ABSTRACT
A great deal of interest has sprung up towards experimental as well as theoretical studies of phonons in low-dimensional solids. This chapter discusses theoretical aspects of phonon physics in low-dimensional solids. It also discusses interactions of surface phonons, electron-phonon interactions in a quantum well, the magneto-phonon effect in two-dimensional systems, and thermal conductivity in superlattices. The chapter presents both the continuum and lattice dynamical theories of surface vibrational modes. It considers surface solutions for the special case of a semi-infinite linear chain and then discusses the semi-infinite three-dimensional case in brief. Information about surface phonons can be extracted by investigating the magnitude and polarisation of the eigenvectors of the dynamical problem. The vibrational properties of a crystal lattice are usually calculated by using the periodic boundary conditions. When dealing with the dynamics of a surface one is faced with the problem of lack of periodicity in the direction normal to the surface.
