Disorder effects in quantum electronic systems have led to a variety of novel phases. Fermionic systems have played a special role in our understanding of such effects. Indeed for fermions, the Pauli principle prevent the fermions to be trapped macroscopically in the minima of the random potential, making the non interacting case worthwhile to study. Disorder then leads to the rich physics of Anderson localization. Using both scaling theories and sophisticated field theoretical techniques, it is now known that electrons are localized by disorder in one and two dimensions, whereas a mobility edge exists in three dimensions. The situation becomes much more complicated when one wants to take into account the electron-electron interaction. Such a question was crucial for the understanding of doped semiconductors. In addition recent experiments in two dimensional electron gas systems have prompted the question of whether a metal-insulator transition could exist in interacting systems (see [2] and references therein), stimulating further interest in this problem. On the theoretical side the question is extremely complicated. Most of the theoretical approaches used for free electrons either fail or become much more complicated when interactions are included which makes it more difficult to obtain unambiguous answers. Perturbative calculations or renormalization group calculations can be made for weak interactions. Unfortunately they scale to strong coupling, which leaves the question of the large scale/low energy physics still open.
展开▼
