Theory of the magnetic susceptibility of narrow-gap semiconductors

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Abstract
The authors present a theory for the magnetic susceptibility ( chi ) of carriers (both electrons and holes) or narrow-gap semiconductors formulated by modifying a general expression for chi for Bloch electrons that includes both spin-orbit and many-body effects. As an example, they calculate chi for PbTe. The momentum matrix elements and energy gaps occurring in the general expression for chi have been evaluated by first diagonalising exactly the conduction and valence band wavefunctions and then treating the resulting states with the other eight double-group basis functions as the L point of the Brillouin zone by using k. pi perturbation theory. Their results indicate that, for both electrons and holes, chi varies monotonically as a function of the carrier concentration, reaches a maximum and then decreases. Since a theory based on the assumption of parabolic bands would have shown a linear variation of chi as a function of the carrier concentration, the departure from this trend emphasises the nonparabolicity of the energy bands in PbTe. An interesting feature of their calculations is that the spin-orbit contribution to chi becomes gradually more important as one goes away from the L point in the Brillouin zone. The magnetic susceptibility of other narrow-gap semiconductors such as PbS and PbSe can be easily calculated from their theory.