First-principles calculation of diamagnetic band structure. II. Spectrum and wave functions

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Abstract
The diamagnetic band structure is calculated by means of a variational method. This is done for the simplest nontrivial crystal potential which is characterized by two elementary wave vectors in the plane normal to the magnetic field. The numerical calculations are highly accurate and provide an energy spectrum which is simultaneously correct in the high-field (Landau) case, in the magnetic breakdown area, and in the low-field (Onsager) regime. For comparison we calculate also the spectrum of the effective Peierls-Onsager Hamiltonian (POH) which has been used so far almost exclusively to describe the diamagnetic phenomena in solids. This semiclassical theory turns out to be in serious disagreement with the first-principles spectrum when the effective POH refers to a degenerate Bloch band. We show also that the invariance group of the POH is different from that of the original Hamiltonian. The structure of the wave functions is analyzed in terms of two superposed space periods, one being related to the Larmor radius, the other to the lattice constant.