How are spin gap and pairing correlations of doped Mott insulators controlled by the geometry of the lattice structure?

Proposals to enhance the spin excitation gap and the pairing correlations i n doped Mott insulators are reviewed. Design and tuning of flat dispersions near the Fermi level extend the critical region of the metal-to-Mott insul ator transition thereby inducing stronger pairing instabilities. Several on e- and two-dimensional decorated lattices are studied. We also discuss the tuning for stronger d-wave pairing instabilities in a microscopic model of high-T-c cuprates. (C) 2000 Elsevier Science B.V. All rights reserved.