Weak localisation theory for lightly doped semiconductor quantum wires

A weak localisation theory for a semiconductor quantum wire, which has a width of the order of the Fermi wavelength, is presented. In our model the electronic motion is essentially one-dimensional and the localisation length L, is much larger than the mean free path I , so that, in contrast to conventional theories a non-localised quantum wire with a total length L < L, but much larger than I is possible. For the static properties, we study the temperature dependence and the subbands effect of the weak localisation. We find that when (the phase coherent length) L, > L , the conductance of the quantum wire depends on L instead of L,, implying a temperature independent behaviour. Our theory explains recent experiments which found temperature independent transport behaviour at very low temperature for narrow AlGaAs/GaAs quantum wire. In studying the AC conductivity, our calculation predicts that, for the quantum wire with L > L, , there exists a critical value of the frequency above which the system is delocalised and the AC conductivity a (w) rises as w2.