David Logan

Abstract:

A simple theory is developed to describe the interplay between Anderson localization and dephasing mechanisms (such as inelastic electron- or exciton-phonon coupling), within the framework of a tight-binding model of spatially disordered systems. Self-consistency is enforced by demanding that only the most probable value of the imaginary part of the site self-energy be self-consistently determined. Dephasing interactions are characterized simply by an energy-independent dephasing rate. When the dephasing rate vanishes the pure localization problem may be examined as the transition is approached from either the localized or the extended regimes; mobility-edge trajectories may thereby be located. In the limit of rapid dephasing the theory correlates with the usual master-equation treatments of incoherent transport. For sufficiently large disorder a nonmonotonic but continuous crossover from coherent to incoherent transport is in general predicted. The problem of Mooij correlation, viewed as a weak-delocalization phenomenon, is also examined: it is suggested that the correlation is not universal as has frequently been supposed. © 1987 The American Physical Society.

Abstract:

We develop a self-consistent theory for the localizability of dipolar excitations, and the interplay between localization and dephasing mechanisms such as exciton-phonon coupling, within the framework of a tight-binding model of topologically disordered systems. When the dephasing rate vanishes the pure Anderson localization problem may be examined, and we find that dipolar excitations are always extended at any finite density. For sufficiently small number density, however, it is found that while no state in the band is ever strictly localized, the excitation transfer rate is exponentially small, and on the time scale of many experimental probes the excitation would effectively appear to be localized. In the limit of rapid dephasing the present theory correlates with the usual master equation treatments of incoherent (Förster) transport. For sufficiently large disorder, examination of the excitation transfer rate as a function of the dephasing rate predicts a nonmonotonic but continuous crossover from coherent to incoherent transport. © 1987 American Institute of Physics.

Abstract:

A mean field theory is developed for a dipolar excitonic insulator transition occurring in matrix-bound systems, paradigms of which are low temperature alkali-doped rare gas solids at low impurity concentration. The excitonic insulator transition is driven primarily by changes in the host matrix density, and is a transition from the normal insulating domain in which the impurity electronic ground state is spherically symmetric, to an excitonic phase in which the impurity atoms possess electric dipole moments. A description is given of the electrical and optical characteristics of the system in both the normal insulating phase and the dipolar excitonic state, and it is shown that a variety of properties characteristic of the excitonic state can be deduced from experiment. Comparison is made with experimental results, with which the theory is shown to be compatible, and it is suggested that the dipolar excitonic state may have been observed widely over many years. © 1986 American Institute of Physics.

Abstract:

A self-consistent theory of localization in a tight-binding model of topologically disordered systems is developed, which explicitly incorporates the influence of irreducible many-body interactions. These interactions are responsible for the detailed band structure of the system and stem from many-body terms in the renormalized perturbation series for the self-energy. The theory employs our previously developed disordered reference system in which the structure of the medium is taken into account, and makes considerable use of statistical mechanical methods which have direct parallels in conventional applications of liquid state theory. The resultant formulation leads to a self-consistent theory for the density of states and the localization characteristics of the system. The central notion of screening is introduced, whereby the simple transfer matrix element is replaced by an energy and density dependent renormalized transfer matrix element. The effect of screening on the mobility edge trajectories is found to be pronounced, and leads to substantially enhanced (diminished) stability of localized state near the upper (lower) band edge in the density of states. © 1986 American Institute of Physics.