On the electron theory of metals

Abstract The most serious defect of the modern theory of metals is the very unsatisfactory manner in which it takes account of the forces of interaction between the valency electrons of the metal. This is well shown in the anomalies characteristic of the electrical properties of the ferromagnetics; from the standpoint of Bloch’s theory they are quite inexplicable, as the criterion of ferromagnetism itself can be formulated only in the language of a more accurate theory which takes account of the exchange effects. The problem of construction such a systematic theory of metals, which could enable us to treat their electric and magnetic properties simultaneously, reduces itself substantially to choosing a suitable approximation scheme. At first sight it would seem most natural to us the scheme applied so successfully by Heisenberg in explaining the phenomena of ferromagnetism. Here the metal is considered, in the zero approximation, as an assembly of isolated electrically neutral atoms; in the following approximations, account is taken of the interaction of the valency electrons not only with the ions of the metal but also with each other. In his Leipzig Report, Bloch asserts that such a scheme affords an adequate tool for dealing with all the characteristic properties of metals, in particular with the electrical conduction. We are, however, of the opinion that this assertion is incorrect, and that, in reality, Heisenberg’s approximation cannot be used in the theory of electrical conduction simply because, in this approximation, the metal is not a conductor. In fact, it can be proved in quite a general manner (for special cases it has already been proved by Slater), that in all the stationary states of Heisenberg’s scheme the total current carried by the valency electrons of the metal is equal to zero; this result does not depend on any one special property of the perturbation equations, but simply follows from the fact that only the non-polar states of the system are chosen as zero approximation, i. e., only those states in which each atom of the metal is electrically neutral. Such a theory considers only those transitions of electrons from one atom to another, in which two electrons simultaneously change places (i. e., only the exchange processes); such transitions cannot of course give rise to an electric current.