Wonderful life at weak Coulomb interaction: increasing of superconducting/superfluid transition temperature by disorder

We have shown that in systems where the Coulomb interaction is strongly suppressed, the superconducting transition temperature may be enhanced by disorder close to the Anderson localization transition. This phenomenon is based on the enhancement by disorder of the matrix element of attraction in the Cooper channel. For enhancement to take place one needs (i) strong disorder which makes the single-particle wave functions strongly inhomogeneous in space and (ii) strong correlation of the patterns of inhomogeneity for different wavefunctions. One case where such correlation is well known is the system close to the Anderson transition. We review the notion of multifractality of wavefunctions in this region and show how the enhancement of T_{c} arises out of the multifractal correlations.