A theory of the Hall effect for Bloch electrons in a weak magnetic field is developed on the base of the Kubo formula. By the use of the modified Bloch functions of Luttinger and Kohn, gauge-invariant expressions are obtained and are first applied to the random lattice problem in a metallic region. Applications are then made to the systematic treatment of interband matrix elements of the current operator, magnetic field and scattering potential in a simple model of periodic potential of one-dimensional weak cosine type. Simple discussions are also made on the strongly correlated electron system. In the case where small number of electrons or holes contribute to the conduction, the proportionality of the inverse of the Hall coefficient not to the number density but to the volume of momentum space occupied by these particles is revealed.
No takes yet. Share an insight, caveat, or question.
Hidetoshi Fukuyama (1969) studied this question.