Fröhlich electron–interface and –surface optical phonon interaction Hamiltonian in multilayercoaxial cylindrical AlxGa1−xAs/GaAsquantum cables

Abstract

Under a dielectric continuum approximation, by adopting the transfer matrixmethod, interface optical (IO) and surface optical (SO) phonon modes, as well as theFröhlich electron–IO (or –SO) phonon interaction Hamiltonian, in a multilayer coaxialcylindrical quantum cable (QC) were deduced and investigated. Numerical calculationson a four-layer AlxGa1−xAs/GaAsQC have been performed. Results reveal that there are four branches of IOphonon modes and one branch of SO phonon modes. When the wavevector in thez directionkz and the azimuthalquantum number mare small, the dispersion frequencies of IO or SO modes sensitively depend onkz andm. Whenkz andm are relatively large,with increasing kzand m,the frequency for each mode converges to the limit frequency value of the IO (orSO) mode in a single heterostructure, and the electrostatic potential distributionof 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 weakerand weaker. The calculation also found that the phonon modes with higherfrequencies have a more significant contribution to the electron–phononinteraction.