Until now we have largely been discussing the properties of correlated systems with integer number of electrons; only in a few places, for example in the sections on charge ordering and on the double exchange, did we touch on some properties of doped correlated systems. But in principle the variety of phenomena which can occur in such systems with the change in electron concentration is quite broad – from a strong modification of magnetic properties up to a possibility of obtaining non-trivial, possibly high-temperature superconducting states.

A number of questions arises when we start thinking about doped strongly correlated systems. Would the system be metallic? And if so, would it be a normal metal described by the standard Fermi liquid theory? In effect, even with partially filled bands the electron correlations can still remain strong, with the Hubbard's U (much) bigger than the bandwidth; thus these questions are really nontrivial.

The other question is, what magnetic properties will result when we dope Mott insulators? As we have argued in Chapter 1 and Section 5.2, for partially filled bands the chances of ferromagnetic ordering are strongly enhanced, whereas Mott insulators with integeroccupation of d-shells are typically antiferromagnetic.

One may also expect that some other, new features could appear in strongly correlated systems with partial occupation of d levels.