Surface-projected spectral densities in crystal with planar defects

Abstract

The full description of the energy spectrum is given for a fcc crystal with a passive interface. Calculations are performed in the framework of lattice dynamics, taking into account nearest-neighbour central interactions. The exact solutions for the projected densities of shear phonons are obtained, and both low-frequency and high-frequency shear waves localized at the interface are described analytically. It is shown that the full set of the eigen-solutions of the boundary-value problem is divided into two classes - symmetrical and antisymmetrical about the plane of the defect. The appearance of the localized interface wave is associated with singularities of the projected density of states at the corresponding edge of the bulk band for a certain value of the two-dimensional wave vector.