SOME COMMENTS ON THE MOTT TRANSITION IN METAL AND SEMICONDUCTORS

The ''Mott transition'' controlled by strong correlations between carr iers of opposite charges, describes the passage from an itinerant meta llic state to a localized insulating state. In semiconductors, carrier s are electrons and holes pertaining to different bands : they bind in to neutral excitons in the insulating phase. A similar effect may occu r within a half-filled single band : a strong repulsion between fermio ns leads to the so called ''Mott-Hubbard transition''. The underlying physics is still unclear : is symmetry breaking a crucial issue ? What is the order parameter near the critical points ? This brief note sum marizes these questions and it points to possibly instructive limits.