Polaron in a superlattice with δ-like potentials

The problem of the polaron spectrum is studied in a superlattice having narrow quantum wells and relatively wide potential barriers. A δ-like superlattice potential is chosen to solve the problem. This model is adequate, if the penetration depth of the electron wave function into the barrier region is much greater than the width of the quantum well. A weak-coupling polaron at low temperature is studied. Only volume phonons are considered. Expressions are obtained for the polaron mass and the shift of the polaron energy under these assumptions. To test the model, numerical calculations were performed for an InAs-GaSb superlattice, whose quantum wells are quite deep (the energy offset of the conduction bands in InAs and GaSb equals 830 meV), narrow (the width of a quantum well corresponds to the width of an InAs monolayer 6 Å), and the barrier width corresponding to the thickness of the GaSb layers equals 150 Å. The assumption that the penetration depth of the wave function is much greater than the barrier width holds well.