Universality aspects of the metal-nonmetal transition in condensed media

Our objective in this paper is to provide a simple, conceptual, framework for describing the metalnonmetal (MNM) transition in systems that can be viewed in terms of a lattice of impurity states embedded in a host matrix. From an extensive analysis of experimental data, we find that a particular (scaled) form of the Mott criterion, $n_c^{\frac{1}{3}}{a}_H^{*}=0.26\mathrm{}\pm 0.05$, is applicable over a range of approximately ${10}^{10}$ in critical densities ($n_c$) and approximately 600 Å in Bohr radii ($a_H^{*}$). Here $a_H^{*}$ is defined as an appropriate radius associated with a realistic wave function for the localized state in the low-electron-density regime. The systems of interest range from tight-binding (Frenkel) metal-atom states in the rare-gas solids to shallow (Wannier-like) states in the group-IV $a$ semiconductors and indium antimonide. The possible origins of this apparent universality have been formulated from a consideration of Berggren's interpretation of the Hubbard model for the transition, as applied to condensed systems. In essence, it appears that the role of the host matrix in the phenomenon of MNM transition is important primarily in the sense that it determines the form of the radial distribution of the (localized) impurity state. We suggest that once these matrix-induced modifications to the (gas-phase) donor state are taken into account, the ensuing transition to the metallic state (at finite impurity concentrations) reduces to a one-electron problem in a suitably renormalized concentration grid.