NONSCATTERED STATES IN A RANDOM-DIMER MODEL

We study a random-dimer model within the context of a tight-binding Hamiltonian in one dimension. This model may be useful in understanding the transport properties of the polyaniline system. As a prelude to our understanding we consider a few simple but relevant models. For these cases we investigate the behavior of the phase of the transmission coefficient. From the study of these models we conclude that many resonances merge around the dimer energy in the random-dimer model. Our subsequent analysis of the random-dimer model proves this conjecture. This analysis, however, does not yield the number of nonscattered states in the system. According to Dunlap, Wu, and Phillips [Phys. Rev. Lett. 65, 88 (1990)] there will be square-root N nonscattered states around the dimer energy. To obtain the number of nonscattered states we study the transmission coefficient. We find that the averaged transmission coefficient yields approximately a Lorentzian curve. Furthermore, there is an energy width where the transmission coefficient is aproximately unity. For a high concentration of dimers and dimer energy well inside the host band we find square-root N nonscattered states. A similar number of nonscattered states is obtained for a low concentration of dimers and dimer energy near the band edge. In general we find a discernable discrepancy between the observed half-width and the calculated half-width. The discrepancy is quite significant when the dimer energy is close to one of the band edges. On the basis of these results we speculate that the averaged half-width scales as N(-lambda) when lambda is a function of both the concentration and the energy of the dimer.