Localisation in impurity bands

The criteria for localisation in a model that is suitable for non-interacting electrons in an impurity band is investigated. It is shown that the critical density of impurities n c is given by n c a H 1 3/=f(W) where a H is a measure of the range of the overlap integral between impurities, and W the diagonal disorder. The apparent discrepancy in the results of Debney and Economou and Antonio (1977) is shown to be model dependent. It is shown that an increase in W leads to an increase in n c as expected from the results of Fritzsche (1979). The case of nearest-neighbour off-diagonal disorder is one dimension is also treated.