What is a Metal?

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Abstract
A survey is given of simple predictive models and operational definitions of the metallic state. The purpose of this work is to highlight the essential features of electron localization versus itinerancy in both crystalline and disordered materials. Particular attention is given to systems that not only extend to the limiting insulating and metallic regimes, but also embrace the transition region between these two canonical states. Examples include the periodic table of the elements, doped semiconductors, metal solutions, expanded (supercritical) metals, transition-metal oxides, and small metallic particles or clusters. The necessary and sufficient conditions for metallic character in these systems are reviewed in terms of the Mott, Hubbard and Anderson views of the metallization process. In addition, the concept of a polarization catastrophe at the metallization onset is introduced, with special reference to both its experimental realization and its predictive ability. The notion of a polarization, or dielectric catastrophe stems from a paper by Herzfeld in 1927, which seems to be the first consideration of metal-insulator transitions in condensed matter. In Mott's original theory of 1949, the transition from insulating to metallic behaviour takes place when an ionic potential, dielectrically screened to nearby atoms, now releases a valence electron. This suggests a connection between the Herzfeld/Mott views of the metal-insulator transition. The corresponding transition in a disordered system is also described; here the concept of a minimum metallic conductivity separating localized and itinerant electron states is reviewed. Finally, a section is devoted to a consideration of the electronic properties of small metallic particles. A preliminary qualitative description is given which centres around the corresponding question ‘How many atoms maketh metal?’