Valley- and spin-occupancy instability in the quasi-one-dimensional electron gas

We study the ground-state energy of quantum wires including exchange and correlation as a function of the valley degeneracy. At high densities (small random-phase approximation parameter r(s) < r(sc)), it is energetically favourable to occupy the two valleys while, at low densities (r(s) > r(sc)), only one valley is occupied. We suggest the possibility of a valley-occupancy instability. The critical density r(sc) of this instability is calculated for cylindrical quantum wires of radius R(0). r(sc) decreases with decreasing R(0) and is small for thin quantum wires. We also calculate the critical density for the spin-occupancy instability and find that correlation effects are less important than for the valley-occupancy instability. We argue that the instabilities can be detected by resistance measurements of one-dimensional quantum wires in the ballistic regime.