Frohlich electron-interface and -surface optical phonon interaction Hamiltonian in multilayer coaxial cylindrical AlxGa1-xAs/GaAs quantum cables

摘要

Under a dielectric continuum approximation, by adopting the transfer matrix method, interface optical (IO) and surface optical (SO) phonon modes, as well as the Frohlich electron-IO (or -SO) phonon interaction Hamiltonian, in a multilayer coaxial cylindrical quantum cable (QC) were deduced and investigated. Numerical calculations on a four-layer AlxGa1-xAs/GaAs QC have been performed. Results reveal that there are four branches of IO phonon modes and one branch of SO phonon modes. When the wavevector in the z direction k(z) and the azimuthal quantum number m are small, the dispersion frequencies of IO or SO modes sensitively depend on k(z) and m. When k(7) and in are relatively large, with increasing k(z) and m, the frequency for each mode converges to the limit frequency value of the IO (or SO) mode in a single heterostructure, and the electrostatic potential distribution of each mode tends to be more and more localized at some interface or surface. Meanwhile, the coupling between the electron-IO or-SO phonon becomes weaker and weaker. The calculation also found that the phonon modes with higher frequencies have a more significant contribution to the electron-phonon interaction. [References: 52]