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.

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

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• Microwave spectroscopic studies of the bilayer electron solid states at low Landau filling in a wide quantum well
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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