Electron-hybridon interaction in a quantum well

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Abstract
The confinement of optical modes of vibration in a quantum well of polar material is described by a theory involving the triple hybridization of LO, TO, and IP (interface polariton) modes, all of which share a common frequency and in-plane wave vector. The resulting hybrids satisfy both mechanical and electromagnetic boundary conditions. The case of a quantum well with infinitely rigid barriers is shown to be one in which there are no interface modes allowed (including IP modes). The resulting guided-mode patterns resemble those obtained from microscopic theory of the AlAs/GaAs system. The hybrids are shown to exhibit strong IP-induced dispersion as a function of in-plane wave vector. Each hybrid has a scalar potential and a vector potential, neither of which is continuous at the interface. Continuity, in this respect, is limited to the energy of coherent interaction with an electron. Quantization leads to a new quantum—the hybridon. The electron-hybridon interaction is described for intrasubband and intersubband scattering in an infinitely deep quantum well. Intrasubband scattering rates are close to those derived using the Huang-Zhu model for the LO2 guided mode. The contribution from IP modes is contained within the hybrids. It is emphasized that pure IP modes do not exist in GaAs. As a result of the lack of interface modes the intrasubband rate approaches zero as the well narrows. The intersubband rate is also calculated.