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

TL;DR

This study numerically explores various quantum phases in wide quantum wells at half filling, revealing the coexistence of fractional quantum Hall states and Wigner crystals, and comparing results with experimental data.

Contribution

It introduces a phase diagram for wide-well quantum wells considering two lowest subbands, identifying new Wigner crystal phases and their relation to experimental observations.

Findings

Identification of a rectangular Wigner crystal in the second subband at low Landau levels.

Discovery of an intermediate incompressible state with two four-flux Pfaffians.

Correlation of theoretical phase diagram with experimental results by Shabani et al.

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.