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Theory of bloch electrons in a magnetic field

1962; Elsevier BV; Volume: 23; Issue: 5 Linguagem: Inglês

10.1016/0022-3697(62)90083-5

1879-2553

Laura M. Roth,

Advanced Chemical Physics Studies

An effective Hamiltonian is obtained for a Bloch electron in a magnetic field. Using a basis set of modified Bloch functions, a momentum space Schrödinger equation is first obtained, which is formally exact but which has interband terms and also has a normalization matrix differing from the unit matrix. A non-unitary transformation is then used to obtain a one-band Hamiltonian to any order in the magnetic field, and this is carried out to second order for at most two-fold degenerate bands including spin-orbit interaction. The result is applied to obtaining the normal magnetic susceptibility of Bloch electrons.