Weak localization in semiconductor quantum wires

Weak-localization negative magnetoresistance is calculated for semiconductor quantum wires with use of the nonequilibrium-Green-function technique. Because of the low electron densities the localization length can become comparable with the phase-coherence length in these systems. A self-consistent treatment of the cooperon by solving a transport equation allows us to describe the transition from weak to strong localization. We take into account the discrete subband structure and calculate the one-particle properties self-consistently. Simple approximative formulas are derived for negative magnetoresistance, for localization length, and for the critical magnetic field which suppresses weak localization. Deviations from the diffusion limit are discussed for phase-coherence length of the order of localization length as well as for phase-coherence length not much larger than scattering length. Numerical results are given for a typical example of a GaAs wire.