Phase transitions in the quantum Hall liquid in a quantum wire

Two scenarios for the collapse of the ν=1 quantum Hall liquid (QHL) state, with the effective quantum wire (QW) width defined by the Fermi vector kF, are studied. Here, ν for the QW is defined as the filling factor of Landau levels (LL) at the center of the QW. In the first one there is no electron redistribution at critical magnetic field View the MathML source, where the Fermi energy, EF, coincides with the bottom of the empty upper spin-split LL. For View the MathML source the ν=1 state is unstable due to exchange-correlation effects and lateral confinement. In the second scenario, a transition to the ν=2 state occurs, with much smaller width, at View the MathML source. The latter scenario is analyzed in the Hartree–Fock approximation (HFA). Here the Hartree contribution to the total energy affects drastically View the MathML source due to strong electron redistribution in the QW. In both scenarios, the exchange-enhanced g-factor is suppressed at Bcr. The critical fields, activation energy, and optical g-factor obtained in the first scenario are very close to the measured ones.