Decoupling of Bloch Bands in the Presence of Homogeneous Fields

Abstract

Wave functions which are valid if a charge moves in a superposition of a periodic electric potential and a uniform magnetic field are constructed. The wave functions are not themselves solutions of the Schroedinger equation, but yield the traditional effective Hamiltonian for this problem. Contrary to the electric field case the mainfold of states linked by the band index does not form a Bloch band; the reason is that the cellular transforms of the Bloch-like functions are modified by the Peierls phase. At present, the derivation of these results is in closed form, but justifiable only to all powers of the magnetic field.'' This was also the case for the previous electric derivation. The limitation may not be genuine. The existence of closed Bloch bands in the presence of a homogeneous electric field is proved; the case of free electrons is given as an example. The results for the magnetic field should be independent of the power series method used for their jnstification. The procedure is extended to crossed electric and magnetic fields. (auth)