Phase diagram for excess electrons in simple fluids

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Abstract
We analyze a model for a thermally equilibrated electron in a static disordered environment. The model provides a caricature of excess electrons in simple liquids. We show that the self-consistent Gaussian approximation to the model can be treated analytically in the different limits of weak and strong coupling to the disorder. In cases of strong coupling, the treatment predicts electron localization consistent with Lifshitz trap scaling. This behavior can be the result of either excluded volume interactions or attractive interactions between the electron and the random sites (i.e., atoms) in the system. In the former case, the Lifshitz traps are voids; in the latter, they are local regions with atomic density in excess of the mean. In the case of weak coupling, the electronic behavior is dominated by extended states, and our treatment is consistent with standard perturbation theory. The theory thus correctly interpolates between different regimes. As a result, it provides a means to examine the competition between different electron-solvent interactions, and the resulting changes from one regime to another. We derive a phase diagram for the regions of crossover between weak coupling and strong coupling. The phase diagram is of a re-entrant form where the weak-coupling regime can result from a competition between repulsive and attractive interactions. Within this regime, over a narrow range of atomic densities, it is shown that the electron mobility can be extremely high.