Random Dimer Model Research Articles

Insulator-metal transitions in random lattices containing symmetrical defects.

We show in this paper, within the context of a tight-binding model, that when defects spanning more than one lattice size contain a plane of symmetry, the standard tendency of disorder to localize electronic states can be suppressed at certain energies in the band. A general transfer-matrix approach is used to show exactly that when such defects are sprinkled at random on a linear chain, \ensuremath{\surd}N (N is the number of states) of the electronic states will remain unscattered by the disorder regardless of the concentration of the defects. The location in the energy band of the unscattered states is determined by the unit transmission condition for a single defect. The delocalization-localization transition recently reported in a series of one-dimensional models, such as the random-dimer model, is shown to result from the general condition of symmetric internal structure. We demonstrate that the continuum limit of these models is simply a collection of randomly placed square barriers (or wells) on a line and show that regardless of the distribution of separations between the barriers, \ensuremath{\surd}N of the electronic states in the vicinity of the zero-reflectance condition will necessarily be extended.

Localization and Its Absence: A New Metallic State for Conducting Polymers

A widely held view in solid-state physics is that disorder precludes the presence of long-range transport in one dimension. A series of models has been recently proposed that do not conform to this view. The primary model is the random dimer model, in which the site energies for pairs of lattice sites along a linear chain are assigned one of two values at random. This model has a set of conducting states that ultimately allow an initially localized particle to move through the lattice almost ballistically. This model is applicable to the insulator-metal transition in a wide class of conducting polymers, such as polyaniline and heavily doped polyacetylene. Calculations performed on polyaniline demonstrate explicitly that the conducting states of the random dimer model for polyaniline are coincident with recent calculations of the location of the Fermi level in the metallic regime. A random dimer analysis on polyparaphenylene also indicates the presence of a set of conducting states in the vicinity of the band edge. The implications of this model for the metallic state in other polymers, including heavily doped polyacetylene, are discussed.

Polyaniline is a random-dimer model: A new transport mechanism for conducting polymers.

We consider here a single randomly protonated strand of the conducting polymer polyaniline and show explicitly that the disorder inherent in this system is described by the random-dimer model of Dunlap, Wu, and Phillips [Phys. Rev. Lett. 65, 88 (1990)] with off-diagonal disorder. We demonstrate exactly that the location in the energy band of the unscattered or conducting states of this model coincides with recent calculations of the location of the Fermi level in the protonated form of the polymer. We argue then that the random-dimer model is capable of explaining the insulator-metal transition in polyaniline.

A SCENARIO FOR THE ABSENCE OF LOCALISATION IN 1-DIMENSION

We review here the random dimer model of a binary alloy which we have recently demonstrated exhibits an absence of localisation. Specifically we show that if one (or both) of the site energies is assigned at random to pairs of lattice sites (that is, two sites in succession), an initially localised particle can become delocalised. We show explicitly that transport obtains in this model because [Formula: see text] of the electronic states are extended over the whole sample. The relevance of this model to the insulator-metal transition in polyaniline is discussed. The dual of the random dimer model is also shown to exhibit an absence of localisation and is shown to be relevant to transmission resonances in Fibonacci lattices.

Absence of localization in a random-dimer model.

We consider here a 1D tight-binding model with two uncorrelated random site energies ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{a}}$ and ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{b}}$ and a constant nearest-neighbor matrix element V. We show that if one (or both) of the site energies is assigned at random to pairs of lattice sites (that is, two sites in succession), an initially localized particle can become delocalized. Its mean-square displacement at long times is shown to grow in time as ${\mathit{t}}^{3/2}$ provided that -2V${\mathrm{\ensuremath{\epsilon}}}_{\mathit{a}}$-${\mathrm{\ensuremath{\epsilon}}}_{\mathit{b}}$2V. Diffusion occurs if ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{a}}$-${\mathrm{\ensuremath{\epsilon}}}_{\mathit{b}}$=\ifmmode\pm\else\textpm\fi{}2V and localization otherwise. The dual of the random-dimer model is also shown to exhibit an absence of localization and is shown to be relevant to transmission resonances in Fibonacci lattices.