  We report an unusual insulating state in one-dimensional quantum wires with a
non-uniform confinement potential. The wires consist of a series of closely
spaced split gates in high mobility GaAs/AlGaAs heterostructures. At certain
combinations of wire widths, the conductance abruptly drops over three orders
of magnitude, to zero on a linear scale. Two types of collapse are observed,
one occurring in multi-subband wires in zero magnetic field and one in single
subband wires in an in-plane field. The conductance of the wire in the collapse
region is thermally activated with an energy of the order of 1 K. At low
temperatures, the conductance shows a steep rise beyond a threshold DC
source-drain voltage of order 1 mV, indicative of a gap in the density of
states. Magnetic depopulation measurements show a decrease in the carrier
density with lowering temperature. We discuss these results in the context of
many-body effects such as charge density waves and Wigner crystallization in
quantum wires.
