Effective-Mass Approximation for Electrons in Crossed Electric and Magnetic Fields

Abstract

A criterion of applicability of the effective-mass approximation to the dynamics of a Bloch electron in crossed electric and magnetic fields is derived based on a treatment of Luttinger and Kohn. The requirements necessary for the diagonalizability of the Hamiltonian for an electron in a periodic crystal field in the presence of a perturbing magnetic field and an electric potential are examined. These requirements lead to a restriction on the ratio of the electric and magnetic fields. The validity of the effective-mass approximation is also considered for higher Landau states in a magnetic field as well as for lowest states of an impurity ion.