Weak and strong localization in low-dimensional semiconductor structures

The dependence of the localization length on the number of occupied subbands N in low-dimensional semiconductors is investigated. The localization length is shown to be proportional to the number of occupied subbands in quasi-one-dimensional quantum wires, while it grows exponentially with N in quasi-two-dimensional systems. Also, a weak localization theory is developed for large N with a well-defined small expansion parameter 1/N. The temperature dependence of the conductivity deduced using this perturbation theory agrees with the experimentally observed dependence.