Effective Hamiltonians and Wavefunctions for Electrons in Deformed Crystals

Abstract

An effective Hamiltonian for electrons in in homogeneously deformed crystals is derived by expanding the wavefunction in terms of Wannier functions of the homogeneously deformed crystal. The physical interpretation of the modulating functions which determine the amplitude of each Wannier function in the expansion, and which are governed by the effective Hamiltonian, is investigated. This leads to strain-dependent expressions for the probability density and current, averaged over the fluctuations within each unit cell. The operators which represent, in the Hilbert space of the . modulating functions, similarly averaged physical observables are introduced and explicit straindependent expressions for the velocity and momentum operators are obtained. Applications of the theory are foreshadowed and its relationship to previous deformation-potential theories is examined.