The motion of a Bloch electron in a static uniform magnetic field is calculated exactly up to second order in the magnetic field in terms of the crystal momentum representation. The magnetic energy of an intrinsic semiconductor at zero temperature is calculated. An explicit expression of the lattice magnetic susceptibility, which consists of the Larmor-like diamagnetic term, the paramagnetic correction term, and additional terms, is presented. As a by-product, the Hamiltonian for the cyclotron motion of a free carrier is obtained in a form which is applicable for arbitrary symmetry and for bands with degeneracies.
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Morita et al. (1963) studied this question.
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