Mott: criterion, 108 insulator

Among the phase transitions where electronic factors play a major role, the most well-known are the metal-insulator transitions exhibited by transition-metal oxides, sulfides, and so on. This subject has been discussed at length.2,23,24 A recent observation26 of some interest is that the metal-nonmetal transition occurs at a critical electron concentration as given by the particular form of the Mott criterion, = 0.26 ... 

The electronic bands of an infinite crystal can cross as a function of some parameter (pressure, concentration etc.). If one treats the e /r,2 term of the electron repulsion correctly, one sees that the crossing transition of the two bands is a first-order phase transition, between the metallic and insulating states. This transition was predicted by Mott in 1946 and has carried his name ever since. In fact, the original Mott criterion does not predict such a transition for Hg, but the criterion was derived for monovalent atoms. For divalent mercury it should not be applicable. Also the semiempirical Herzfeld criterion, which was very successful in predicting the insulator to metal transition in compressed xenon, predicts bulk Hg to be non-metallic. All this seems to imply that Hg is a rather special case. 

Another criterion for metallicity arises from electron localization induced by disorder proposed by Anderson. Electrons diffuse when the disorder is small, but at a critical disorder they do not diffuse (giving rise to zero conductivity). A transition from the metallic to the insulating state occurs as the disorder increases. Mott proposed that there exists a minimum metallic conductivity, a j , or maximum metallic resistivity, pmax. for which the material may still be viewed as being metallic, prior to the localization of electrons due to disorder. The Omin is given by where I is the mean free path of the electrons. Mott s... 

Omin criterion assumes that the disorder-driven metal-insulator transition is discontinuous, but the scaling theory predicts it to be continuous. It is, however, found that o i or p ax is a useful experimental criterion and represents the value of conductivity where the temperature coefficient of resistance changes sign from metal-like (-h) to insulator-like (—) behaviour. The value of Mott s pmax is aTOund 1-10 mohm cm in oxide systems. 

The aforementioned ab initio DODS scheme so far possesses very few applications. Some general considerations based on the total electronic density (for which a criterion similar to Mott s criterion in the case of metal-insulator transition d could be formulated) and experience... 

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