level with $\bar{\nu }=1/3$ and its particle-hole conjugate filling factor 2/3, reproduces incompressible states at $4/13$ and $5/17$ filling factors. We further estimate the thermodynamic limit of the ground state energies and calculate the lowest energy gap for neutral collective excitations of these states.

Published version

References in corpus (10)

• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Fractional Quantum Hall Effect in Graphene: Quantitative Comparison between Theory and Experiment
• Spinful Composite Fermions in a Negative Effective Field
• Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study
• Fractional Quantum Hall Effect at Landau Level Filling nu=4/11
• Observation of Incompressibility at $\nu =4/11$ and $\nu =5/13$
• Transition from Free to Interacting Composite Fermions away from $\nu$=1/3
• Possible realization of a chiral p-wave paired state in a two component system
• Anomalously low magnetoroton energies of the unconventional fractional quantum Hall states of composite fermions

Cited by in corpus (11)

• Fermi wave vector for the non-fully spin polarized composite-fermion Fermi sea
• Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states
• 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
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Bubble phase at $\nu =1/3$ for a spinless hollow-core interaction
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor
• Cascade of fractional quantum Hall states in 2D system