Interplay between fractional quantum Hall liquid and crystal phases at low filling

Abstract

The nature of the state at low Landau-level filling factors has been a longstanding puzzle in the field of the fractional quantum Hall effect. While theoretical calculations suggest that a crystal is favored at filling factors $\nu \lesssim 1/6$, experiments show, at somewhat elevated temperatures, minima in the longitudinal resistance that are associated with fractional quantum Hall effect at $\nu =$ 1/7, 2/11, 2/13, 3/17, 3/19, 1/9, 2/15 and 2/17, which belong to the standard sequences $\nu =n/(6n\pm 1)$ and $\nu =n/(8n\pm 1)$. To address this paradox, we investigate the nature of some of the low-$\nu$ states, specifically $\nu =1/7$, $2/13$, and $1/9$, by variational Monte Carlo, density matrix renormalization group, and exact diagonalization methods. We conclude that in the thermodynamic limit, these are likely to be incompressible fractional quantum Hall liquids, albeit with strong short-range crystalline correlations. This suggests a natural explanation for the experimentally observed behavior and a rich phase diagram that admits, in the low-disorder limit, a multitude of crystal-FQHE liquid transitions as the filling factor is reduced.

13 pages, 10 figures, published version

References in corpus (46)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement entropy in fermionic Laughlin states
• Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level
• Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Ground state phase diagram of 2D electrons in a high Landau level: - DMRG study
• Band Structure of the Fractional Quantum Hall Effect
• The half-filled Landau level: the case for Dirac composite fermions
• Transition from an electron solid to the sequence of fractional quantum Hall states at very low Landau level filling factor
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• Correlation lengths of Wigner crystal order in two dimensional electron system at high magnetic field
• Melting of a 2D Quantum Electron Solid in High Magnetic Field
• Theoretical Search for Nested Quantum Hall Effect of Composite Fermions
• Odd- and even-denominator fractional quantum Hall states in monolayer WSe${}_2$
• Wigner Crystals in the lowest Landau level at low filling factors
• Sharp Tunneling Resonance from the Vibrations of an Electronic Wigner Crystal
• The nature of composite fermions and the role of particle hole symmetry: A microscopic account
• 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
• Laughlin-Jastrow-correlated Wigner crystal in a strong magnetic field
• Composite Fermions Waltz to the Tune of a Wigner Crystal
• Evidence for Two Different Solid Phases of Two Dimensional Electrons in High Magnetic Fields
• State Counting for Excited Bands of the Fractional Quantum Hall Effect: Exclusion Rules for Bound Excitons
• Competing Fractional Quantum Hall and Electron Solid Phases in Graphene
• Microscopic verification of topological electron-vortex binding in the lowest-Landau-level crystal state
• Competing Crystal Phases in the Lowest Landau Level
• Crystallization in the Fractional Quantum Hall Regime Induced by Landau-level Mixing
• Hamiltonian Theory of the Composite Fermion Wigner Crystal
• Fractional Quantum Hall States at 1/3 and 5/2 Filling: the Density-Matrix Renormalization Group Calculations
• Repulsive Interactions in Quantum Hall Systems as a Pairing Problem
• Probing the geometry of the Laughlin state
• Fractional Quantum Hall Effect at $\nu =2+4/9$
• Comparison of the density-matrix renormalization group method applied to fractional quantum Hall systems in different geometries
• Fractional Quantum Hall Effect and Wigner Crystal of Two-Flux Composite Fermions
• 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
• Magnetic Field Induced Insulating Phases at Large $r_s$
• Working principles of doping-well structures for high-mobility two-dimensional electron systems
• Transition from a fractional quantum Hall liquid to an electron solid at Landau level filling nu = 1/3 in tilted magnetic fields
• Search for exact local Hamiltonians for general fractional quantum Hall states
• Neutral Collective Modes in Spin-Polarized Fractional Quantum Hall States at Filling Factors 1/3, 2/5, 3/7, and 4/9
• Entanglement Spectroscopy and its Application to the Quantum Hall Effects

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• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Competition between fractional quantum Hall liquid and Wigner solid at small fillings: Role of layer thickness and Landau level mixing
• Correlated states of 2D electrons near the Landau level filling $\nu =1/7$
• A Highly Correlated Topological Bubble Phase of Composite Fermions
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• From Fractional Quantum Anomalous Hall Smectics to Polar Smectic Metals: Nontrivial Interplay Between Electronic Liquid Crystal Order and Topological Order in Correlated Topological Flat Bands
• Developing fractional quantum Hall states at even-denominator fillings 1/6 and 1/8
• Competing Laughlin state and Wigner crystal in bilayer graphene
• Competing Many-Body Phases at Small Fillings in Ultrahigh-Quality GaAs 2D Hole Systems: Role of Landau Level Mixing
• Bubble phase at $\nu =1/3$ for a spinless hollow-core interaction
• Very high-energy collective states of partons in fractional quantum Hall liquids
• Evidence for Topological Protection Derived from Six-Flux Composite Fermions
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Developing fractional quantum Hall states at $\nu$ = $\frac{1}{7}$ and $\frac{2}{11}$ in the presence of significant Landau level mixing
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Interlayer-correlated fractional quantum Hall state in a trilayer electron system
• Disorder-induced strong-field strong-localization in 2D systems
• Topological states in double monolayer graphene
• Topological Protection in a Landau Flat Band at $\nu =7/11$, a Candidate Filling Factor for Unconventional Correlations