Landau Spectrum and Line Broadening in Real Metals

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Abstract
The purpose of this investigation was to determine the natural width or broadening of the Landau levels of the conduction electrons in a perfect crystal when a uniform magnetic field is present. The eigenvalues and eigenfunctions of the effective-Hamiltonian equation have been found in the WKB approximation. Connection formulas good for all energies (including the region near the top of the barrier) were used to connect the nearly degenerate solutions in adjacent zones. The energy levels were found to be essentially discrete except in the immediate vicinity of open orbits. The effective-Hamiltonian solutions have been related to the solutions of the exact Hamiltonian. We have demonstrated that the effective-Hamiltonian formalism omits no source of level broadening (except for interband effects) since our solutions are completely consistent with the requirements of a group-theoretical treatment of the exact Hamiltonian.