Interaction Hamiltonian Between an Electron and Interface Optical Phonons in a Four-Layer Heterostructure

The interaction Fröhlich-like Hamiltonian between an electron and interface optical phonons in a four-layer heterostructure (FLHS) is obtained by means of the orthonormal eigenmodes of interface optical phonons given recently. The electron-phonon coupling functions and their plots for a FLHS and its special cases, an asymmetric trilayer heterostructure (asymmetric single quantum well) and a step quantum well, are given and discussed. We find that the three branches of higher-frequencies are more important for the electron-phonon interaction than the other three in the six branches of interface modes in a FLHS. Moreover, we also find that the situation in an asymmetric trilayer heterostructure is similar to that of a FLHS.