Conduction regimes in expanded liquid mercury

In this paper we present a coherent physical picture of four electronic transport regimes in expanded liquid mercury. We propose that the first two metallic regions, i.e., the propagation regime ($\rho >11.0\mathrm{}$ g ${\mathrm{cm}}^{-3\mathrm{}}$) and the diffusion regime ($9.2<\mathrm{}\rho <11.0\mathrm{}$ g ${\mathrm{cm}}^{-3\mathrm{}}$), are separated from the semiconductor regime ($\rho <7.8\mathrm{}$ g ${\mathrm{cm}}^{-3\mathrm{}}$) by a third conduction regime where the material is microscopically inhomogenous with regard to electron transport. Density fluctuations in a one-component system characterized by a mean interatomic spacing $2r_s$ were handled by considering the density-density-correlation function. The latter is characterized by the Ornstein-Zernike decay length $\xi$ and by the Debye short correlation length $b$. The necessary conditions $b>\mathrm{}2\mathrm{}{r}_s$ and $b>\mathrm{}\xi$ imply the existence of structual fluctuations which are independent when separated by more than $2b$. Local electronic structure and local response functions will exist in a disordered material provided that the phase coherence length $l$ of the electronic wave functions is appreciably shorter than $b$, and given that quantum corrections associated with the inhomogeneities, i.e., tunneling and kinetic-energy contributions, are small. The transport properties of such a system were handled by a general effective-medium theory, which was formally reduced to the problem of transport in a two-component system. Assuming that liquid mercury in the density range 9.3-8.0 (g ${\mathrm{cm}}^{-3\mathrm{}}$) is characterized by a sufficiently large value of $b$, we were able to provide a complete semiquantitative interpretation of the transport data accounting for the slow variation of the Hall mobility, and for the volume and temperature coefficients of the conductivity in that density region. The analysis of the conductivity data together with our statistical fluctuation theory results in a value of $b=15\mathrm{}$ Å for the average radius of the density fluctuation, whereupon the requirements of internal consistency of our picture are well satisfied. To establish the validity of the semiclassical percolation picture we have provided estimates of the magnitude and relative importance of tunneling and kinetic-energy effects, establishing that these corrections are quantitatively small for this high-temperature system. In the inhomogenous regime, density fluctuations lead to localization and percolation, and the metal-nonmetal transition should be envisioned in terms of a continuous change of the conductivity.