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Abstract:

A theory is developed to describe the electronic densities of states and localization characteristics of a multiband tight-binding model for a system characterized by quenched liquid-like disorder. For the case of an sp ³ system, and with parameters appropriate to fluid mercury at an independent electron level of description, the role of localization is found to be important: localized Fermi-level states persist up to densities considerably higher than that at which the s-p band gap closes. © 1990 American Institute of Physics.

Abstract:

The quantum mechanics of energy flow in many-dimensional Fermi resonant systems has several connections to the theory of Anderson localization in disordered solids. We argue that in high dimensional and highly quantum mechanical systems the energy flow can be modeled as coherent transport on a locally but weakly correlated random energy surface. This model exhibits a sharp but continuous transition from local to global energy flow characterized by critical exponents. Dephasing smears the transition and an interesting nonmonotonic dependence of energy flow rate on environmental coupling is predicted to occur near the transition. © 1990 American Institute of Physics.

Abstract:

From an exact theory presented in a previous paper (see Logan and Winn, 1988), the authors develop systematically an approximate single-site description for the density of states of a random tight-binding model characterised by quenched liquid-like disorder. The resultant theory is formally equivalent to the single super-chain approximation (SSCA) introduced by Wertheim (1973) in the context of classical dielectric theory. The authors show that the SSCA is equivalent to the effective-medium approximation (EMA) of Roth (1976), and further, for a simple choice of the pair distribution function, that the SSCA/EMA is formally equivalent to the mean spherical approximation of liquid-state theory. For a Yukawa transfer matrix element, an analytic solution of the SSCA/EMA is derived and its predictions discussed. A comparison is also made with the Matsubara-Toyozawa approximation (1961) to illustrate the effect of including the structural characteristics of the system. Finally, the authors discuss some straightforward extensions of the theory including incorporation of site-diagonal disorder, multiple-hopping processes, and the effects of orbital overlap.

Abstract:

An analysis is given for the configurationally averaged Green functions of a random multi-level tight-binding model characterised by quenched liquid-like disorder, using graph-theoretical methods. An exact self-consistency equation for the average diagonal Green function matrix, G(z), is derived, from which follow the partial densities of states (DOS). From the exact description, various approximate theories for G(z) may be developed systematically. The authors examine in particular three tractable theories for the case of a two-band system: the Hubbard approximation, the Matsubara-Toyozawa approximation and the single super-chain approximation (SSCA) which is equivalent to the effective medium approximation (EMA) of Roth (1974, 1976). With Yukawa transfer matrix elements the SSCA/EMA is solved analytically by exploiting direct analogies with the theory of classical binary liquid mixtures. For all three theories the material parameter dependence of the DOS is examined systematically and comparatively, with particular regard to band overlap effects which may lead to a metal-insulator transition.