Phase transitions in the quantum Hall liquid in a quantum wire

Abstract

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 k F , 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 B cr ( 1 ) , where the Fermi energy, E F , coincides with the bottom of the empty upper spin-split LL. For B < B cr ( 1 ) 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 B cr ( 2 ) . The latter scenario is analyzed in the Hartree–Fock approximation (HFA). Here the Hartree contribution to the total energy affects drastically B cr ( 2 ) due to strong electron redistribution in the QW. In both scenarios, the exchange-enhanced g -factor is suppressed at B cr . The critical fields, activation energy, and optical g -factor obtained in the first scenario are very close to the measured ones.