Fractional quantum Hall states versus Wigner crystals in wide quantum wells in the half-filled lowest and second Landau levels

Abstract

We investigate numerically different phases that can occur at half filling in the lowest and the first excited Landau levels in wide-well twodimensional electron systems exposed to a perpendicular magnetic field. Within a twocomponent model that takes into account only the two lowest electronic subbands of the quantum well, we derive a phase diagram that compares favorably with an experimental one by Shabani et al. [Phys. Rev. B 88, 245413 (2013)]. In addition to the compressible composite-fermion Fermi liquid in narrow wells with a substantial subband gap and the incompressible twocomponent (331) Halperin state, we identify in the lowest Landau level a rectangular Wigner crystal occupying the second subband. This crystal may be the origin of the experimentally observed insulating phase in the limit of wide wells and high electronic densities. In the second Landau level, the incompressible Pfaffian state, which occurs in narrow wells and large subband gaps, is also separated by an intermediate region from a large-well limit in which a similar rectangular Wigner crystal in the excited subband is the ground state, as for the lowest Landau level. However, the intermediate region is characterized by an incompressible state that consists of two four-flux Pfaffians in each of the components.

arXiv comment18 pages, 18 figures; published version with new appendix (discussion of the role of wave function overlap in the crystalline phases), updated references

References in corpus (43)

• Evidence for an Anisotropic State of Two-Dimensional Electrons in High Landau Levels
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Strongly Anisotropic Transport in Higher Two-Dimensional Landau Levels
• The Ground State of a Two-Dimensional Electron Liquid in a Weak Magnetic Field
• Exact results for interacting electrons in high Landau levels
• Insulating and Fractional Quantum Hall States in the N=1 Landau Level
• Anisotropic States of Two-Dimensional Electron Systems in High Landau Levels: Effect of an In-Plane Magnetic Field
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• 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
• More Realistic Hamiltonians for the Fractional Quantum Hall Regime in GaAs and Graphene
• Landau level mixing and the emergence of Pfaffian excitations for the 5/2 fractional quantum Hall effect
• Evidence for a Bilayer Quantum Wigner Solid
• Possibility of p-wave pairing of composite fermions at $\nu =1/2$
• The Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width
• Competition between quantum-liquid and electron-solid phases in intermediate Landau levels
• Landau Level Mixing in the Perturbative Limit
• Observation of a Fractional Quantum Hall State at $\nu =1/4$ in a Wide GaAs Quantum Well
• Particle-Hole Symmetry Breaking and the 5/2 Fractional Quantum Hall Effect
• Wigner Crystals Phases in Bilayer Quantum Hall Systems
• Observation of fractional quantum Hall effect at even-denominator 1/2 and 1/4 fillings in asymmetric wide quantum wells
• Quantum Hall Phase Diagram of Second Landau-level Half-filled Bilayers: Abelian versus Non-Abelian States
• Quantum Hall Phase Diagram of Half-filled Bilayers in the Lowest and the Second Orbital Landau Levels: Abelian versus Non-Abelian Incompressible Fractional Quantum Hall States
• The plasma picture of the fractional quantum Hall effect with internal SU(K) symmetries
• Phase Diagrams for the $\nu$ = 1/2 Fractional Quantum Hall Effect in Electron Systems Confined to Symmetric, Wide GaAs Quantum Wells
• Microscopic Theory of the Reentrant IQHE in the First and Second Excited LLs
• Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells
• Collective Modes of Quantum Hall Stripes
• Fractional quantum Hall effects in bilayers in the presence of inter-layer tunneling and charge imbalance
• Tunneling-driven breakdown of the 331 state and the emergent Pfaffian and composite Fermi liquid phases
• Fractional quantum Hall state at ν=1/4 in a wide quantum well
• Fractional Quantum Hall Effect in the Second Landau Level: the Importance of Inter-Composite-Fermion Interaction
• Possible Reentrance of the Fractional Quantum Hall Effect in the Lowest Landau Level
• Microwave spectroscopic observation of distinct electron solid phases in wide quantum wells
• Variational Monte Carlo study of spin polarization stability of fractional quantum Hall states against realistic effects in half-filled Landau levels
• Anisotropic states of two-dimensional electrons in high magnetic fields
• Microwave spectroscopic studies of the bilayer electron solid states at low Landau filling in a wide quantum well
• Subband Engineering Even-Denominator Quantum Hall States
• Two-Component Fractional Quantum Hall Effect in the Half-Filled Lowest Landau Level in an Asymmetric Wide Quantum Well
• Correlation-hole induced paired quantum Hall states in lowest Landau level

Cited by in corpus (17)

• Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
• Wigner crystallization in topological flat bands
• Two-component quantum Hall effects in topological flat bands
• Geometric Resonance of Composite Fermions near Bilayer Quantum Hall States
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Topological phase transition between composite-fermion and Pfaffian daughter states near ν = 1/2 FQHS
• Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells
• Observation of An Anisotropic Wigner Crystal
• Taming Landau level mixing in fractional quantum Hall states with deep learning
• Microwave spectroscopic observation of a Wigner solid within the 1/2 fractional quantum Hall effect
• Valley-tunable, even-denominator fractional quantum Hall state in the lowest Landau level of an anisotropic system
• RD-NMR spectra of the crystal states of the two-dimensional electron gas in a quantizing magnetic field
• Exotic Bilayer Crystals in a Strong Magnetic Field
• Interaction-driven transition between the Wigner crystal and the fractional Chern insulator in topological flat bands
• Fractional quantum Hall state at $\nu =1/2$ with energy gap up to 6 K, and possible transition from one- to two-component state
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Disorder-driven phase transitions in bosonic fractional quantum Hall liquids