Early models of extended state conduction

The ideas about conduetion near the mobility edge have changed substantially in recent years and are still in a state of flux, with several different models being developed. It is helpful to begin with the first model developed by Mott around 1965-70 (see Mott and Davis (1979) Chapter 2) to see how the ideas have evolved and to understand the underlying physical concepts. 

A parameter needed to locate the mobility edge and to calculate is 

The next step in the theory is to calculate the conductivity above and below the mobility edge. In the Anderson model, locali2ed states are defined by a decreasing probability that the electron diffuses a larger distance from its starting point. Mott and Davis (1979 Chapter 1) prove that the dc conductivity in the localized states is zero at T = 0 K. They use the Kubo-Greenwood formula for the conductivity, 

The matrix elements vanish when the states are localized and the conductivity below E is zero. 

Several different approaches have been used to calculate the conductivity at the mobility edge, each giving the same result that, 

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