The role of strong electronic correlations in the metal-to-insulator transition in disordered LiAl_yTi_(2-y)O₄

The compound LiAl_yTi_(2-y)O_4 undergoes a metal-to-insulator transition for y_c ~0 .33. This system, in the absence of strong electronic correlations, is a prototypical example of quantum site percolation. However, it is known that the effects of disorder produced by such a percolating lattice are insufficient to explain this transition: a quantum site percolation model predicts y_c ~ 0.8, well above the experimental value. We have included an on-site Hubbard interaction into a model of this compound, using a real-space Hartree-Fock approach, and have found that for a Hubbard energy equal to 1.5 times the non-interacting bandwidth one obtains y_c~0.35. Further, as a function of increasing Hubbard energy, we find that an Altshuler-Aronov suppression of the density of states, delta N(E) ~ sqrt(| E-E_F |), reduces the density of states at the Fermi energy to zero at the critical Hubbard interaction. Using this ratio of correlation to hopping energy one is led to a prediction for the value of near-neighbour superexchange J/t~1/3 which is similar to that for the cuprate superconductors.