Nature of states in a random-dimer model: Bandwidth-scaling analysis.

Abstract

The scaling properties of the energy spectra of a random-dimer system are studied to discern the nature of the states at and around the dimer energy (${\mathrm{\ensuremath{\epsilon}}}_{0}$). The system is described by a tight-binding Hamiltonian. The scaling behavior of bandwidths for \ensuremath{\Vert}${\mathrm{\ensuremath{\epsilon}}}_{0}$\ensuremath{\Vert}2 shows that the system contains extended states in the neighborhood of ${\mathrm{\ensuremath{\epsilon}}}_{0}$. This result is further substantiated by the scaling behavior of the total bandwidth. The number of nonscattered states is found to increase with the increase in chain length. The scaling behavior of bandwidths also shows that the width of the nonscattered states depends on the dimer energy and its concentration in the sample. These results are consistent with results obtained from the transmission coefficient analysis. When the dimer energy is at the band edge (${\mathrm{\ensuremath{\epsilon}}}_{0}$=\ifmmode\pm\else\textpm\fi{}2), the bandwidth scaling analysis shows that states around ${\mathrm{\ensuremath{\epsilon}}}_{0}$ are algebraically localized. This result is further substantiated by the behavior of the site Green function. The significance of our results in understanding the anomalous electrical conductivity in polyaniline is discussed.