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. B = /eB 26 nm/ B[T]. The well width can even lead to the formation of novel FQHSs, such as the ones observed at ν = 1/2 and 1/4 in the lowest LL. [18][19][20][21] The reminiscence with even-denominator states in bilayer quantum Hall systems 22 hints at a multi-component origin later confirmed theoretically both for symmetric [23][24][25][26][27] and asymmetric 28,29 quantum wells in terms of a (331) Halperin state 30 that competes with the compressible composite-fermion Fermi liquid (CFFL) 31 and, under certain circumstances, 24,25,28,32 with a Pfaffian. 5,6 Furthermore, these liquid phases compete with an insulating phase in the limit of very large well widths. 21In the present paper, we investigate the competition between quantum liquids and WCs at half filling in wide quantum wells within a twocomponent model originally proposed in Ref. 23. Within this model, only the two lowest electronic subbands, due to the well confinement potential, are taken into account whereas higher sub-arXiv:1503.09132v2 [cond-mat.mes-hall] 15 Dec 2015

We investigate theoretically the fractional quantum Hall effect at half-filling in the lowest Landau level observed in asymmetric wide quantum wells. The asymmetry can be achieved by a potential bias applied between the two sides of the well. Within exact-diagonalization calculations in the spherical geometry, we find that the incompressible state is described in terms of a two-component wave function. Its overlap with the ground state can be optimized with the help of a rotation in the space of the pseudospin, which mimics the lowest two electronic subbands.