Optical studies of the metal-nonmetal transition in a metal—rare-gas disordered system

Abstract

In this paper we report the results of an experimental study of the optical properties in the energy range 0.65-3.80 eV of binary mixtures of Hg and Xe at 6 K over the concentration range $X=1.0\ensuremath{-}0.47$ atomic fraction Hg. A new optical criterion for the specification of the metal-nonmetal transition (MNMT) is advanced which predicts that the real part of the low-frequency dielectric function should decrease abruptly with increase of the metal concentration beyond the MNMT. This prediction is borne out for the Hg-Xe system and was used to specify the concentration ${X}_{M}=0.80\ifmmode\pm\else\textpm\fi{}0.02$ for the MNMT. Subsequently, we have analyzed the frequency-dependent conductivity of the Hg-Xe films in terms of the random-phase model, which was extended to handle a system with two overlapping bands. The theoretical results were used to fit simultaneously the dc conductivity and the optical properties with a model density of states in the concentration range $0.47>~X>~0.88$. The marked overestimate of the dc conductivity calculated from the fit of the random-phase model for mercury concentrations $X<0.80$ was interpreted in terms of the termination of the strong-scattering metallic regime where the states at the Fermi energy become localized. The composition ${X}_{M}=0.80\ifmmode\pm\else\textpm\fi{} 0.02$, making the MNMT obtained from the onset of localization, is in excellent agreement with the independent estimate based on an optical criterion and with the onset of a positive temperature coefficient of the dc conductivity. Our analysis provides an unambiguous identification of the MNMT in this disordered material and draws a distinction between the MNMT (${X}_{M}=0.80\ifmmode\pm\else\textpm\fi{}0.02$) and the conductivity onset (${X}_{C}=0.69\ifmmode\pm\else\textpm\fi{}0.01$) in these low-temperature binary mixtures. We propose that the topological percolation threshold marks the conductivity transition and that in the composition range ${X}_{C}<~X<~{X}_{M}$ thermally activated hopping prevails, while a Mott-Anderson MNMT is exhibited at $X={X}_{M}$.