Adams representation and localization in a magnetic field

The localization problem of a Bloch electron in a magnetic field is investigated by using the concepts of the Adams representation and of von Neumann lattices. Bloch functions in a magnetic field are derived, and their properties are established. The magnetic Adams representation, based on these functions, is constructed. It is characterized by a magnetic band index and a magnetic quasimomentum →κ, and is analogous to the Adams representation in the Bloch theory. It is shown that the problem of localization in a magnetic field is closely related to the corresponding problem in the theory of von Neumann lattices.