General Theory of Magnetic Pseudopotentials

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Abstract
A general magnetic-pseudopotential theory has been developed for Bloch electrons in a magnetic field. This theory is a generalization of the earlier formulations of Misra and Roth, and Misra, and it includes the effects of spin and spin-orbit interaction. In this method, tight-binding and orthogonalized-plane-wave functions are constructed which have the symmetry of the magnetic Bloch functions and which form a complete set for the wave function of the Hamiltonian of the crystal in a magnetic field. These are used as basis states for the wave function of an eigenstate of the problem, and an effective Hamiltonian is obtained which includes the magnetic pseudopotential. The magnetic pseudopotentials due to Misra and Roth, and Misra, and zero-field pseudopotentials, are obtained from this general magnetic pseudopotential in appropriate limits. The expression for the magnetic pseudopotential has been obtained in a form such that it can be calculated to any order in the magnetic field. This expression is further simplified for metals. The immediate purpose of this formulation is to calculate the total magnetic susceptibility of metals and alloys.

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