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Breakdown of the atomic dipole approximation for the quantum well interband dipole matrix element

The origin of large dipole matrix elements for interband optical transitions in low-bandgap quantum wells is illustrated using the exact numerical solution of a one-dimensional model. The usual effective mass approximation of the wavefunction as a single product of a slowly varying envelope function modulating a band edge Bloch function is not adequate in this case. Inclusion of at least one other term in the envelope function expansion of the wavefunction involving another band is necessary to get the correct result. It is shown that the omission of these extra terms leads to qualitatively incorrect charge oscillation under optical excitation.