Wannier Functions for Lattices in a Magnetic Field II: Extensions to Irrational Fields

This paper extends earlier work on the definition of Wannier functions for Bloch electrons in a magnetic field. Extensions to irrational as well as rational magnetic fields are defined, and their properties investigated. The results are used to give a generalisation of the Peierls effective Hamiltonian which is valid when the magnetic flux per unit cell is close to any rational number.