Bargmann’s theorem and position-dependent effective mass

Abstract

The physical significance of Galilean transformations applied to effective-mass (EM) equations for Bloch electrons in Wannier representation is discussed and contrasted with that of Galilean coordinate transformations applied to the free-particle Schrödinger equation. Mass constraints imposed on the latter by Bargmann’s (1954) superselection rule do not extend to the EM, and criticisms of the position-dependent EM concept which have invoked Bargmann’s theorem are shown to be without foundation. Other criticisms concerning the nonuniqueness and non-Hermiticity of effective Hamiltonians which employ this concept to describe crystals of graded composition are discussed, and it is argued that the problems are associated with the heuristic nature of the virtual-crystal model which is adopted rather than with the position-dependent EM.