Position-dependent effective masses in semiconductor theory

Abstract

The motion of free carriers (electrons and holes) in semiconductors of nonuniform chemical composition is sometimes described by means of a Hamiltonian possessing a position-dependent effective mass. In previous work we have shown that position-dependent masses lead to inconsistencies on account of Bargmann's theorem, which postulates that a coherent superposition of states of different masses (wave packets) is forbidden. We have also shown how to circumvent this selection rule. We derive an extension of Bargmann's theorem to the effect that Hamiltonians with position-dependent masses are not Galilean invariant. Furthermore, it is also shown that the customary derivation of position-dependent effective-mass Hamiltonians is by no means unique. There exist, in general, many nonequivalent Hamiltonians within the same approximation, all derivable from the basic many-body Hamiltonian, as long as the concept of a position-dependent mass is maintained. Because of the lack of uniqueness and the lack of Galilean invariance of variable-effective-mass theories it seems appropriate to abandon the concept of a position-dependent mass. In previous work we have shown how to do this successfully.