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Role of percolation in determining critical composition for the M‐I transition in transition metal oxides
Author(s) -
Holcomb D.F.
Publication year - 1999
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/(sici)1521-3889(199911)8:7/9<649::aid-andp649>3.0.co;2-7
Subject(s) - condensed matter physics , percolation (cognitive psychology) , coulomb , transition metal , physics , mott transition , tight binding , work (physics) , materials science , electron , hubbard model , thermodynamics , electronic structure , quantum mechanics , chemistry , superconductivity , biochemistry , neuroscience , catalysis , biology
Among members of a large family of non‐stoichiometric transition metal oxides which exhibit a M‐I transition, Na x WO 3 and its compensated relative Na x Ta y W 1— y O 3 have been particularly thoroughly investigated by experimentalists. On the theory side, recent work by Dücker, 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 Dücker, 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 σ ( T = 0 K ) ≡ σ (0) ∝ ( x — x c ) v . Fragmentary data from Na x WO 3 , Na x Ta y W 1— x O 3 and LaNi x Co 1— x O 3 give value of v lying between 1.6 and 2.5, the range of exponents typically found in various percolation models.