Electron gas in channels in strong magnetic fields

The physics of an electron gas in a strong magnetic field in channel geometries is discussed. For very narrow channels, the electrons form a one-dimensional (1D) ‘‘Fermi sea’’ with a concomitant 2$k_F$ charge-density-wave (CDW) instability. For a 1D spinless electron gas in the absence of a magnetic field, there is usually a competition between the ‘‘superconducting’’ and CDW instabilities so that the CDW instability does not occur. Because of the spatial dependence of the exchange interaction in the effective 1D Hamiltonian in the present case, the conventional cancellation between these instabilities becomes incomplete and a CDW instability results. The transition from a one-dimensional ‘‘Fermi sea’’ with a 2$k_F$ CDW instability to a two-dimensional situation which exhibits the fractional quantized Hall effect as the channel width is increased is investigated. As the width is increased, except under some special circumstances that correspond to odd-denominator filling factors when the gap is not changed much, the gap in the excitation spectrum undergoes a damped oscillation. We interpret the oscillation in terms of the formation of clusters due to multiparticle exchange and its breakup.