Localization transition in a ballistic quantum wire

The many-body wave function of localized states in one dimension is probed by measuring the tunneling conductance between two parallel wires, fabricated in a GaAs/AlGaAs heterostructure. Tunneling conductance in the presence of a magnetic field perpendicular to the plane of the wires serves as probe of the momentum space wave function of the wires. One of the two wires is driven into the localized regime using a density tuning gate, whereas the other wire, still in the regime of extended electronic states, serves as a momentum spectrometer. As the electron density is lowered to a critical value, the state at the Fermi level abruptly changes from an extended state with a well-defined momentum to a localized state with a wide range of momentum components. The signature of the localized states appears as discrete tunneling features at resonant gate voltages, corresponding to the depletion of single electrons and showing Coulomb-Blockade behavior. Typically 5-10 such features appear, where the one-electron state has a single-lobed momentum distribution, and the few-electron states have double-lobed distributions with peaks at ± kF. A theoretical model suggests that for a small number of particles (N<6), the observed state is a mixture of ground and thermally excited spin states.