Role of percolation in determining critical composition for the M-I transition in transition metal oxides

摘要

Among members of a large family of non-stoichiometric transition metal oxides which exhibit a M-I transition, NaxWO3 and its compensated relative NaxTayW1-yO3 have been particularly thoroughly investigated by experimentalists. On the theory side, recent work by Ducker, et al.[1] has significantly advanced our understanding of the physics of the metal-insulator transition in these bellwether materials. This work confirms that for these tight-binding materials, a "pseudo-gap" in the density of states arises as a consequence of large values of the Coulomb interaction term U. The work also leads to the conclusion that the one-electron Anderson localization mechanism, which considers variations in the local carrier binding energy, is not the critical factor in setting the value of x(c), the critical impurity concentration for the M-I transition. But predictions of actual values of x(c) remain elusive. I will show that percolation ideas, long waiting in the wings, give a clear picture of values of x(c) in a number of 3d, 4d, and 5d perovskites with non-magnetic transition metal ions. The geometrical ideas associated with percolation modeling generate a picture of a "linkage" transition, to supplement, not substitute for, the results of the three-band Anderson-Mott-Hubbard model used by Ducker, et al. A test of the appropriateness of percolation models to describe a M-I transition is the determination of the value of v in the relationship sigma(T = 0K) = sigma(0) proportional to (x - x(c))(v). Fragmentary data from NaxWO3, NaxTayW1-xO3 and LaNixCo1-xO3 give value of v lying between 1.6 and 2.5, the range of exponents typically found in various percolation models. [References: 17]