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PACS 63. 22.+m, 68.65.Hb, 68.65.Ac Within the dielectric continuum model, we calculate the interface phonons in multilayered spherical nanostructures. The effect of the alloying in the shell material, together with the change in the embedding medium are also analyzed. In all investigated heterostructures, the interface characteristics experiment a constantlike tendency at critical geometrical parameter g c , whose values are sensitively determined by the ratio between dielectric constants of constitutive materials. We observe that the asymptotic limiting interface frequencies slightly depend on the embedding medium. For special cases, the high-index phonon branches cross each other for specific values of geometrical parameter g. This crossing-over critically depends on the core-to-shell dielectric constants ratio and on the type of host material. Also, we observe that the presence of Ga-impurity in the shell material makes the highest shell-like modes independent both on the geometrical parameter g and on the orbital index l.

Within the framework of the dielectric continuum (DC) model, we analyze the axial interface optical phonon modes in a double system of nanoshells. This system is constituted by two identical equidistant nanoshells which are embedded in an insulating medium. To illustrate our results, typical II-VI semiconductors are used as constitutive polar materials of the nanoshells. Resolution of Laplace's equation in bispherical coordinates for the potentials derived from the interface vibration modes is made. By imposing the usual electrostatic boundary conditions at the surfaces of the two-nanoshell system, recursion relations for the coefficients appearing in the potentials are obtained, which entails infinite matrices. The problem of deriving the interface frequencies is reduced to the eigenvalue problem on infinite matrices. A truncating method for these matrices is used to obtain the interface phonon branches. Dependences of the interface frequencies on the ratio of inter-nanoshell separation to core size are obtained for different systems with several values of nanoshell interdistance. Effects due to the change of shell and embedding materials are also investigated in interface phonon modes.

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