EFFECTIVE HAMILTONIANS FOR BLOCH ELECTRONS IN A MAGNETIC FIELD.
OREGON UNIV EUGENE DEPT OF PHYSICS
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It is shown for electrons in a periodic potential and a uniform magnetic field that there exists a Hermitian mixed-band effective Hamiltonian of the form W sub alpha, gamma p-eAc, where p is the momentum and A is the vector potential. The off-diagonal elements in W sub alpha, gamma make it possible to describe interband effects such as magnetic breakdown. An orthogonal set of basic functions relates the effective Hamiltonian to the equivalent one-electron configuration-space Hamiltonian. Spin effects are neglected. The above statements are verified both in general by using the group properties of the magnetic translation operator and by expanding in powers of the magnetic field strength. The latter approach is necessary for relating the function W sub alpha, gamma k used in constructing the effective Hamiltonian to the electronic band structure.
- Quantum Theory and Relativity